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Work, Energy,
And Power
Honors Physics
Lecture Notes
Energy
Topics
5-01 Work
5-02
5-03
5-04
5-05
Kinetic Energy & the Work Energy Theorem
Gravitational Potential Energy
Spring Potential Energy
Systems and Energy Conservation
5-06 Power
Energy
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:
W  Fd cos θ
Energy
Work
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
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
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
Object falls in a gravitational field
m
Wg  Fg d cos θ
mg
h
Wg  mgh cos 0
m
Wg = mgh
Energy
Work
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
Work done by forces that oppose the direction of motion, such
as friction, will be negative.
v
f
Centripetal forces do no work,
they are always perpendicular
to the direction of motion.
d
v
Fc
Energy
Work
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
Friction acts on moving object
m
m
d
f
Wf  fd cos θ
f  mN
Wf  μmgd cos 180o
f  mmg
Wf  μmgd
Energy
Work
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
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
Kinetic Energy and the Work Energy Theorem
Force acts on a moving object
vf
vi
Kinetic
Energy
F
m
x
 F  ma
v f2  v i2  2ax
v f2

v i2

F
 2  x
m
m v f2  v i2
Fx 
2

a
F
m
mv 2
2
mv f2 mv i2
Fx  Work 

2
2
Work  Δ Kinetic Energy
Energy
Kinetic Energy and the Work Energy Theorem (Problem)
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
2
The quantity 12 mv 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.
Kinetic Energy and the Work Energy Theorem (Problem)
(a) If the KE of an arrow is doubled, by what factor has its
speed increased?
Kinetic Energy and the Work Energy Theorem (Problem)
(b) If the speed of an arrow is doubled, by what factor does its
KE increase?
Kinetic Energy and the Work Energy Theorem
Work done is equal to the change in the kinetic energy:
Wnet  KEf  KEi
• If the net work is positive, the kinetic energy increases.
• If the net work is negative, the kinetic energy decreases.
Energy
Gravitational Potential Energy
When an object is thrown upward.
Positive work
done by the
gravitational
force
Negative work
done by the
gravitational
force
Earth
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
Gravitational Potential Energy
In raising a mass m to a height h, the
work done by the external force is
y2
Fex
mt
h
Wext  Fextd cos   where   0
 mg y 2  y1 
Wext  mgh
mg
y1
We therefore define the gravitational
potential energy:
PE g  mgh
Energy
Gravitational Potential 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 height.
(D) the power supplied to the object by the force.
Gravitational Potential Energy (Problem)
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.
Spring Potential Energy
x
F = kx
F
Favg
Work
kx
kx2
2
0
x
Energy
Spring Potential Energy
The restoring force of a spring is
Fs  kx
where k is called the spring
constant, and needs to be
measured for each spring.
The force required to compress
or stretch a spring is:
Fp  kx
Energy
Spring Potential 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:
kx2
PES 
2
F
Favg
Work
kx
kx2
2
0
x
Energy
Spring Potential Energy
The quantity 12 kx2 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 displacement.
(D) the power supplied to the object by the force.
Spring Potential Energy (Problem)
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?
F  kx
mg  kx

mg

2.5 kg  9.8 m/s 2
x 

k
53 N/m

 0.46 m
46 cm  15 cm  61 cm - mark
Energy
Systems and Energy Conservation
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:
Total Mechanical Energy  KE  PE
And its conservation:
ΔKE  ΔPE  0
Energy
Systems and Energy Conservation
If there is no friction, the speed of a roller coaster will depend
only on its height compared to its starting height.
y
Energy
Systems and Energy Conservation
Ball dropped from rest falls freely from a height h.
Find its final speed.
mv 2
2
mgh
Wg  KE
h
mv 2
mgh 
2
v  2gh
v
Energy
Systems and Energy Conservation
A block of mass m compresses a spring (force constant k) a
distance x. When the block is released, find its final speed.
v
m
m
x
kx2
2
Ws  KE
kx2 mv 2

2
2
mv 2
2
kx2
v
m
Energy
Systems and Energy Conservation
When released from rest, the block slides to a stop.
Find the distance the block slides.
Friction (m)
m
vf = 0
m
k
x
kx2
Ws 
2
d
mmgd
Ws  Wf
kx2
 mmgd
2
kx2
d
2mmg
Energy
Systems and Energy Conservation
A block released from rest slides
freely for a distance d.
vi = 0
mgh
Wg  KE
d
h

Find the final
speed of the
block
mv 2
2
h
sin  
d
h = d sin()
V=?
mv 2
mgh 
2
mv 2
mgd sin  
2
v  2gd sin 
Energy
Power
Power is the rate at which work is done –
Average Power 
Work Energy Transformed

Time
Time
In the SI system, the units of power are Watts:
1Watt  1
Joule
Second
The difference between walking and running up
these stairs is power – the change in gravitational
potential energy is the same.
Energy
Power
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
F
Fr
d
W Fd
P

 Fv
t
t
Energy
Power (Problem)
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?
Fnet = ma
a = (20m/s – 0)/5.0s = 4.0 m/s2
Fnet = (1000 kg)(4.0 m/s2) = 4000 N
P = Fvave
P = (4000N)[(0 + 20 m/s)/2]
P = (4000N)(10 m/s)
Power =
40,000 W
Energy