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Chapter 4: Energy

Energy ~ an ability to accomplish change

Work: a measure of the change produced by a force

Work = force through the displacement

portion of the force along displacement * displacement

W = F cos x

x

F cos

F F

F cos x

F F

W = F cos x W = F x x

F cos 90 = F

F F

W = 0

Units: 1Newton . 1 meter = 1 joule = 1J

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A person pulls a crate 20 m across a level floor using a rope 30° above the horizontal, exerting a 150 N force on the rope. How much work is done?

x

F F

W = F cos x

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Work done against gravity:Work = force through the displacement W = F cos x

force * portion of displacement along forcegravity

force is always vertical => work = weight* height liftedW = mghWork depends on height onlyWork does not depend upon path

h

Eating a banana enables a person to perform about 4.0x104 J of work. To what height does eating a banana enable a 60-kg woman to climb?

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Power: the rate at which work is done

Power work done

time interval

P =Wt

units : Watts(W ) Joulessecond

Js

An electric motor delivers 15 kW of power for a 1000 kg loaded elevator which rises a height of 30m. How much time does it take the elevator to reach the top floor from the ground floor?

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Force, speed and power

P =W

t

Fxcost

Fvcos

P Fv (when F and v are parallel)

Efficiency: how effective is power delivered

Eff

power output

power input

Pout

Pin

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Energy: the capacity to do work•Kinetic Energy: energy associated with motion•Potential Energy: energy associated with position•Rest Energy, Thermal Energy, ...

Kinetic Energy, from motion in a straight line

W Fx ma xv f

22ax (initially at rest)

W m ax mv f

2

2

KE =1

2mv2

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Potential Energy

energy associated with position

gravitational potential energy

Work done to raise an object a height h: W = mgh

= Work done by gravity on object if the object descends a height h.

identify source of work as Potential Energy

PE = mgh

other types of potential energy

electrical, magnetic, gravitational, compression of spring ...

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Conservation of Energy

Conservation Principle: For an isolated system, a conserved quantity keeps the same value no matter what changes the system undergoes.

Conservation of Energy: The total amount of energy in an isolated system always remains constant, even though energy transformations from one form to another may occur.

Usually consider initial and final times:

Ei = Ef

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Example: A skier is sliding downhill at 8.0 m/s when she comes across an icy patch (negligible friction) 10m high. What is the skier’s speed at the bottom of the patch?

h

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Conservative and Nonconservative Forces

Conservative forces are forces whose work can be expressed as a change in PE.

Conservative forces are the forces which give rise to PE.

The work done by a conservative force is independent of the path of the object, and depends only on the starting point and the ending point of the objects path.

When considering forces and energies

Work-Energy Theorem

how “outside world” interacts with an object

Work done on an object = change in object’s KE

+ change in object’s PE

+ work done by object

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Example: A 25-kg box is pulled up a ramp 20 m long and 3.0 m high by a constant force of 120 N. If the box starts from rest and has a speed of 2.0 m/s at the top, what is the force for friction between the box and ramp?

20m

F = 120N

3.0m

W = Wf + KE + PEW = F sWf = Ff s

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Problem 41: In the operation of a pile driver, a 500 kg hammer is dropped from a height of 5m above the head of a pile If the pile is driven 20 cm into the ground with each impact, what is the force of the hammer on the pile when struck.

hammer: PE -> KE

does this much work on pile

work is through a distance of 20 cm.