# Chapter 5 “Work and Energy”

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```					Chapter 5 “Work and Energy”
Honors Physics
Terms
In science, certain terms
have meanings that are
different from common
usage.
Work, Energy and Power are
three of them.
Work
– Objectives:
– 1. Recognize the difference between
the scientific and ordinary definitions of
work.
– 2. Define work by relating it to force
and displacement.
– 3. Identify where work is being
performed in a variety of situations.
– 4. Calculate the net work done when
many forces are applied to an object.
Work
For the purposes of this
class:
Work is not where you go to
after school. Work doesn’t
mean sweat. Work doesn’t
equal a paycheck.
Scientific Work
Work is force x distance x cos q
W = F·d·cos q
Note that no Work is done by a
force at 90° to the direction of
motion, cos q = 0.
If work is done in the direction of
motion then cos q = 1.
Work requires some movement.
Signs of Work
Units are N·m or Joules, J.
Force applied on the object
that results in a displacement
in the same direction is
positive, +W.
The opposite results in –W.
The area under a Force vs
Displacement graph = Work.
When is work done?
– Work is not done on an object unless
the object is moved through the
application of a force.
– If you balance your Physics book above
on your head for 5 hours, not only will
you not learn any Physics through
osmosis, but no work will be done on
the book because it does not move.
When is work done?
– If more than one force is acting on an
object, the net work can be found by
first finding the net force.
–         Wnet=Fnetd cosθ

– Work has SI units of N times meters
(N▪m) or joules (J).
Example
A 20.0 kg suitcase is raised 3.0 m above a
platform by a conveyor belt. How much
work is done on the suitcase?
Example
5.9 x 102   J
A tugboat pulls a ship with a constant net
horizontal force of 5.00 x 103 N and
causes the ship to move through a
harbor. How much work is done on the
ship as it moves a distance of 3.00 km?
Example
1.5 x 107   J
Example
A weight lifter lifts a set of weights a
vertical distance of 2.00 m. If a constant
net force of 350 N is exerted on the
weights, what is the net work done on the
weights?
Example
7.0 x 102   J
Example
A shopper in a supermarket pushes a cart
with a force of 35 N directed at an angle
of 25˚ downward from the horizontal.
Find the work done by the shopper on the
cart as the shopper moves along a 50.0 m
length of aisle.
Example
1.6 x 103   J
Example
If 2.0 J of work is done in raising a 180 g
apple, how far is it lifted?
Example
1.1 m
Energy
Objectives:
1. Identify several forms of energy.
2. Calculate kinetic energy for an object.
3. Apply the work-kinetic energy theorem
to solve problems.
4. Distinguish between kinetic and
potential energy.
5. Classify different types of potential
energy.
6. Calculate the potential energy
associated with an object's position.
Energy
Energy comes in many forms.
Electrical, chemical, heat, and
atomic are just a few
examples.
A good definition of Energy is
the ability to do work.
Categories of Energies
Scientists divide energy into
two basic categories:
mechanical and non-
mechanical. All those
energies listed on the
previous slide and more can
be classified as mechanical or
non-mechanical.
Kinetic Energy
The kinetic energy (KE) of an
object is the amount of
“work” stored by that object
due to its motion. The
velocity of the object is the
most influential component.
KE = ½ mv2
Example
A 6.0 kg cat runs after a mouse at 10.0
m/s. What is the cat's kinetic energy?
Example
3.0 x 102   J
Calculate the speed of an 8.0 x 104 kg
airliner with a kinetic energy of 1.1 x 109
J.
Example
1.7 x 102   m/s
Example
Two bullets have masses of 3.0 g and 6.0
g, respectively. Both are fired with a
speed of 40.0 m/s. Which bullet has more
kinetic energy? What is the ratio of their
kinetic energies?
Example
The bullet with the greater mass; 2 to 1
Work-Kinetic Energy Theorem
The net work done by a net
force acting on an object is
equal to the change in kinetic
energy.
W net = DKE = KEf- KEi
Example
A student wearing frictionless in-line
skates on a horizontal surface is pushed
by a friend with a constant force of 45 N.
How far must the student be pushed,
starting from rest, so that her final kinetic
energy is 352 J?
Example
7.8 m
Example
A 2.0 x 103 kg car accelerates from rest
under the actions of two forces. One is a
forward force of 1140 N provided by the
traction between the wheels and the
road. The other is a 950 N resistive force
due to various frictional forces. Use the
work-kinetic energy theorem to determine
how far the car must travel for its speed
to reach 2.0 m/s.
Example
21 m
Example
– A 2.1 x 103 kg car starts from rest at
the top of a driveway that is sloped at
an angle of 20.0° with the horizontal.
An average frictional force of 4.0 x 103
N impedes the car's motion so that the
car's speed at the bottom of the
driveway is 3.8 m/s. What is the length
of the driveway?
Example
5.0 m
Potential Energy
The potential energy (PE) of
an object is the amount of
“work” stored by that object
due to its position. The
“height” of the object is the
most influential component.
Types of Potential Energy
For gravitational potential
energy:
PEg = mgh
For elastic potential energy:
PEelastic= ½ kx2
k is the spring constant and x
is the distance the spring is
compressed or stretched.
Elastic Potential Energy
Elastic potential energy is the energy
stored in any compressed or stretched
object.
The kinetic energy of an object moved by
a spring comes from the potential
energy stored in the spring.
The length of the spring when no external
forces are acting on it is called the
relaxed length.
When an external force compresses or
stretches the spring, elastic potential
energy is stored.
Example
When a 2.00 kg mass is attached to a
vertical spring, the spring is stretched
10.0 cm such that the mass is 50.0 cm
above the table.
a. What is the gravitational potential
energy associated with this mass
relative to the table?
b. What is the spring's elastic
potential energy if the spring
constant is 400.0 N/m?
c. What is the total potential energy?
Example
– a. 9.81 J
– b. 2.00 J
– c. 11.81 J
Example
A spring with a force constant of 5.2 N/m
has a relaxed length of 2.45 m. When a
mass is attached to the end of the spring
and allowed to come to rest, the vertical
length of the spring is 3.57 m. Calculate
the elastic potential energy stored in the
spring.
Example
3.3 J
Example
– A 40.0 kg child is in a swing that is
attached to ropes 2.00 m long. Find the
gravitational potential energy associated
with the child relative to the child's
lowest position under the following
conditions:
– a. when the ropes are horizontal.
– b. when the ropes make a 30.0°
angle with the vertical.
– c. at the bottom of the circular arc.
Example
– a. 785 J
– b. 106 J
– c. 0.00 J
Conservation of Energy
– Objectives:
– 1. Identify situations in which
conservation of mechanical energy is
valid.
– 2. Recognize the forms that conserved
energy can take.
– 3. Solve problems using conservation
of mechanical energy.
The Law of Conservation of Energy
Energy can’t be created or
destroyed, however, it can be
transferred. When you burn
gasoline in your car the
chemical energy is
transferred to heat energy,
etc.. Total energy is always
conserved.
Mechanical Energy
Mechanical energy is the sum
of the kinetic energy and all
forms of potential energy
that are assoicated with an
object or system.
ME = KE + SPE
Conservation of Mechanical Energy
In the absence of friction,
mechanical energy is
conserved. Remember that
friction produces heat and
heat is not a mechanical
energy.
MEi = MEf
Conservation of Mechanical
Energy
– In the absence of friction, the total
mechanical energy remains the same.
– Conservation of mechanical energy
–        Mei=MEf
– If the only force acting on an object is
the force due to gravity, then
–        ½ mvi2 + mghi = ½ mvf2 + mghf
– If other forces (besides friction) are
acting on an object, add the appropriate
potential energy formulae.
Example
– A small 10.0 g ball is held to a slingshot
that is stretched 6.0 cm. The spring
constant is 2.0 x 102 N/m.
– a. What is the elastic potential energy of
the slingshot before it is released?
– b. What is the kinetic energy of the ball
just after the slingshot is released?
– c. What is the ball's speed at that
instant?
– d. How high does the ball rise if it is shot
directly upward?
Example
– a.   0.36 J
– b.   0.36 J
– c.   8.5 m/s
– d.   3.7 m
Example
A bird is flying with a speed of 18.0 m/s
over water when it accidentally drops a
2.00 kg fish. If the altitude of the bird is
5.40 m and friction is disregarded, what is
the speed of the fish when it hits the
water?
Example
20.7 m/s
Example
A 755 N diver drops from a board 10.0 m
above the water's surface. Find the
diver's speed 5.00 m above the water's
surface. Then find the diver's speed just
before striking the water.
Example
9.9 m/s; 14.0 m/s
Example
– An Olympic runner leaps over a hurdle.
If the runner's initial vertical speed is
2.2 m/s, how much will the runner's
center of mass be raised during the
jump?
Example
0.25 m
Power
– Objectives:
– 1. Relate the concepts of energy, time,
and power.
– 2. Calculate power in two different
ways.
– 3. Explain the effects of machines on
work and power.
Simple Machines
Simple machines change the
direction or magnitude of the
exerted force but do not
change the work done. The
usually trade distance for
effort.
POWER
Power is the rate at which
work is done. It also
describes the rate of energy
transfer.
P = W/Dt or F d/Dt or F (speed)
The unit is Watt (W)
1 horsepower = 746 W
Example
– Two horses pull a cart. Each exerts a
force of 250.0 N at a speed of 2.0 m/s
for 10.0 min.
– a. Calculate the power delivered by
the horses.
– b. How much work is done by the
two horses?
Example
– a. 1.0 x 103 W
– b. 6.0 x 105 J
Mechanical Advantage
Mechanical Advantage (MA) is
the ratio of the effort force
compared to the resistance force.
MA = Fr/Fe or Wout = Win
Frdr = Fede
Fr/Fe = de/dr
Ideal Mechanical Advantage
IMA = de/dr

Efficiency = Wo/Wi x 100%
= MA/IMA x 100%

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