16MT42

APPLIEED PHYSICS

QAMAR IQBAL CHOHAN(16MT42)

SUBMITTED TO ENGR:MUDASIR MEMON

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Boyle’s Law

Boyle’s Law states that

• the pressure of a gas is inversely related to its volume when T and n are constant.

• if volume decreases, the pressure increases.

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In Boyle’s Law, the product P x V is constant as long as T and n do not change.

P1V1 = 8.0 atm x 2.0 L = 16 atm L

P2V2 = 4.0 atm x 4.0 L = 16 atm L

P3V3 = 2.0 atm x 8.0 L = 16 atm L

Boyle’s Law can be stated as P1V1 = P2V2 (T, n constant)

PV Constant in Boyle’s Law

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Boyles’ Law and Breathing

During an inhalation,

• the lungs expand.

• the pressure in the lungs decreases.

• air flows towards the lower pressure in the lungs. Copyright © 2005 by Pearson Education, Inc.

Publishing as Benjamin Cummings

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Boyles’ Law and Breathing

During an exhalation,

• lung volume decreases.

• pressure within the lungs increases.

• air flows from the higher pressure in the lungs to the outside.

Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings

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Learning Check

For a cylinder containing helium gas indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant).

1) pressure decreases2) pressure increases

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Solution

For a cylinder containing helium gas indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant):1) Pressure decreases B2) Pressure increases A

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Learning Check

A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T constant), is the new volume represented by A, B, or C?

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Solution

A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At a higher pressure (T constant), the new volume is represented by the smaller balloon A.

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If the sample of helium gas has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)?

A) 3.2 L B) 6.4 L C) 12.8 L

Learning Check

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SolutionIf the sample of helium gas has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)?

A) 3.2 L

V2 = V1 x P1 P2

V2 = 6.4 L x 0.70 atm = 3.2 L 1.40 atm

Volume decreases when there is an increase in the pressure (temperature is constant.)

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Charles’ Law

In Charles’ Law,• the Kelvin

temperature of a gas is directly related to the volume.

• P and n are constant.

• when the temperature of a gas increases, its volume increases.

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Charles’ Law: V and T

• For two conditions, Charles’ Law is writtenV1 = V2

(P and n constant) T1 T2

• Rearranging Charles’ Law to solve for V2

T2 x V1 = V2 x T1

T1 T1

V2 = V1 x T2

T1

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Learning Check

Solve Charles’ Law expression for T2.

V1 = V2T1 T2

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Solution

V1 = V2T1 T2

Cross multiply to give V1T2 = V2T1

Isolate T2 by dividing through by V1V1T2 = V2T1V1 V1T2 = T1 x V2 V1

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A balloon has a volume of 785 mL at 21°C. If the

temperature drops to 0°C, what is the new volume of

the balloon (P constant)?

1. Set up data table:Conditions 1 Conditions 2V1 = 785 mL V2 = ?T1 = 21°C = 294 K T2 = 0°C = 273 K

Be sure to use the Kelvin (K) temperature ingas calculations.

Calculations Using Charles’ Law

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Calculations Using Charles’ Law (continued)

2. Solve Charles’ law for V2:

V1 = V2

T1 T2

V2 = V1 x T2 T1

V2 = 785 mL x 273 K = 729 mL 294 K

DRAG FORCESAP Physics C

Here is the situation! Suppose you drop a marble into a graduated cylinder

full of glycerin. Obviously there will be some drag force acting on the marble. Initially the marble will have some acceleration but after a short time the marble will be moving downward at constant speed.

Physicists have a name for this “constant speed” the marble reaches…it is “Terminal Velocity”. The acceleration at this “Terminal Velocity” is zero.

Think about this: As the marble moves downward through the glycerin, the acceleration of the marble decreases from some downward value to zero at terminal velocity.

Force Diagram

Let the drag force provided by the glycerin be defined by: kvFd

Such that the drag force increases proportionally with the velocity.

kv

mg

Now write Newton’s Second Law equation for the marble. makvmgF

Finding Terminal Velocity

makvmgFkv

mg

Remember that the key to “terminal velocity” is a = 0 so…

0 kvmgNow solve for velocity… in this case terminal velocity k

mgvT

Momentum

Momentum is a property of moving matter.

Momentum describes the tendency of objects to keep going in the same direction with the same speed.

Changes in momentum result from forces or create forces.

Momentum

The momentum of a ball depends on its mass and velocity.

Ball B has more momentum than ball A.

Momentum and Inertia

Inertia is another property of mass that resists changes in velocity; however, inertia depends only on mass.

Inertia is a scalar quantity. Momentum is a property of moving mass

that resists changes in a moving object’s velocity.

Momentum is a vector quantity.

Momentum

Ball A is 1 kg moving 1m/sec, ball B is 1kg at 3 m/sec. A 1 N force is applied to deflect the motion of each ball. What happens? Does the force deflect both balls equally?

Ball B deflects much less than ball A when the same force is applied because ball B had a greater initial momentum.

Kinetic Energy and Momentum

Kinetic energy and momentum are different quantities, even though both depend on mass and speed.

Kinetic energy is a scalar quantity. Momentum is a vector, so it always depends on

direction.

Two balls with the same mass and speed have the same kinetic energy but opposite momentum.

Calculating Momentum

The momentum of a moving object is its mass multiplied by its velocity.

That means momentum increases with both mass and velocity.

Velocity (m/sec)Mass (kg)

Momentum (kg m/sec) p = m v

Conservation of Momentum

The law of conservation of momentum states when a system of interacting objects is not influenced by outside forces (like friction), the total momentum of the system cannot change.

If you throw a rock forward from a skateboard, you will move backward in response.

Conservation of Momentum

Collisions in One Dimension

A collision occurs when two or more objects hit each other.

During a collision, momentum is transferred from one object to another.

Collisions can be elastic or inelastic.

Collisions

Force is the Rate of Change of Momentum

Momentum changes when a net force is applied.

The inverse is also true: If momentum changes,

forces are created. If momentum changes

quickly, large forces are involved.

Force and Momentum Change

The relationship between force and motion follows directly from Newton's second law.

Change in momentum(kg m/sec)Change in time (sec)

Force (N) F = D p D t

FRICTION

What happens when you jump on a sled on the side of a snow-covered hill?

You can predict that the sled will slide down the hill.

Now think about what happens at the bottom of the hill.

Does the sled keep sliding? You can predict that the sled will

slow down and stop.

Why does the sled’s motion change on the side of the hill and then again at the bottom?

In each case, unbalanced forces act on the sled.

The force of gravity causes the sled to accelerate down the hill.

The force of friction eventually causes the sled to stop

These two forces affect many motions on earth

When a sled moves across snow, the bottom of the sled rubs against the surface of the snow.

In the same way, the skin of a firefighter’s hands rubs against the polished metal pole during the slide down the pole.

The force that two surfaces exert on each other when they rub against each other is called friction.

Friction

The Causes of Friction In general, smooth surfaces

produce less friction than rough surfaces.

The strength of the force of friction depends on two factors: How hard the surfaces push

togetherThe types of surfaces involved

The skiers in Figure 4 get a fast ride because there is very little friction between their skis and the snow.

The reindeer would not be able to pull them easily over a rough surface such as sand.

Friction also increases if surfaces push hard against each other.

If you rub your hands together forcefully, there is more friction than if you rub your hands together lightly.

A snow-packed surface or a metal firehouse pole may seem quite smooth.

But, as you can see in Figure 5, even the smoothest objects have irregular, bumpy surfaces.

When the irregularities of one surface come into contact with those of another surface, friction occurs.

Figure 5A Smooth Surface? If you look at the polished surface of an aluminum alloy under a powerful microscope, you’ll find that it is actually quite rough.

Sliding Friction Sliding friction occurs when two solid

surfaces slide over each other. Sliding friction can be useful. For example, you can spread sand on an

icy path to improve your footing. Ballet dancers apply a sticky powder to

the soles of their ballet slippers so they won’t slip on the dance floor.

And when you stop a bicycle with hand brakes, rubber pads slide against the tire surfaces, causing the wheels to slow and eventually stop.

On the other hand, sliding friction is a problem if you fall off your bike and skin your knee!

Static Friction Four types of friction are shown in Figure 6. The

friction that acts on objects that are not moving is called static friction.

Because of static friction, you must use extra force to start the motion of stationary objects.

For example, think about what happens when you try to push a heavy desk across a floor.

If you push on the desk with a force less than the force of static friction between the desk and the floor, the desk will not move.

To make the desk move, you must exert a force greater than the force of static friction.

Once the desk is moving, there is no longer any static friction.

However, there is another type of friction—sliding friction.

Rolling Friction When an object rolls across a surface,

rolling friction occurs. Rolling friction is easier to overcome than

sliding friction for similar materials. This type of friction is important to

engineers who design certain products. For example, skates, skateboards, and

bicycles need wheels that move freely.

So engineers use ball bearings to reduce the friction between the wheels and the rest of the product.

These ball bearings are small, smooth steel balls that reduce friction by rolling between moving parts.

Questions?

THE ENDALWAYS POLITE TO EVERY ONE