Energy

Energy

m

m

m

Physics 2053Lecture Notes

Energy

5-01 Work

5-02 Kinetic Energy & the Work Energy Theorem

5-03 Gravitational Potential Energy

5-04 Spring Potential Energy

5-05 Systems and Energy Conservation

Energy

5-06 Power

Topics

Work

The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:

θcosFdW

Energy

What is the correct unit of work expressed in SI units?

A) kg m2/s2

B) kg m2/s

C) kg m/s2

D) kg2 m/s2

Work

Energy

How much work did the movers do (horizontally) pushing a 160 kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?

Work

Energy

Can work be done on a system if there is no motion?

A) Yes, if an outside force is provided.

B) Yes, since motion is only relative.

C) No, since a system which is not moving has no energy.

D) No, because of the way work is defined.

Work

Energy

m

h

m

mg

Wg = mgh

Object falls in a gravitational field

θcosdFW gg

0cosmghWg

Work

Energy

A 50 N object was lifted 2.0 m vertically and is being held there. How much work is being done in holding the box in this position?

A) more than 100 J

B) 100 J

C) less than 100 J, but more than 0 J

D) 0 J

Work

Energy

Work done by forces that oppose the direction of motion, such as friction, will be negative.

Centripetal forces do no work, they are always perpendicular to the direction of motion.

f

v

d

v

Fc

Work

Energy

Does a centripetal force acting on an object do work on the object?

A) Yes, since a force acts and the object moves, and work is force times distance.

B) No, because the force and the displacement of the object are perpendicular.

C) Yes, since it takes energy to turn an object.

D) No, because the object has constant speed.

Work

Energy

d

m

f

Friction acts on moving object

θcosfdWf

mgdμWf

Nf

mgf of 180cosmgdμW

Work

Energy

The area under the curve, on a Force versus position (F vs. x) graph, represents

A) work.

B) kinetic energy.

C) power.

D) potential energy.

Work

Energy

On a plot of Force versus position (F vs. x), what represents the work done by the force F?

A) the slope of the curve

B) the length of the curve

C) the area under the curve

D) the product of the maximum force times the maximum x

Work

Energy

Kinetic Energy and the Work Energy Theorem

vivf

x

m

F

ax2vv 2i

2f

xmF

2vv 2i

2f

mF

a

2

vvmFx

2i

2f

2

mv

2

mvWorkFx

2i

2f

Energy Kinetic ΔWork

2mv2

KineticEnergy

Force acts on a moving object

maF

Energy

A baseball (m = 140 g) traveling 32 m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

Kinetic Energy and the Work Energy Theorem (Problem)

. Energy

The quantity is

A) the kinetic energy of the object.

B) the potential energy of the object.

C) the work done on the object by the force.

D) the power supplied to the object by the force.

221 mv

Work

Energy

(a) If the KE of an arrow is doubled, by what factor has its speed increased?

Kinetic Energy and the Work Energy Theorem (Problem)

Energy

(b) If the speed of an arrow is doubled, by what factor does its KE increase?

Kinetic Energy and the Work Energy Theorem (Problem)

Energy

Work done is equal to the change in the kinetic energy:

• If the net work is positive, the kinetic energy increases.

• If the net work is negative, the kinetic energy decreases.

ifnet KEKEW

Kinetic Energy and the Work Energy Theorem

Energy

When an object is thrown upward.

Earth

Negative workdone by the

gravitationalforce

Positive workdone by the

gravitationalforce

Gravitational Potential Energy

Energy

Gravitational Potential Energy

An object can have potential energy by virtue of its position.

Familiar examples of potential energy:

• A wound-up spring

• A stretched elastic band

• An object at some height above the ground

Energy

We therefore define the gravitational potential energy:

Fext

mg

y1

y2

h

In raising a mass m to a height h, the work done by the external force is

0 where cosdFW extext

mgh W

yymg

ext

12

mghPEg

m

Gravitational Potential Energy

Energy

The quantity mgh is

A) the kinetic energy of the object.

B) the gravitational potential energy of the object.

C) the work done on the object by the force.

D) the power supplied to the object by the force.

Work

Energy

How high will a 1.85 kg rock go if thrown straight up by someone who does 80.0 J of work on it? Neglect air resistance.

Gravitational Potential Energy (Problem)

Energy

F = kx

F

0

x

x

Work

22kx

kx

Spring Potential Energy

avgF

Energy

where k is called the spring constant, and needs to be measured for each spring.

The restoring force of a spring is

kxFs

The force required to compress or stretch a spring is:

kxFp

Spring Potential Energy

Energy

The force increases as the spring is stretched or compressed further. We find that the potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written:

F

0 x

Work

22kx

kxavgF

2kx

PE2

S

Spring Potential Energy

Energy

The quantity is

A) the kinetic energy of the object.

B) the elastic potential energy of the object.

C) the work done on the object by the force.

D) the power supplied to the object by the force.

221 kx

Work

Energy

A spring (with k = 53 N/m) hangs vertically next to a ruler. The end of the spring is next to the 15 cm mark on the ruler. If a 2.5 kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?

Spring Potential Energy (Problem)

Energy

Systems and Energy Conservation

Potential energy can only be defined for conservative forces.

ConservativeForces

Non-conservativeForces

Gravitational

Elastic

Electric

Friction

Air Resistance

Energy

We distinguish between the work done by conservative forces and the work done by nonconservative forces.

PΔKEΔWNC

We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies:

Systems and Energy Conservation

Energy

If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign.

This allows us to define the total mechanical energy:

0PEΔKEΔ

PEKEEnergy Mechanical Total

And its conservation:

Systems and Energy Conservation

Energy

If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height.

y

Systems and Energy Conservation

Energy

hKEWg

2mv

mgh2

gh2v v

mgh2

2mv

Ball dropped from rest falls freely from a height h.Find its final speed.

Systems and Energy Conservation

Energy

mm

x

v

KEWs

2mv

2kx 22

m

kxv

2

A block of mass m compresses a spring (force constant k) a distance x. When the block is released, find its final speed.

2kx2

2

2mv

Systems and Energy Conservation

Energy

mk

m

x

fs WW

mgd2

kx2

mg2kx

d2

d

v = 0

When released from rest, the block slides to a stop.Find the distance the block slides.

2

2kxsW mgd

Systems and Energy Conservation

Friction ()

Energy

m

m

d

vo = 0

V = ?

h

KEWg

2mv

mgh2

2

mvsinmgd

2

singd2v

mgh2

2mv

h = d sin()

dh

sin

Systems and Energy Conservation

A block released from rest slidesfreely for a distance d.

Find the final speed of the block

Energy

Power

Power is the rate at which work is done –

The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.

In the SI system, the units of power are watts:

TimeWork

Power Average Time

dTransforme Energy

SecondJoule

1Watt1

Energy

Power is also needed for acceleration and for moving against the force of gravity.

The average power can be written in terms of the force and the average velocity:

v

FFR

d

tW

P t

Fd Fv

Power

Energy

A 1000 kg sports car accelerates from rest to 20 m/s in 5.0 s. What is the average power delivered by the engine?

Power (Problem)

Energy