Chapter 3 Momentum and Energyc4f40062 3f30 405a a19b 3a4938c3ecf5

8/12/2019 Chapter 3 Momentum and Energyc4f40062 3f30 405a a19b 3a4938c3ecf5

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Hewitt/Suchocki/Hewitt

Conceptual Physical Science Fourth

Edition

Chapter 3:

MOMENTUM AND ENERGY


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Momentum: inertia in motion

Momentum

p = momentum (kg*m/s) : m = mass (kg) : v = velocity (m/s)

p = mv

Image from: momentumhockey.com


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Momentum Example

How much momentum does a truck with a mass of

10,000 kg have if it is moving at 10 m/s?

p = m * v = 10,000 * 10 = 100,000kg * m

s

kg*m

s

As you can see from the above example, the units for momentum are:


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Conservation of Momentum

DEFINITION:In the absence of an external force, the momentum of a system

remains unchanged.

Example: Collisions

Net momentumbefore collision= Net momentumaftercollision

Two types of collisions:

1. Elastic CollisionsTwo objects collide, and then bounce off one another.

2. Inelastic CollisionsTwo objects collide, stick together, then continue moving

attached to one another.


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Elastic Collision:isdefined as a collision whereupon objects collideand then move separately.

(The elastic balls bounce!)


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Elastic Collision Calculation

v = 5 m/sm = 2 kg m = 1 kg

Momentum of blue cart:

pmv

p 2kg 5m

s

p10kg m

s

pmv

p 1kg 0msp0

kgms

Momentum of red cart:

Momentum before collision =

Momentum of blue cart + momentum of red cart = 10+ 0= 10 kgm/s= Momentum after collision

Momentum of blue cart:

pmv

p 2kg 0m

s

p 0kgm

s

10 mv

10 1kg *v

v10 ms

Velocity of red cart:

A cart of 2-kg moving at 5 m/s runs into another 1-kg cart sitting still. If the blue cart comes to a

stop after the collision, what is the velocity of the red cart after the collision?


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Inelastic Collision:

is defined as a collision whereupon colliding objects

become tangled or coupled together. (Inelastic

collisions are often sticky.)


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Inelastic Collision Calculation

m = 500 kg m = 500 kgv = 10

m/s

A cart of 500 kg moving at 10 m/s runs into another 500 kg cart sitting still. If they lock together,

what is their velocity after the collision?

Momentum of green cart:

pmv

p 500 kg 10m

s

p 5000kgm

s

pmv

p 500 kg 0 msp0

kgms

Momentum of purple cart:

Momentum before collision =

Momentum of green cart + momentum of purple cart = 5000+0= 5000 kgm/s= Momentum after collision

m = 500 kg m = 500 kg

p(m1m2)v final

5000 kg m s 500 kg 500 kg v final5000 kg m s(1000k g)v

final

v final5m

s

Momentum of both carts:


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Work ExampleHow much work needs to be done to accelerate a 500 kg object 3 m/s2to 2 meters?

Step 1: Define what you know.

Step 2: Figure out what you need to solve for.

Step 3: Refer to your equation sheet and decide what

equation to use.

Step 4: Since the problem does not give you force,

we will need to use the equation for force (F=ma)

to ultimately solve for work.

Step 6: Solve.

m = 500 kg

a = 3 m/s2

d = 2 m

W = ?

W = Fd

W = Fd = (ma)d

Step 5: Place the values from Step 1 into the

equation.W = (500 kg)(3 m/s2)(2 m)

W = 3000 J


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Power

Power =Work

time

P =W

t

DEFINITION:

The amount of work done per time ittakes to do it.

UNIT:

Joules/Second = J/S = Watt


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Power

Example: How much power is needed to accelerate a 2000 kg car 5

m/s2a distance of 200 meters in 10 seconds? (Hint: it is a lot!)

PowerWork

time

Power Force* distancetime

P(2000kg)(5

m

s2)(200m)

10s

P2,000,000J

10s200,000

J

s

P200,000W


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Energy

Energy

defined as that which produces changes in matter

Energy cannot be created nor destroyed, only changed in form

Effects of energy observed only when

it is being transferred from one place to another

or it is being transformed from one form to another

Both work and energy are measured in Joules.

!


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(Gravitational) Potential Energy

The upward force when moved at constant velocity is the weight, mg, of the object. Sothe work done in lifting it through height h is:

W = PE = m*g*h

Work done equals Force required to move it upward the vertical distance moved:

W = F*d

DEFINITION:

The amount of gravitational potential energy possessed by an elevated object is equal

to the work done against gravity in raising it.


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Equation for gravitational potential energy:PE = weight (W)height (h)

or

PE = mass (m) x gravity (g) x height (h)

Gravitational potential energy examples:

Anything at an elevated height

For an object to get potential energy

someone, or something must do work

to get the object to that elevation.


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Example: potential energy of 10-N ball is the same inall 3 cases because work done in elevating it is the same


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Example:

How much work do you perform to lift a 25 kg barbell 2

meters? How much potential energy does a 25 kg weight

have when you lifted it?WorkWeight* distance

Work (mg)* height

Work (25kg)(10m

s2)(2m)

Work (250N)(2m)

Work 500J

PE (mg)* h

PE (25kg)(10m

s2)(2m)

PE (250N)(2m)PE 500J

As you can see, the amount of Work you did to lift the barbell is the same as the

amount of gravitational Potential Energy the object has!


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Kinetic Energy

KineticEnergy

is defined as the energy of a moving body

Equation for kinetic energy:

KE = kinetic energy : m = mass : v = velocity

small changes in speedlarge

changesin

KE

Since it is Energy, the units are the same as work andPotential Energy: Joules

KE = m*v2


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ProportionalityThe relative directions variables change.

Exponentially proportional:

KE = m v21

d2Intensity =

Variables are exponentially proportional if one increases as the other increases

(or decreases) by apower of the variable (such as a square).

KE

v

Intensity

d


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Kinetic Energy

Example:

How much Kinetic Energy does a 10 kg object have moving at

10 m/s?

KE 12* mass*speed2

KE1

2(10kg)(10

m

s)2

KE(5kg)(100m2

s

2 )

KE500J

***Show that 2 times the mass results in 2 times the Kinetic Energy while 2 times

the speed results in 4 times the Kinetic Energy!


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Kinetic Energy

How does 2 times the mass result in 2 times the KE but

2 times the velocity is 4 times the KE?

KE1

2 (2*mass)(speed2

)

KE1

2(20kg)(10

m

s)2

KE (10kg)(100m2

s2 )

KE1,000J

KE1

2 (mass)(2*speed)2

KE1

2(10kg)(20

m

s)2

KE (5kg)(400m2

s2)

KE 2,000J

The reason for the difference is that speed has more effect on KE because it is

squared where mass is not!


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Conservation of Energy

Example: energy transforms without net loss or net

gain in the operation of a pile driver


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Conservation of Energy

POTENTIAL ENERGY AT THE TOP =

KINETIC ENERGY AT THE BOTTOM

PEtopKEbottom

(mgh)top(1

2mv 2)bottom

gh

1

2 v2

2ghv2

2ghvbottom

Derivation.

Chapter 3 Momentum and Energyc4f40062 3f30 405a a19b 3a4938c3ecf5

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