Many Y12 Exam Q's Word

1.

A floating fire tender is testing its pumps. The hose in use is being directed vertically upwards but the water is being blown to the left by a strong sideways wind. The scale diagram below traces the path of one water droplet in the jet.

10 m s c a le 10 m h2

h

1

s e a le v e l

Use the scale diagram to find h1, the height above sea level of the outlet of the hose. ........................................................ Use the scale diagram to find h2, the maximum height above sea level of the droplet. ........................................................(2)

By considering the vertical motion of the droplet and ignoring the effect of air resistance.

La Sainte Union Catholic Secondary School

1

(i)

show that the vertical velocity of the water leaving the hose is approximately 19 m s1 .............................................. ..............................................(2)

(ii)

calculate the time taken for the droplet to reach its maximum height. .............................................. .............................................. Time = ...................(2)

(iii)

calculate the time taken for the droplet to fall from maximum height to sea level. .............................................. .............................................. Time = .................(2)


2

Use the scale diagram and your last two answers to determine the average horizontal velocity of the droplet. ........................................................ ........................................................ ........................................................ ........................................................ Average speed = .................(3)

It is suggested that the wind speed is the same as the average horizontal velocity of the droplet. Comment on the validity of this suggestion. ........................................................ ........................................................ ........................................................ ........................................................(1) (Total 12 marks)

2.

A shot putter asks an A level physics student to help improve his performance. The student sketches the diagram shown below and makes some measurements. u A B C

D

The shot is stationary at position A. The shot leaves the putters hand at point B. (angle from horizontal at which shot leaves hand) = 34.5 u (speed at which shot leaves hand) = 12.9 m s1


3

Show that the initial vertical component of u is about 7 m s1. (1)

Calculate the time between the athlete releasing the shot at B and it reaching C, the highest point in its path. Time = (2)

The total time of flight of the shot, from it leaving B to landing at D, is 1.71 s. Comment on this time in relation to your previous answer. (2)

Calculate the horizontal distance travelled by the shot between B and D. Horizontal distance = (2)


4

The shot has mass 5.00 kg. Show that the shots kinetic energy as it leaves his hand at B is about 420J. (1)

The acceleration of the shot from A to B takes 0.229 s. The student suggests that the average power the shotputter is developing during the putt might be calculated as follows: Power = energy transferred/time taken = 420 J/0.229 s = 1830 W

Suggest two reasons why this figure is lower than the actual power developed. (2)

Suggest briefly how the student might have made the measurements of u. (2) (Total 12 marks)

3.

When the driver of a car brakes hard, as in a traffic accident, the car may skid until it comes to rest. The thermal energy generated by friction between the tyres and the road surface melts some of the rubber, leaving a skid mark. The police often use measurements of the skid marks to calculate the speeds of cars involved in accidents.


5

In order to determine the speed of a car involved in an accident, they must first find the frictional force between the wheels and the ground. This is done using a test car which is put into a deliberate skid.

These are the results obtained for a test car: Speed when brakes applied = 11.5 m s1 Stopping time = 1.68 s Mass of car = 1400 kg

Show that the deceleration of the car is about 7 m s2. Assume that the deceleration is constant. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)

Calculate the frictional force between the wheels and the ground. ............................................................................................................................................... ............................................................................................................................................... Frictional force = ................................................(2)

At the scene of a car accident the length of the skid marks is 20.0 m. The speed limit is 18 m s1. Use a suitable calculation to show why the driver should not be charged with speeding. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)


6

State one assumption you made in the calculation above. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(1) (Total 9 marks)

4.

A student stands on some bathroom scales (which read weight in newtons). At t = 1.0 s she starts to crouch down, taking 1.0 s to do so, and then remains stationary in that position. The graph shows how the reading R on the scales changes. 1 R/ N 1 0 0 0 2 0 0

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State the students weight. Weight ......................................................(1)

Calculate the students mass. .......................................................................................................................................................... .......................................................................................................................................................... Mass = .......................................................(2)

Figure 1 shows the student standing still on the bathroom scales in the period t = 0 s to t = 1.0 s. R and W represent the reaction force (the reading on the scales) and the students weight respectively. F i g u r e 1 F i g u r e 2

R

W Complete Figure 2 to show the values of the two forces which act on the student at t = 1.2 s.(2)

Calculate the students acceleration at t = 1.2 s. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... Acceleration = .....................................................(3)


8

Describe the motion of the students centre of mass in terms of its velocity and acceleration during the period 1.3 s to 2.0 s. t = 1.3 s to t = 1.5 s: .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... t = 1.5 s to t = 2.0 s: .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(4) (Total 12 marks)


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5.

The graph below shows the altitude (height above sea level) of the space shuttle during part of its descent after re-entering the Earths atmosphere. 9 A 5 d 0 0 e 0 0 / 0 0 m

l t i t u 9 0

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Use the graph to show that the vertical component of the shuttles velocity at 300 s is about 1 70 m s downwards. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. .................................................................................................................................................(3)


10

The vertical component of the shuttles velocity at 400 s is 38.0 m s downwards. Calculate the average vertical acceleration between 300 s and 400 s and state its direction. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. Acceleration = ................................................ Direction = .....................................................(3)

1

The shuttle has a mass of 2.0 10 kg. Calculate the average weight of the shuttle between 300 s and 400 s. 1 (Over this range of altitudes, average gravitational field strength, g = 9.6 N kg .) ................................................................................................................................................. ................................................................................................................................................. Weight = .........................................................(1)

6

Calculate the average upward vertical force on the shuttle between 300 s and 400 s. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. Average upward vertical force = ....................(3) (Total 10 marks)


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6.

The diagram shows a stationary cable car which is used to take passengers between different areas in a theme park. C a b le 2 .5 C ar 2 .5

Add labelled arrows on the diagram above to show the three forces acting on the car.(2)

The weight of the car plus passengers is 18 000 N. Calculate the tension in the cable for the car in the diagram. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Tension = ........................................................(3)

A display outside the cable car station gives the following information: Maximum speed of cars Number of cars Mass of empty car Power of motor 4 m s1 54 1250 kg 500 kW

The cars are moved by a continuous loop of cable pulled by a motor. In the morning the system is started from rest, with all 54 cars being accelerated to a speed of 4 m s1. Show that the total kinetic energy of all the empty cars is then about 500 000 J. ............................................................................................................................................... ...............................................................................................................................................(3)


12

Assuming all of the power of the motor is used to accelerate the cars, calculate how long they will take to reach their maximum speed. ............................................................................................................................................... ............................................................................................................................................... Time = ............................................................(2)

Suggest a reason why they are likely to take longer than this to reach their maximum speed. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(1) (Total 11 marks)

7.

The skydiver in the diagram is falling with a constant velocity.

Mark and label the forces acting on the skydiver.(2)

Discuss the forces acting on the skydiver when he is falling with constant velocity. ............................................................................................................................................... ...............................................................................................................................................(2)


13

The weight of the skydiver and parachute is about 690 N. Show that the mass of the skydiver and parachute is about 70 kg. ............................................................................................................................................... ...............................................................................................................................................(1)

The skydiver falls 2000 m at a constant velocity. Calculate the gravitational potential energy lost during this process. ............................................................................................................................................... ............................................................................................................................................... Gravitational potential energy lost = ...............................................................(2)

A student suggests We can use gravitational potential energy lost = kinetic energy gained to calculate the constant velocity of the skydiver. Comment on this suggestion. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2) (Total 9 marks)


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8.

An exciting new ride in a theme park is described as follows: The vehicle plus riders takes only a few seconds to accelerate to a spine-tingling 53 m s . Then (with motor off) it shoots vertically upwards to the height of a forty-two storey building and pauses. The mass of the vehicle plus riders is 1800 kg. Calculate the kinetic energy of the loaded 1 vehicle at a speed of 53 m s . ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. Kinetic energy = .............................................(2)1

Show that from a starting speed of 53 m s , the theoretical maximum height the vehicle could reach with the motor off would be about 140 m. Ignore resistive forces. ................................................................................................................................................. ................................................................................................................................................. .................................................................................................................................................(3)

1

The actual height reached is 126 m. Show that the total loss of energy from the vehicle during 5 the vertical climb to 126 m is about 3 10 J. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. .................................................................................................................................................(2)


15

Calculate a value for the average resistive force acting on the vehicle during the climb. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. Average resistive force = ...............................(2)

Calculate the time for the vehicle plus riders to make the vertical climb to 126 m. State an assumption that you make. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. Time = ............................................................ Assumption: ........................................................................................................................... .................................................................................................................................................(3) (Total 12 marks)

9.

Two of the worlds biggest roller-coasters are Apollos Chariot in Busch Gardens, USA, and The Big One in Blackpool, England. The principle of all roller-coasters is that gravitational potential energy possessed by the vehicle at the top of a track is converted into kinetic energy at the bottom. In Apollos Chariot the vehicle drops a vertical distance of 64 m from rest. Show that the expected speed of the vehicle at the bottom of the track is about 35 m s . ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)1


16

State one assumption you have made in this calculation. ...............................................................................................................................................(1)

The Busch Gardens brochure states that the speed of Apollos Chariot at the bottom is in fact 1 1 32.5 m s . Suggest and explain one reason why the speed might be less than 35 m s . ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)

Calculate the efficiency of this energy conversion as the vehicle runs down the track. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Efficiency = ...............................................(3)

Vehicles on The Big One fall through an almost identical vertical distance to those on Apollos 1 Chariot; but the owners of The Big One claim that the speed at the bottom is 38 m s . Assume their claim is truthful, and that the vertical falls are the same. Suggest how the vehicles 1 on The Big One could have a speed of 38 m s at the bottom. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(1) (Total 10 marks)


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10.

On the River Rhone there is a spectacular series of hydroelectric power plants at Gnissiat in the French Jura mountains. At the visitor centre, the following information is given about the biggest of the seven hydroelectric power plants: Electrical energy supplied in one year Height through which water falls Maximum output Average daily capacity 6.1 10 J 64.5 m 6 420 10 W 6 3 28 10 m15

Show that the amount of water described as average daily capacity can provide energy of 13 about 2 10 J as it passes through this hydroelectric power plant. 3 (1 m of water has a mass of 1000 kg.) ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................(2)

Calculate the efficiency of the system over one year. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Efficiency = .........................................................(3)

Calculate the average electrical power output over the whole year. (1 year = 3.16 10 s) ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Power = ...............................................................(2)

7


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Suggest a reason why the power output varies over the course of a year. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................(1) (Total 8 marks)

11.

Information given about a ski lift states the following: This lift transports 2800 people to the top each hour The vertical rise is 420 m The cable travels at 5.0 m s1 The maximum power consumption of the motor is 364 000 W

Assume throughout this question that the average mass of a skier plus equipment is 90 kg. Show that the rate at which energy is converted to gravitational potential energy is about 300 000 W. ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................(3)

Show that the total kinetic energy given to the skiers on the lift in one hour is about 3 106 J. ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................(2)


19

Calculate the rate, in watts. at which energy is converted to kinetic energy. ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... Rate of energy conversion = ............................................... W(1)

A student is asked to explain why the motor power consumption (364 000 W) is considerably more than the rate at which energy is converted to gravitational potential energy (about 300 000 W). His answer is kinetic energy and heat. Discuss each of his answers in more detail. Kinetic energy: ................................................................................................................ ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................

Heat: ............................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................(4) (Total 10 marks)


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12.

The passage below is taken from the marketing material supplied by a manufacturer of electrically heated showers. Most electric showers draw cold water direct from the main supply and heat it as it is used day or night. Not only are they particularly useful for those who do not have a stored water supply, but they are versatile because every home can have one. Write a word equation to describe the energy transfer which takes place in an electric shower. ........................................................ ........................................................ ........................................................ ........................................................(2)

Rewrite the equation using the appropriate formulae. ........................................................ ........................................................(1)

The technical data supplied by one manufacturer states that their most powerful shower system is fitted with a 10.8 kW heating element and can deliver up to 16 litres of water per minute. Show that the showering temperature is about 25 C if the temperature of the mains water is 15 C and the shower is used at its maximum settings.

(Specific heat capacity of water = 4200 J kg1 K1 Mass of 1 litre of water = 1.0 kg) ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................(3)


21

The marketing material includes the statement: Please remember that during the colder months, flow rates may need to be reduced to allow for the cooler temperature of incoming cold water. Calculate the flow rate required for an output of 40 C when the incoming water temperature is 10 C. ........................................................ ........................................................ ........................................................ ........................................................ Flowrate = .................(2)

The maximum steady current drawn by the unit is about 45 A. However, when the shower is first turned on the current is much higher for a short time. Suggest a possible explanation. ........................................................ ........................................................(1) (Total 9 marks)


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13.

Next to the 3000-year-old Drombeg circle in Ireland is a stone-lined pit known as a Fulacht Fiadh. It is believed that this was used as a cooking place for meat caught by hunters. The pit was filled with water. Large stones were heated in a fire and then placed in the water to bring it to the boil and cook the meat. In experiments to test this idea it was found that the water in the pit started to boil after twentytwo heated stones had been added. The total mass of the added stones was 198 kg and the mass of water was 513 kg. Show that this gives a minimum temperature for the fire of about 900 C. Specific heat capacity of water Average specific heat capacity of stone Initial temperature of water Temperature of boiling water = 4200 J kg C 1 1 = 1100 J kg C = 18 C = 100 C1 1

.......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(4)

Explain why the temperature of the fire would be higher than the calculated value. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(2) (Total 6 marks)


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14.

The diagram shows a sky diver.

Sketch the airflow around the sky diver on the diagram.(1)

Add three labelled arrows to the diagram to identify the forces acting on the sky diver.(2)

What is the relationship between these forces when the sky diver is falling with terminal velocity? ...............................................................................................................................................(1)


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For some falling objects it is possible to use Stokes law to help estimate the terminal velocity. State why this would not be appropriate for this sky diver. ............................................................................................................................................... ...............................................................................................................................................(1)

Show that the upthrust force is about 4 N. Volume of sky diver = 0.35 m . 3 3 Density of surrounding air = 1.2 kg m (i.e. 1 m of air has a mass of 1.20 kg). ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)3

Comment on the size of this force and its effect on the sky divers terminal velocity. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)

The sky diver slows her descent by opening her parachute. Give one word which describes the airflow after the parachute has opened. ...............................................................................................................................................(1) (Total 11 marks)


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15.

The process of turbulence was described in verse by the British meteorologist, Lewis F. Richardson: Big whorls have little whorls, Which feed on their velocity, And little whorls have lesser whorls, And so on to viscosity. Suggest what the author means by the word whorl. (1)

Draw diagrams in the boxes below to show laminar and turbulent flow. Describe these flow patterns. Laminar flow

Description: (2)


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Turbulent flow

Description: (2)

Turbulence can be used to reduce the rate of flow of a fluid. Explain this statement in terms of energy transfers. (2) (Total 7 marks)


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16.

A one-person spherical submarine called Explorer is used for underwater exploration. EXPLORER SPHERICAL SUBMARINE Diameter: 1.60 m Mass of empty submarine: 2000 kg Maximum mass of contents including water in buoyancy tanks: 110 kg BUOYANCY Buoyancy tanks can be flooded with sea water and emptied by compressed air. VIEWING Thick acrylic viewports provide visibility. Young modulus of acrylic is 3.0 109 Pa. Use the information given above to answer the questions below.

Calculate the weight of the submarine when carrying maximum load. ............................................................................................................................................... ............................................................................................................................................... Weight = ........................................................(1)

The submarine is at rest just above the seabed. (i) State the magnitude of the upthrust on the submarine. ....................................................................................................................................

(ii)

Give a reason for your answer. .................................................................................................................................... ....................................................................................................................................(2)


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The weight of the submarine is adjusted so that it rises with a constant velocity of 0.5 m s1. (i) How would this change in weight of the submarine be achieved? .................................................................................................................................... ....................................................................................................................................

(ii)

Calculate the viscous force on the submarine using Stokes Law. Viscosity of water = 1.2 103 kg m1 s1. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... Viscous drag force = ..............................................

(iii)

The actual viscous drag force will be much greater. Suggest why. ....................................................................................................................................(4)

At the operating depth, the pressure of water causes a stress on the viewports of 1.1 106 Pa. Calculate the strain which would result from this stress. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)

Acrylic is a polymer. Describe its molecular structure. ............................................................................................................................................... ...............................................................................................................................................(1) (Total 10 marks)


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17.

Some people think that all raindrops fall at the same speed; others think that their speed depends on their size. Calculate the speed of a raindrop after it has fallen freely from rest for 0.2 s. ............................................................................................................................................... ............................................................................................................................................... Speed = .(1)

The raindrop falls for longer than 0.2 s. Explain why its acceleration does not remain uniform for the whole of its fall. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)

Show that the mass of a 0.5 mm diameter spherical raindrop is less than 1 107 kg. 1.0 m3 of water has a mass of 1.0 103 kg ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)


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Calculate the raindrops terminal velocity. Assume that the upthrust from the air is negligible. Explain your working clearly. Viscosity of air = 1.8 105 kg m1 s1. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Terminal velocity = (3)

Sketch a graph to show how the raindrops velocity increases from rest to terminal velocity. Add a scale to the velocity axis.

V e lo c ity

T im e(3)

Explain how the terminal velocity would be different for a larger raindrop. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(1) (Total 12 marks)


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18.

The diagram shows part of a theme park ride. P a s se n g e r s h u ttle

T rack 30 m N o t to s c a le G ro u n d le v e l S tu d e n t

Tunnel 25 m

T rack

The ride commences with a vertical fall which starts from rest 30 m above ground level. It then continues a further 25 m down a vertical tunnel before levelling out. Calculate the speed at the bottom of the vertical tunnel. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Speed = ..(2)

State one assumption you have made. ............................................................................................................................................... ...............................................................................................................................................(1)


32

A student decided that this would be a good opportunity for a large-scale experiment to measure g, the acceleration of free-fall due to gravity. She stood near the tunnel entrance and used a stop-watch to measure the time for the passenger shuttle to fall to ground level. The measured time was 2.1 s. Show that this gives a value for g of about 14 m s2. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)

Suggest why this result is very different from the accepted value. Explain your answer. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)

Suggest two ways in which the student could have improved this experiment. 1. ........................................................................................................................................... ............................................................................................................................................... 2. ........................................................................................................................................... ...............................................................................................................................................(2)


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The data sheet for the ride says Maximum g-force = 4.5. This means that the maximum acceleration of the shuttle is 4.5g. Calculate the maximum resultant force on the shuttle. (Mass of shuttle = 5000kg) ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Maximum force = ..(2) (Total 11 marks)

19.

Nomlas is a new material intended for fishing rods. R od

L in e

W a te r

su rfa c e


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Complete the table below for the four other properties of materials listed. Property Desirable for rod Not desirable for rod Reason

Strong

Needs a large force before it breaks

Elastic

Brittle

Hard

Tough

(Total 8 marks)


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20.

Oil is used as a lubricant in a car engine. The viscosity of the oil is one property that determines the best oil to use under particular conditions. A student uses the apparatus shown to investigate the flow rate of engine oil at different temperatures. She finds that her results give a straight line graph if she plots the log10 of the flow rate against temperature as shown below. Log T h e rm o m e te r10

( f lo w r a te )

O il

T e m p e ra tu r e H e a tin g c o il S to p c lo c k

Give one reason for choosing to plot the log10 of the flow rate. ............................................................................................................................................... ...............................................................................................................................................(1)

What does the graph tell you about the effect that heating the oil has on its flow rate? ............................................................................................................................................... ...............................................................................................................................................(1)

How is viscosity related to the flow rate? ............................................................................................................................................... ...............................................................................................................................................(1)


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Multigrade oils have now been developed to overcome the need for changing engine oil with seasonal temperature changes. This involves adding special polymers to the oil. Explain the term polymer. ............................................................................................................................................... ...............................................................................................................................................(1)

These polymers curl up at lower temperatures but open up and take up more space at higher temperatures. Suggest how adding the polymers enables the same engine oil to be used all year round. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)

The type of flow of oil in the engine will vary from laminar to turbulent depending on the temperature, the flow rate and the shape of the tube the oil is flowing through. Use diagrams to explain what is meant by the terms laminar flow and turbulent flow.

............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)


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The student needs to make the heating coil for her apparatus. She calculates that it requires a resistance of 1.2 and plans to use nichrome wire with a diameter of 5.0 104. Calculate the length of wire she will need for the heater. (Resistivity of nichrome = 1.1 106 ) ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Length of wire = ........................................(3) (Total 12 marks)

21.

A nylon tow rope used for towing a car has the force-extension graph shown below. 4 F o rc e /k N 3

2

1

0 0 0 .1 0 .2 0 .3 0 .4 0 .5 E x te n s io n /m 0 .6


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Mark the graph with two crosses labelled: P at the limit of proportionality, Y at the yield point.(2)

The 4.0 m long rope has an effective cross-sectional area of 3.0 105 m2. Calculate the Young modulus of the nylon. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Young modulus = .....................................................(3)

On the graph grid, draw lines to show how force would vary with extension if the nylon rope had (i) (ii) twice the length (label this graph L), three times the cross-sectional area (label this graph A).

Explain your reasoning in each case. (i) .......................................................................................................................................... ............................................................................................................................................... (ii) ......................................................................................................................................... ...............................................................................................................................................(4)


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In use the original rope stretches by 0.20 m. Calculate the energy stored in the rope. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Energy stored = ............................................(2)

Explain why a longer rope would be less likely to break when used for towing. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(1) (Total 12 marks)

22.

For many years surgeons have used metal implants to repair broken bones and joints. It is important to understand how the properties of the implant materials compare with bone so that comfortable and long-lasting repairs can be made. One important property of the implant material is its stiffness. How is stiffness calculated? ............................................................................................................................................... ...............................................................................................................................................(1)

Explain the difference between stiffness and the Young modulus. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2)


40

The picture shows an X-ray of a hip joint after surgery to replace the weakened joint with an implant

A woman needs a hip replacement operation. Calculate the stress in the bone just below her hip when she is standing still.

Assume that the mass supported by this hip is 30 kg and that the bone just below her hip is of circular cross-section with radius = 2.0 102 m. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)


41

A manufacturer of hip replacements is considering using a new polymer of Young modulus 2 109 Pa. Explain whether this is a suitable material for hip replacements. The Young modulus of bone is 1 1010 Pa. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(2) (Total 8 marks)

23.

The following passage shows part of a students revision notes which contain several errors. Identify four of the errors in the students notes and suggest corrections for the errors.

W a v es A l l w a v es r eq u i r e a m ed i u m t o t r a v el i n . W a v es c a r r y t h e m ed i u m f r o m p l a c e t o p l a c e. T h e h ei gh t o f t h e c r es t o f a w a v e, o r t h e d ep t h o f t h e t r o u gh , i s c a l l ed t h e a m p l i t u d e. T h e d i s t a n c e b et w een t w o c r es t s i s t h e w a v el en gt h . T h e n u m b er o f w a v es p er s ec o n d i s t h e f r eq u en c y . W a v el en gt h C r es t

A m pl itu d e

T r o u gh

1 .0 s

e. g. H er e t h er e a r e 3 w a v es i n o n e s ec o n d , s o t h e f r eq u en c y i s 3 k i l o h er t z .Error ...................................................................................................................................... Correction .............................................................................................................................. ...............................................................................................................................................


42

Error ...................................................................................................................................... Correction .............................................................................................................................. ...............................................................................................................................................

Error ...................................................................................................................................... Correction .............................................................................................................................. ............................................................................................................................................... Error ...................................................................................................................................... Correction .............................................................................................................................. ...............................................................................................................................................(Total 8 marks)

24.

In a railway system the rails are exposed to high stresses which can lead to the development of small cracks. For safety the regular testing and monitoring of rails in service is a vital requirement. Ultrasonics can be used as a method of quick, non-destructive testing without removing the rails. Give one reason why it is important to have a quick, non-destructive method of testing rails without removing them. ............................................................................................................................................... ...............................................................................................................................................(1)


43

Ultrasonics involves the use of sound waves with frequencies above 20 kHz, the maximum frequency usually audible to human beings. Describe sound waves passing through a steel rail in terms of the displacement of the particles in the steel. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)

The speed of sound in steel is 5900 m s1 and the frequency used is 4.0 106 Hz. Show that the wavelength of the ultrasonic waves is about 1.5 103m. ............................................................................................................................................... ...............................................................................................................................................(2)

What is meant by frequency? ............................................................................................................................ ............................................................................................................................................... wave1ength? ......................................................................................................................... ...............................................................................................................................................(3)


44

Ultrasonic fault detectors are mounted on a special coach which can carry out testing at high speeds. The velocity-time graph below records the motion of the coach while testing a length of track. V e lo c ity /m s 201

10

0 0 20 40 60 80 100 120 T im e /s

Use the graph to find the length of track tested. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Length = ...............................................................(3) (Total 12 marks)


45

25.

Extract from The Last Word, New Scientist magazine. Question: While listening to the radio tuned to a frequency of 94.6 MHz (1 MHz= 1 106 Hz), I realised that I could either make the radio signal loud or reduce it almost to nothing by moving about the room or simply by leaning backwards or forwards. What caused this problem? Answer: The reason for your problem is that radio signals, of wavelength about 3 metres, are being reflected off the walls, floor and ceiling of the room - and, of course, off you. The signals therefore reach the radio by at least two different paths. This leads to an effect called superposition. By trial and error you can place your body in a position to cause this cancellation effect and then by moving by about 75 cm you can hear the signal clearly.

What is meant by superposition? ............................................................................................................................................... ...............................................................................................................................................(2)

Explain why the body in one particular place can cause a cancellation effect. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3)


46

Explain why stepping forwards by 75 cm could be enough to change the effect from cancellation to a loud signal. ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................(3) (Total 8 marks)

26.

A childs vibrating toy is made to work by pulling and releasing a string. The toy vibrates, making a buzzing sound, as the string rewinds. A student investigates the action of the toy. She pulls the string and attaches the free end to a support. When released, the toy climbs up the string, vibrating the string as it rises. S u p p o r t

S

t r i n

g

N

o t

t o

s c a l e

T

o

y

The diagram shows the appearance of the string when its length is 0.24 m. At this position the vibrations show maximum amplitude.


47

The student observes that standing waves have been set up at this position of the toy. Explain how standing waves are produced. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(3)

Mark one antinode on the diagram.(1)

The student then takes the toy apart and records these results. Length of string Mass of string Weight of toy = 0.24 m 4 = 1.5 10 kg = 0. 17 N

State the tension in the string when supporting the toy as shown in the diagram. Tension = ............................................................(1)

Calculate the mass per unit length of the string. .......................................................................................................................................................... .......................................................................................................................................................... Mass per unit length = ........................................(2)


48

Show that the speed of the wave produced on the string in the diagram is about 20 m s . .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(2)

1

Calculate the frequency of the vibration of the string in the diagram. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... Frequency = ........................................................(3) (Total 12 marks)

27.

A recorder, a common musical instrument, can be modelled as a tube of air open at both ends. The air at both ends therefore remains at normal air pressure. The diagrams below show how the air molecules in the recorder are displaced at two different moments during one cycle of the fundamental note. The two moments are separated by T/2, where T is the time period. N D o i s p m o r m a l a i r p r e s C s ou m e p r r e s s i o n N o r m a l a i r p r e s

f

l a c e m o l e c u

e n t l e s

l N o r m a l a i r p r e s R s au r r e e f a c t i o n N o r m a l a i r p r e s

T l a t e r 2


49

Explain whether the ends of the recorder have nodes or antinodes for pressure. ................................................................................................................................................. ................................................................................................................................................. .................................................................................................................................................(2)

Write down a relationship between the length l of the recorder and the wavelength of the fundamental note it produces. .................................................................................................................................................(1)

The length l of the recorder is 0.28 m. Calculate the fundamental frequency of the note it 1 produces. Speed of sound in air = 330 m s . ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. Frequency = ....................................................(3)

Calculate the period T of the fundamental note. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. Period = ..........................................................(2)


50

State one other frequency which might be present in the note produced by this recorder. Explain your choice in terms of nodes and antinodes for pressure along the recorder. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. .................................................................................................................................................(3) (Total 11 marks)

28.

When a person is looking at a distant object, all the refraction of light can be assumed to be taking place at the cornea (the front surface of the eye). The lens is used to help the cornea bring nearer objects into focus. Explain the phrase refraction of light. .......................................................................................................................................................... ..........................................................................................................................................................(1)

State the cause of refraction. .......................................................................................................................................................... ..........................................................................................................................................................(1)

A person is looking at a distant object. A clear image is formed on the retina which is 2.0 cm from the cornea. Calculate the power of the cornea. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(2)


51

As people get older, the lens in an eye can develop a cataract. The lens can then be removed in an operation and replaced by a plastic lens of fixed focal length. Explain the effect that this operation will have on a persons normal range of vision. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(2)

A new device is being developed which contains six overlapping lenses as shown in diagram A. This device will replace the single eye lens. As the muscles in the eye contract when looking at something close up, the six lenses overlap more as shown in diagram B.

A

B

The maximum combined power produced by this device and the cornea is 54 D. Calculate the closest distance at which an object can be placed and still be clearly seen. Assume the device and cornea are 2.0 cm from the retina. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(3)


52

State and explain the advantage this device has compared to a conventional plastic lens replacement. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................(2) (Total 11 marks)

29.

A three-year-old child at a barbecue was heard to remark: The trees look like jelly theyre all wobbly. She was looking at the trees over the top of the hot barbecue. Heated, less dense air was rising from the barbecue in uneven layers, changing the direction of the light from the trees in a varying pattern. Name this process of changing the direction of the light by air of different densities. .................................................................................................................................................(1)

The diagram shows a ray of light from the trunk of each tree reaching the child before the barbecue is lit. A B C

V

i e w a b o v

f r o e

m

C

h

i l d


53

After the barbecue is lit, a layer of hotter, less dense air is between the child and the trees. Complete the diagram below to show a ray of light from each of the trees A, B and C reaching the child. The ray A has been started for you. A V i e w a b o v f r o e m H o t a i r B C D i s t a n t t r e e s

C

h

i l d

(3)

Complete the diagram below to show the apparent position of the tree trunks as viewed through the layer of

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