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Q07. Conservation of Energy

Q07.Conservation of Energy

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Q07.Conservation of Energy. A 0.20- kg particle moves along the x -axis under the influence of a stationary object. The potential energy is given by : U ( x ) = (8.0 J / m 2 ) x 2 + (2.0 J / m 4 ) x 4 - PowerPoint PPT Presentation

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Page 1: Q07.Conservation of Energy

Q07. Conservation of Energy

Page 2: Q07.Conservation of Energy

1. A 0.20-kg particle moves along the x-axis under the influence of a stationary object. The potential energy is given by :

U(x) = (8.0 J/m2) x2 + (2.0 J/m4) x4

where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:

1. 0

2. 2.5 m/s

3. 5.7 m/s

4. 7.9 m/s

5. 11 m/s

Page 3: Q07.Conservation of Energy

21

2mv U x const 2 2

1 0 0 1

2v v U x U x

m

2 2 42 2 41

25.0 / 8.0 / 1.0 2.0 / 1.0

0.20v m s J m m J m m

kg

2125 /m s

1 11. /v m s

Page 4: Q07.Conservation of Energy

2. A 2.2-kg block starts from rest on a rough inclined plane

that makes an angle of 25° with the horizontal. The

coefficient of kinetic friction is 0.25. As the block

goes 2.0 m down the plane, the mechanical energy of the

Earth-block system changes by:

1. 0

2. –9.8 J

3. 9.8 J

4. –4.6 J

5. 4.6 J

Page 5: Q07.Conservation of Energy

cosfE W mg L

25

2.2 kg = 0.25

20.25 2.2 9.8 / cos25 2.0kg m s m

9.8 J

Page 6: Q07.Conservation of Energy

3. A block of mass m is initially moving to the right on a

horizontal frictionless surface at a speed v. It then

compresses a spring of spring constant k. At the

instant when the kinetic energy of the block is equal to

the potential energy of the spring, the spring is

compressed a distance of:

1.

2.

3. (1/4) m v2

4. m v2 / 4k

5.

/ 2v m k

/4

vm k

/v m k

Page 7: Q07.Conservation of Energy

2 2 21 1 12

2 2 2mv K k x k x

2

mx v

k

Page 8: Q07.Conservation of Energy

4. A 700-N man jumps out of a window into a fire net 10 m

below. The net stretches 2 m before bringing the man

to rest and tossing him back into the air. The

maximum potential energy of the net, compared to it's

unstretched potential energy, is:

1. 300 J

2. 710 J

3. 850 J

4. 7000 J

5. 8400 J

Page 9: Q07.Conservation of Energy

700 10 2 8400U mgh N m m J

10 m

2 m

Page 10: Q07.Conservation of Energy

5. A toy cork gun contains a spring whose spring constant

is 10.0 N/m. The spring is compressed 5.00 cm and then

used to propel a 6.00-g cork. The cork, however, sticks

to the spring for 1.00 cm beyond its unstretched length

before separation occurs. The muzzle velocity of this

cork is:

1. 6.32 m/s

2. 1.63 m/s

3. 2.00 m/s

4. 2.08 m/s

5. 2.45 m/s

Page 11: Q07.Conservation of Energy

2 23 2 2 21 16 10 10.0 / 5.00 10 1.00 10

2 2kg v N m m m

2.00 /v m s

5cm 1cm

Page 12: Q07.Conservation of Energy

6. A small object of mass m, on the end of a light cord, is held

horizontally at a distance r from a fixed support as shown.

The object is then released. What is the tension in the cord

when the object is at the lowest point of its swing?

1. m g / 2

2. m g

3. 2 m g

4. 3 m g

5. m g r

Page 13: Q07.Conservation of Energy

2vT mg m

r

mg

T

21

2mv m g r

3T mg

Page 14: Q07.Conservation of Energy

6. A small object of mass m starts at rest at the position shown

and slides along the frictionless loop-the-loop track of radius

R. What is the smallest value of y such that the object will

slide without losing contact with the track ?

1. R /4

2. R /2

3. R

4. 2 R

5. zero

Page 15: Q07.Conservation of Energy

21

2mg y mv

2mvmg n mg

R

1

2mg y mgR

1

2y R

Page 16: Q07.Conservation of Energy

7. A ball of mass m, at one end of a string of length L,

rotates in a vertical circle just fast enough to prevent the

string from going slack at the top of the circle. The speed

of the ball at the bottom of the circle is:

1.

2.

3.

4.

5.

3gL

2gL

7gL

5gL

4gL

Page 17: Q07.Conservation of Energy

2vg

L 2v gL

2 21 12

2 2m V mv mgL

2 2 4V v gL 5gL

5V gL

At top, T = 0 :

E Conservation :

Page 18: Q07.Conservation of Energy

8. A rectangular block is moving along a frictionless path

when it encounters the circular loop as shown. The block

passes points 1,2,3,4,1 before returning to the horizontal

track. At point 3:

1. its mechanical energy is a minimum

2. the forces on it are balanced

3. it is not accelerating

4. its speed is a minimum

5. it experiences a net upward force

Page 19: Q07.Conservation of Energy

E const1. its mechanical energy is a minimum

2. the forces on it are balanced

3. it is not accelerating

4. its speed is a minimum

5. it experiences a net upward force

2

ˆmv

rF y

mF

a

2max

1

2mv E mg y