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CBA Review #2 Mechanics and Thermal Physics. Work-Energy Momentum Conservation Impulse Thermodynamics. Work and Energy. Work = Fd Units = Joules. F = magnitude of the force d = magnitude of the displacement. A 100N force acts on a box 1.5m to the right.

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CBA Review #2 Mechanics and Thermal Physics

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### CBA Review #2 Mechanics and Thermal Physics

Work-Energy

Momentum Conservation

Impulse

Thermodynamics

### Work = Fd Units = Joules

F = magnitude of the force

d = magnitude of the displacement

A 100N force acts on a box 1.5m to the right.

How much work did the force do?

Work = 100(1.5) = 150 J

### Kinetic Energy – Energy of Motion

KE = (1/2)mv2

Example: Find the kinetic energy of a 20kg mass moving at 10 m/s.

KE = (1/2)mv2 = (1/2)(20)(10)2 = 1000J

Example: If you double your velocity, what happens to the KE?

KE (new) = (1/2)m(2v)2 = 4KE(original)

### Work Energy Theorem

Work Done = DKE

or

Fd = ½mvf2 – ½mvi2

### Example

A 10.0N force acts on a 4.00kg box initially at rest. If the force pushes the box 3.00 meters, what I the final velocity of the box?

Fd = ½mvf2 – ½mvi2

10(3) = (1/2)4vf2– 0

30 = (2)vf2

vf2 = 15

vf = 3.87 m/s

## Energy Types

Stored Energy – Potential Energy

Energy of Motion – Kinetic Energy

### Gravitational Potential Energy

The work you do to lift an object is

equal to its increase in gravitational PE.

Work to lift = PE = mgh

h = vertical distance from ground level.

### Example

How much work does a 100kg person do walking up a flight of stairs

that takes her 10m off of the ground?

Work = increase in PE = mgh = 100(9.8)10 = 9800 Joules.

### Total Mechanical Energy, E

E = KE + PE

If there is no friction, the total mechanical energy is conserved.

This means KE + PE is always the same number.

So if KE drops, PE must rise. If PE drops, KE must rise.

Another way to say this, is that KE is converted to PE, or PE is converted to KE.

### Example

A 1 kg rock is dropped from rest from a building 20m high. Fill in the table.

PE at the top is mgh =

1(9.8)(20) = 196J

0

196J

196J

KE at the top is zero.

98J

196J

98J

147J

49J

196J

E at the top (and everywhere)

is 0 + 196J = 196J

196J

196J

0

PE at the bottom is zero…………

## Momentum and Energy in Collisions

### Definition of Momentum

The symbol p stands for momentum.

Momentum is the product of mass and

velocity.

p = mv

### Examples of calculating momentum

A 2000kg car is moving at 30m/s. What is

the momentum of the car?

p = mv = (2000kg)(30 m/s) = 60,000 kg m/s

A .1 kg bullet has a momentum of 50 kg m/s. How fast is it moving?

v = p/m = 50/.1 = 500 m/s

### The Vector Nature of Momentum

Momentum is a vector – it points in the same

direction as the velocity.

In one dimension, momentum pointing to the right is positive.

Momentum pointing to the left is negative.

### Example:

Find the momentum of each ball. Be careful of the signs!

Answer: For the 3kg ball, p = 3(20) = 60 kg m/s

For the 10 kg ball, p = 2(-10) = -20 kg m/s

### Newton’s 2nd Law in terms of Momentum

Favg = maavg = mDv/Dt = (pf – pi)/ Dt = Dp/Dt

FavgDt = Dp

Impulse = Change in momentum

### Example

A 50N force is applied to a 20kg particle moving at 4m/s.

The force is applied for 4 seconds.

1. What is the impulse?

Impulse = FDt = 50(4) = 200 N.s

2. How fast is the particle moving after 4 seconds?

Impulse = Dp I = mvf – mvi 200 = 20vf - 20(4)

vf= (200 + 80) /20 = 14 m/s

### Conservation of Momentum

Momentum is Conserved for Collisions

Total momentum = Total momentum

before the collision after the collision

Pbefore = Pafter

### Completely Inelastic Collisions

• When two objects hit and stick together.

• Or, the reverse of this – when one object

breaks apart into two objects.

Momentum is Conserved

Total momentum = Total momentum

before the collision after the collision

Pbefore = Pafter

### Example

A cannon ( mass = 500kg) fires a cannon ball ( m = 50kg) at 40m/s.

How fast does the cannon move after it fires the cannon ball?

Before: Pi = 0

After: Pf = mballvball + mcannonvcannon

Pi = Pf

0 = mballvball + mcannonvcannon

(-mballvball )/mcannon =vcannon = (-50)(40)/500 = -4 m/s

### Example

A car mass = 1kg moving at 3m/s hits another 1kg car and they stick together.

How fast are they moving after they stick together?

Pi = mvi = 1(3) = 3 Pf = 2mv = 2v 2v = 3, v = 1.5 m/s

### Example

A car mass = 10kg moving at 2m/s hits another 15kg car moving to the left at

3m/s and they stick together. How fast are they moving after they stick together?

Pi = m1v1i + m2v2i = 10(2) + 15(-3) = -25

Pf = m1v1f + m2v2f = (m1 + m2 )vf = 25vf

-25 = 25vf vf = -25/25 = -1 m/s

### Elastic Forces - Hooke’s Law

F = kx PE = kx2

k =spring constant in N/m

Thermodynamics

• Name the three methods of heat transfer and give an example of each.

• Conduction: typically through solidsThe handle of a pot also gets hot

• Convection: hot gas/liquid risesConvection oven, or hot magma rises inside the core of the earth

• Radiation: transfer without mediumThe sun warms the earth through space

Thermodynamics

• What happens to metal when heated?

• Like most materials, metal expands when heated.

### Heat Energy, Q

Heat to raise the temperature of a

substance with no phase change:

Q = mcDT

Heat required for a change of state:

Q = mL

Thermodynamics

• What is entropy?

• Entropy is a measure of the disorder in a system. Without the input of work, the entropy of a system will always increase. The entropy of the universe is constantly increasing. For example:

• Ice :

• High order

• Low entropy

• Ice melted

• Less order

• Higher entropy

### Method of Mixtures

m1c1DT1 + m2c2DT2 = 0

400g of water at 50 degrees C is mixed with 600g

of water at 70 degrees C. What’s the final

temperature?

400(1)(Tf -50) + 600(1)(Tf -70) = 0

1000Tf - 62000 = 0 Tf = 62 degrees C.