Notes - Energy

A. Work and Energy

What is Energy? Energy is the ability to produce

change in an object or its environment.

Examples of forms of energy: solar, thermal, mechanical (PE and KE), chemical

Moving objects What kind of energy does a moving

object have? Kinetic energy Where does it come from? Comes from work done on an object Equation: KE = 1/2 mv2

Units: Joules (J)

How is work calculated? What are its units?

W = Fd 1 Nm = 1 Joule Note: work can be done ON an

object, and work can be done BY an object

Work

How are work and kinetic energy related to each other?

W = KE Work-Energy Theorem Work done produces changes in

kinetic energy Work is done only when there is a

change in position of an object

Work and Kinetic Energy

So….are you doing work on a book when you carry it across the room?

NO…Force is upward, displacement is forward…at least part of the force must be in the direction of the displacement ()

Does the sun do work on the Earth? NO…Force is toward center of circle,

displacement is in direction of velocity ()

So……..

Sketch:

Resolve force into components, use only the component acting in the direction of the motion.

What if the force is acting at an angle?

FvFhFd

Example:

Joe Bleau is pushing a shovel along a driveway. The force applied to the shovel is 25N at an angle of 60° with the horizontal for a distance of 30 meters. Find the work done by Mr. Bleau. Neglect friction.

Solution:

FvFhF = 25Nd = 30m= 60°

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Fh = F cosθ

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=25N(cos60°)

=12.5N

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W = Fhd =12.5N(30m) = 375Nm = 375J

Graph:

Area under the curve

How can you find work on a force-displacement graph?

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Solution: Rectangle:

Triangle:

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4Nx12m = 48Nm = 48J

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4Nx8m

2=16Nm =16J

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Total 48J +16J = 64J

Example:

John pushed a crate across the floor of a factory with a horizontal force. The roughness of the floor changes and John must exert a force of 20N for 5m, then 35N for 12m, then 10N for 8m. (a) Draw a graph of force as a function of distance, and (b) Find the work John does pushing the crate.

Graph:

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(20Nx5m) + (35Nx12m) +10Nx8m) = 600JFind the area under the curve:

35

30

25

20

15

10

5

0

0 5 10 15 20 25Force (N)distance (m)

Example:

Mike pulls a sled across level snow with a force of 225N along a rope that is 35° above the horizontal. If the sled moved a distance of 65.3m, how much work did Mike do?

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W = Fd

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=Fhd

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=F cosθd

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W = 225N(cos35)(65.3m)

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=1.2x104 J

B. Power

How can we calculate power? What are its units?

Power - rate at which energy is transferred (rate at which work is done).

P = W/t = Fd/t = Fv 1 J/s = 1 watt

Example:

An electric motor lifts an elevator that weighs 1000N a distance of 5 meters in 10 seconds. What is the power in watts? In kilowatts?

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P =W

t=Fd

t

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=500 watts

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=1000N(5m)

10s

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500 watts(1 kw

1000 watts) = 0.5 kw

Which takes more power - lifting a pile of books all at once or lifting each one individually?

10 books

Lift time =1 sec

Lift distance=

1 meter

Book weight=

1 Newton

All at once:

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P =Fd

t

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=10N(1m)

1s=10watts

One at a time:

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10P =10(Fd

t)

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=10(1N(1m)

1s) =10watts

C. Kinetic Energy What is kinetic energy? How is it related to

work done on an object? Kinetic energy is energy of motion. KE = 1/2 mv2

Comes from work done on an object Units - Joules (J)

Example:

An 875 kg. car speeds up from 22 m/s to 44 m/s. What are its initial and final kinetic energies, and how much work was done on the car to increase its speed?

Solution:

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KE =1

2mv 2

m=875 kgvi=22m/svf=44m/s

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KE i =1

2875kg(22m /s)2 = 2.12x105J

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KE f =1

2875kg(44m /s)2 = 8.47x105J

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W = ΔKE =KE f −KE i

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=8.47x105J − 2.12x105J = 6.35x105J

D. Potential Energy

What is potential energy? PE is stored energy. In what forms can energy be stored? Gravitational Spring Chemical

What is gravitational potential energy?

Comes from work done against gravity PE = mgh (similar to W = Fd because force

to lift an object is its weight mg, and distance lifted is height)

Units - Joules (J)

Example:

A 2 kg book is lifted from the floor to a shelf 2.1 meters above the floor. What is the gravitational potential energy relative to the floor?

What is the gravitational potential energy relative to the head of a 1.65 meter tall person?

YOU NEED A REFERENCE LEVEL

Solution:

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PE = mgh

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PE = 2kg(9.8m

s2)(2.1m) = 41.2J

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PE = 2kg(9.8m

s2)(2.1m −1.65m) = 8.8J

What is elastic PE?

Stored energy in a spring PEs = 1/2 kx2

Units - Joules (J) k is spring constant in N/m x is spring stretch in m

Hooke’s Law

What is Hooke’s Law? F = kx x is the change in spring length, m F is the force applied to the spring, N K is spring constant, N/m

How can you determine k from a force-displacement graph? Graph:

Force(N)

Spring stretch (m)

Slope is k

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yΔx

=F

x= k

Conservation of Energy

What is the Law of Conservation of Energy?

The total energy in a closed system is constant.

In mechanical systems, the work equals the sum of the KE and PE, and work done against friction

How does friction affect energy conversions?

Some energy is lost as heat Total energy TE = PE + KE + IE IE is internal energy (heat)

Collisions Elastic vs. Inelastic In a collision, colliding bodies change shape. KE

is temporarily converted to PE during compression, then back to KE

Elastic collision - PE is converted completely back to KE…….KE is conserved

Inelastic collision - some KE is lost (changed to other forms)

In both types of collisions, momentum is conserved

Conservation of Energy Examples:Pendulum Sketch:

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Conservation of Energy Examples:Falling Object

Sketch:

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Conservation of Energy Examples:Slide

Sketch:

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Slide Animation: