Work and Kinetic EnergyWork and Kinetic Energy

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Energy Energy (and mass)(and mass) is Conserved is Conserved

Energy is “Conserved” meaning it can not be created nor destroyed Can change formCan be transferred

Total Energy does not change with time.

This is a BIG deal!10

EnergyEnergyForms

Kinetic Energy Motion (Today)Potential Energy Stored (Wednesday)Heat laterMass (E=mc2) p122

Units Joules = kg m2 / s2

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Work by Constant ForceWork by Constant Force

Only component of force parallel to direction of motion does work!W = F r cos

r

F

r

F

r

F

rF

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A) W>0 B) W=0 C) W<0

1)

2)

3)

4)

Example: Ball TossExample: Ball Toss

You toss a ball in the air.

What is the work done by gravity as the ball goes up?A) Positive B) Negative C) Zero

What is the work done by gravity as the ball goes down?A) Positive B) Negative C) Zero

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Work by Constant ForceWork by Constant ForceExample: You pull a 30 N chest 5 meters

across the floor at a constant speed by applying a force of 50 N at an angle of 30 degrees. How much work is done by the 50 N force?

30

50 N

T

mg

N

f

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Where did the energy go?Where did the energy go?Example: You pull a 30 N chest 5 meters

across the floor at a constant speed, by applying a force of 50 N at an angle of 30 degrees.

How much work did gravity do?

How much work did friction do?

mg

90

r

T

mg

N

f

f r

180

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Kinetic Energy: MotionKinetic Energy: MotionApply constant force along x-direction to

a point particle m.

Work changes ½ m v2

Define Kinetic Energy K = ½ m v2

W = K For Point Particles

)(21

:recall 20

2xxx vvxa

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Example: Block w/ frictionExample: Block w/ friction A block is sliding on a surface with an initial speed of 5

m/s. If the coefficent of kinetic friction between the block and table is 0.4, how far does the block travel before stopping?

5 m/s

mg

N

f x

y

Y direction: F=ma

Work

W = K

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Falling Ball ExampleFalling Ball Example

Ball falls a distance 5 meters, What is final speed?

Only force/work done is gravity

mg

Example: block on inclineExample: block on incline

5kg

30o

25N4.5m

A 5kg block is at rest on a frictionless incline. It is pulled 4.5m by a 25N force. What is the final velocity of the block?

Work by Variable ForceWork by Variable ForceW = Fx x

Work is area under F vs x plot

Spring F = k x» Area = ½ k x2 =Wspring

Force

Distance

Work

Force

Distance

F=kx

Work

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SummarySummaryEnergy is ConservedWork = transfer of energy using force

Can be positive, negative or zeroW = F d cos()

Kinetic Energy (Motion)K = ½ m v2

Work = Change in Kinetic EnergyW = K

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