# Work and Energy ```S-29
This cat is not happy.
He is in need of a hair
dryer.
List five sources of
energy that might be
able to produce
electricity for him.
Work and Energy
AP Physics
Chapter 6
Work and Energy
6.1 Work Done by a Constant Force
6.1 Work Done by a Constant Force
Work – the product of the magnitude of the
displacement times the component of the
force parallel to the displacement
W  Fr
(your book replaced r with d)
Or (dot product)
W  Fr cos
Work is measure in Joules (Energy)
6-1
6.1 Work Done by a Constant Force
If Force an displacement are in the same
direction
Work is done, velocity increases, energy of
the object increases
If Force is opposite to displacement, negative
work is done, energy decreases
6-1
6.1 Work Done by a Constant Force
If there is no motion, or the force is
perpendicular to motion, no work is done,
there is no change in velocity, there is no
change in energy
6-1
6.1 Work Done by a Constant Force
As long as Force and displacement are
parallel, work is done
6-1
6.1 Work Done by a Constant Force
Example: A person pulls a 50 kg crate 40m
along a horizontal floor by a constant force of
100N @ 37o. The coefficient of friction is
0.20. What is the work done by each force
acting on the crate?
N
F
Free body diagram
f
W
6-1
6.1 Work Done by a Constant Force
By W?
N
F
f
W
6-1
6.1 Work Done by a Constant Force
Example: A person pulls a 50 kg crate 40m along a
horizontal floor by a constant force of 100N @ 37o. The
coefficient of friction is 0.20. What is the work done by each
force acting on the crate?
Work done by F?
W  Fr cos 
W  (100)(40) cos 37
W  3195 J
N
F
f
W
6-1
6.1 Work Done by a Constant Force
Example: A person pulls a 50 kg crate 40m along a
horizontal floor by a constant force of 100N @ 37o. The
coefficient of friction is 0.20. What is the work done by each
force acting on the crate?
Work done by f?
W  fr cos 
f  N
N  F sin   mg  0
N  (50)(9.8)  100 sin 37  430
f  (.2)(430)  86
W  (86)(40) cos180  3440 J
N
F
f
W
6-1
6.1 Work Done by a Constant Force
Example: A person pulls a 50 kg crate 40m
along a horizontal floor by a constant force of
100N @ 37o. The coefficient of friction is
0.20.
What is the net work done on the object?
W  WF  W f
W  3195  (3440)  245 J
6-1
Work and Energy
6.2 Work Done by a Varying Force
6.2 Work Done by a Varying Force
Work is the area under a Force vs.
displacement graph.
If force changes at a constant
rate,
1
W  2 ( F  F0 )d
Otherwise we use calculus
to calculate the area
x
W   F ( x)dx
x0
6-2
Work and Energy
6.3 Kinetic Energy, &amp; the Work-Energy Principle
6.3 Kinetic Energy, &amp; the Work-Energy Principle
W

Fx

max
Energy – the ability to do work
2
2
v

v
Sufficient for Mechanical Energy 0  2ax
2
2
v

v
0
 to motion
2x
Equation
2
1
K  2 mv
 v 2  v02 
W  m
x
 2x 
Work-Kinetic Energy
W  K
 v 2  v02 
W  m

 2 
W  12 mv 2  12 mv02
6-3
S-30
A rocket powered 2000kg truck can go from 0
to 27 m/s in 3.5 s.
A. What is the acceleration of the truck?
B. What is the displacement of the truck?
C. How much
work was
done on the
truck?
6.3 Kinetic Energy, &amp; the Work-Energy Principle
Work-Kinetic Energy Theorem (Work-Energy
Principle) – the net work done on an object is
equal to the change in the object’s kinetic
energy
Work-Kinetic Energy Physlet
6-3
6.3 Kinetic Energy, &amp; the Work-Energy Principle
A 1000 kg car traveling 26.7 m/s can brake to
a stop in 20 m. What is the force applied by
the brakes?
N
Free Body Diagram?
f
mg
6-3
6.3 Kinetic Energy, &amp; the Work-Energy Principle
A 1000 kg car traveling 26.7 m/s can brake to
a stop in 20 m. What is the force applied by
the brakes?
N
Solve W  Fd cos 
W  Fd cos180   Fd
W  K
 Fd  12 mv 2  12 mv02
 Fd   12 mv
2
0
mv02 (1000)(26.7) 2
F

 17800 N
2d
2(20)
f
mg
6-3
6.3 Kinetic Energy, &amp; the Work-Energy Principle
A 1000 kg car traveling 26.7 m/s can brake to
a stop in 20 m. If the car is now traveling
twice as fast, how far must it travel to stop?
N
 Fd   12 mv02
mv02 (1000)(53.4)2
d

 80m
2F
2(17800)
f
mg
6-3
Work and Energy
6.4 Potential Energy
6.4 Potential Energy
Potential Energy – due to position or
configuration
Gravitational Potential Energy – (Ug) due to
position above the earths surface
U g  mgy
6-4
6.4 Potential Energy
Elastic Potential Energy – due to the position
of a spring
Hooke’s Law
Fs  kx
Determining a Spring
Constant
Equation for Elastic Potential Energy
U s  kx
1
2
2
Elastic Potential Energy
k=spring constant
6-4
Work and Energy
6.5 Conservative and Nonconservative Forces
6.5 Conservative and Nonconservative Forces
Conservative Forces – independent of
pathway (gravity)
Energy can be returned (conserved)
Nonconservative Forces – depends on
pathways (friction)
Energy can not be returned
Physlet
6-5
S-31
A unfortunate 45 kg child never learned to
slide on anything but his face. If his face and
the dirt have a coefficient =0.4, and he is
running at 11 m/s when he starts his slide how
much work is done by friction by the time he
comes to a stop?
Work and Energy
6.6 Mechanical Energy and its Conservation
6.6 Mechanical Energy and its Conservation
If no energy is lost to nonconservative forces
E  E0
We can expand that to include the types of
energy we have
K  U g  U s  K 0  U g0  U s0
Principle of Conservation of Mechanical
Energy-energy just switches forms
6-6
6.6 Mechanical Energy and its Conservation
If energy is lost to nonconservative forces
E  E0  WNC
For example if the energy was lost to friction
K  U g  U s  K 0  U g0  U s0  fr
6-6
Work and Energy
6.7 Problem Solving Using Conservation of ME
6.7 Problem Solving Using Conservation of ME
1. List the types of energy before the reaction
2. List the types of energy after the reaction
3. Consider any non conservative forces
6-7
S-32
The 75 kg Henry (French)
jumps off a cliff that is 102
m high. Assuming that the
bungee has a resting length
of 40 m, follows Hooke’s
Law, and stops the guy 3 m before he hits the
surface, what is the elastic constant of the
bungee cord?
Work and Energy
6.8 Other Forms of Energy
6.8 Other Forms of Energy
1.
2.
3.
4.
Electric
Nuclear
Thermal
Chemical
6-8
6.8 Other Forms of Energy
Law of Conservation of Energy – The total
energy is neither increased nor decreased
in any process.
Energy can be transformed from one form
to another.
6-8
Work and Energy
6.10 Power
6.10 Power
Power – the rate at which work is done
W
P
t
Measured in watts
Often convenient to write in terms of force
W Fr
P

 Fv
t
t
6-9
S-33
The worlds strongest woman lifts 186 kg
upward a distance of 0.75 m. Assuming that
the mass accelerated upward from rest the
whole distance in
0.44s,
A. What is the work
done by the dainty
B. How much power
did she generate?
S-34
Mike is not a very impressive driver. He
drives his 1500 kg minivan into the living room
of his mom’s house. If the van was traveling
at 20 m/s and came to a stop in 2 m, what is
the average force on
Mike and the van?
S-35
I can use the conservation of energy to calculate changes in position or speed
Tarzan (and his very 50’s family) are out
swinging on their vine. The vine is 45 m long
and makes and angle of 10o
to the vertical. If Tarzan
(m=105 kg) runs at 15 m/s
and jumps on the vine, what
will be the vertical angle at
the highest point the vine
reaches?
S-36
I can use the conservation of energy to calculate changes in position or speed
Sven likes to ride
his pogo stick really
high. If he has
a mass of 115 kg,
and manages
to reach a maximum
height of
13 m when the
spring is
compressed 0.4 m,
what is the constant of the spring?
S-37
I can use the conservation of energy to calculate changes in position or speed
The worlds biggest
swing drops 19
stories (57 m). If our
150 kg chubby
champion ran at 11 m/s to
jump off the cliff, and the
rope was 89 m long,
what is his velocity at
the bottom? Treat this
as a pendulum
S-38
I can use the conservation of energy to calculate changes in position or speed
Big Mouse Trap!
S-39
Don’t mess with this
dog. If he has a mass
of 25 kg (all muscle)
and hits the 5 kg
pendulum going
7.2 m/s, what will be
the maximum vertical
angle the rope makes.
The string is 8 m long.
S-40
I can relate transformations between kinetic and potential energy
Using your brilliant knowledge of energy,
why has the style of the high jumping
changed over the years from
A. Scissor
S-41
A 112 kg weasel running at 32 m/s trips
and rolls into a ball. He rolls up a 45m
long frictionless hill that makes an
angle of 22o to the horizontal. At the
top of the hill, falls off a cliff that is 120
below his starting point. He falls on a
spring that compresses 1.5 m before
shooting him back into the air. He
passes his girlfriend who is sitting in a
tree that is 81 m tall. What is his
velocity as he passes his girlfriend?
S-42
This is a ridiculously
huge rabbit