Download Chapter 5: Work and Energy

5-1 What is Work

Is any work done in these situations?
 You hold a heavy chair at arm’s length for
several minutes…
 You carry a bucket of water along a
horizontal path while walking at constant
velocity.
 According to the scientific definition of
work… no work is done.

If these are not work, then when is work
done on an object?
5-1 Work

Work is done on an object when some
forces cause a displacement of the
object (a change in position).
 Imagine that your car runs out of gas, and you
need to push it to the side of the road.
 You exert some force on the car to change its
position. That means that you are doing work
on the car.
 The work that you do on the car is equal to the
magnitude of the force times the magnitude of
the displacement of the car.
W = Fd
 The unit for work is the joule (J) named
after James Joule. 1 J = 1 Nm
Work

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Work is done only when the force is parallel to
the displacement.
If the force is perpendicular to the
displacement of an object, work is not done on
the object.
When the force on an object and the object’s
displacement are in different directions, only
the component of the force that is parallel to
the object’s displacement does work.
If θ is the angle between the displacement and
your applied force, we can calculate the work
done on the object by using the equation:
W = Fdcosθ
Net Work (Wnet)

If many forces are applied to an object, we
can find the net work being done on the
object by using the equation:
Wnet = Fnetd(cos θ)
To calculate work, use the following equations:
W = Fd
W = Fdcosθ
Wnet = Fnetd(cos θ)
Concept check
Decide whether any work is being done in each
situation. If so, identify the object (s) on which
work is being done.
1. A teacher applies a force to a wall and
becomes exhausted
2. A book falls off a table and free falls to the
ground
3. A rocket accelerates through space.

Concept Check answers
A teacher applies a force to a wall and becomes
exhausted
a) NO. this is not work. The wall is not displaced. A
force must cause a displacement in order for work to
be done.
2) A book falls off a table and free falls to the ground
a) YES. This is work, there is a force (gravity) which
acts on the book which causes it to be displaced in a
downward direction.
3) A rocket accelerates through space.
a) Yes. There is a force (expelled gases push on the
rocket) which causes the rocket to be displaced
through space.
1)
Work

Work is a scalar quantity (force that has
magnitude but no direction)
 Can be + or –
 Is + when force is in the same direction as
displacement
 Is - when the force is opposite the displacement
○ Cosθ is negative for angles greater than 90⁰
○ Cosθ is positive for angles less than 270 ⁰
○ If  = 0⁰, then cos  ⁰ = 1 ( work is done)
○ If  = 90⁰, then cos  ⁰ = 0 (W=0)
Work and speed

If the work done on an object results
only in a change in the object’s speed,
the sign of the net work tells you if the
speed is increasing or decreasing
 Net work +, the object speeds up and the
net force does work on the object
 Net work -, the object slows down and work
is done by the object on another object
Sample 5A

How much work is done on a vacuum
cleaner pulled 3.0m by a force of 50.0 N
at an angle of 30⁰ above the horizontal?
 * Only the horizontal component of the applied
force is doing work on the vacuum cleaner.
HW: Practice 5A 1-4
5-2 Energy
Kinetic Energy
Kinetic energy is the energy associated
with an object in motion.
 Kinetic energy depends on the speed
and mass of an object.
 To find the kinetic energy of an object,
we use the equation:
KE = ½ mv2
(kinetic energy is measured in joules (J),
like work)

Work-Kinetic Energy Theorem
The Work-Kinetic Energy Theorem tells
us the work that is done on an object
while the object changes speed.
ΔKE = Wnet
KEf – KEi= Wnet
½ mvf2 – ½ mvi2 = Wnet
 Velocity is sometimes ΔV which equals
Vf - Vi
 When net work > 0, speed is increasing
 When net work < 0, speed is decreasing

Sample 5B
A 7.00 kg bowling ball moves at 3.00
m/s. How much kinetic energy does the
bowling ball have? How fast must a 2.45
g table-tennis ball move in order to have
the same kinetic energy as the bowling
ball? Is this speed reasonable for a
table-tennis ball?
 Do practice 5B

Potential Energy
The stored energy of an object is called
potential energy.
 Gravitational potential energy is the
potential energy due to an object’s elevated
position.
 The amount of g.p.e. possessed by an object
is equal to the work done against gravity in
lifting it. PE = mgh
Where h is the height - the distance above
some chosen reference level, such as the
ground or the floor of a building

Elastic Potential Energy



The potential energy stored in a compressed or
stretched object is called elastic potential
energy.
PEelastic = ½ kx2
When an external force compresses or stretches
the spring, elastic potential energy is stored in the
spring.
x is the distance that the spring is stretched or
compressed; units for x is meters (m).
 The amount of energy depends on the distance that the
spring is compressed or stretched from its natural length.

k is the spring constant, which is the spring’s
resistance to being stretched or compressed; units
for k are Newtons per meter (N/m)
5-2
Sample Problem 5D
 Classwork
:Practice 5D 1,2,3
 Homework: Section Review 1-5
5-3
Conservation of Energy
If a ball is suspended in the air how
much kinetic energy does it have?
 If we drop the ball, how much
potential energy does it have the
instant before it hits the ground?
 When the ball is halfway down, can
you predict what the PE would be?

Mechanical Energy
 The
Energy changes form but the
TOTAL energy remains the same.
 What kind of Energy is PE & KE?
 Mechanical Energy is the TOTAL
energy
ME = KE + SPE
Types of Energy
Energy
NonMechanical
Mechanical
Kinetic
Chemical
Potential
Gravitational
Elastic
internal
electrical
Conservation of Mechanical
Energy Principle
any friction the total
mechanical energy remains the
same.
 Without
 Friction does negative work and
decreases the amount of energy
 If Friction is present the law of MEC
does not apply.
 The Law of MEC occurs even when
acceleration varies
ME = KE + SPE
MEi = MEf
•Initial mechanical energy = final mechanical
energy
(in the absence of friction)
•The formula used depends on the form of
Energy in the problem.
•If the only force acting on an object is the
force due to gravity, then
(KE=1/2 mv2 and PE=mgh)
½ mvi2 + mghi = ½ mvf2 + mghf
•If other forces (besides friction) are acting on an
object, add the appropriate potential energy
formula. (ie Pee )
Example 5E

Starting from rest, a child zooms down a
frictionless slide with an initial height of 3.00
m. What is her speed at the bottom of the
slide? Assume she has a mass of 25.0 kg.
 Homework Practice 5E 1-5 &
Section Review 1-3
5-4
Power



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Power is the rate at which work is done.
The time it takes to do work is just as
important as the amount of work that is
done.
Take 2 identical cars
Car #1 can go 0-27 m/s (60 mph) in 4
seconds
Car #2 takes 8 seconds to get up to the
same speed
 What’s the difference?
Power
Car # 1 has a ‘souped up’ engine.
 Each engine does work to accelerate
the car, but the ‘souped up’ one does
it MORE QUICKLY.
 Power is work done per unit of time

P = W/Dt or F d/Dt (the def. of work)
P=FV (force x speed)
P=mgd/Dt
Power
The unit is Watt (W)
 1 horsepower = 746 W
 * remember, the distance moved per

unit of time is just the speed!
Machines with different power ratings
(lawnmowers, etc) do the same work
in different amounts of time.
 The total amount of the work is the
same.

Sample 5F

A 193kg curtain needs to be raised
7.5m, at constant speed, in as close
to 5.0s as possible. The power
ratings for three motors are listed as
1.0kW, 3.5kW and 5.5kW. Which
motor is best for the job?
Homework
 Practice
5F 1, 3,4,5
 Section Review 1-3
Mechanical Energy
 Conserved
quantity
 Mechanical energy is the sum of the
kinetic energy and all the forms of
potential energy in an object
(remember that an object can have
elastic potential energy and
gravitational potential energy).
 ME = KE + ΣPE
Conservation of Mechanical Energy
When friction is absent, the amount of
mechanical energy remains constant, or is
conserved.
 The initial amount of mechanical energy will
equal the final amount of mechanical energy.
MEi = MEf

KEi + ΣPEi = KEf + ΣPEf
KEi + PEelastic, i + PEg, i = KEf + PEelastic, f + PEg, f
½ mvi2 + ½ kxi2 + mghi = ½ mvf2 + ½ kxf2 + mghf
Power
Power is the rate at which work is done.
 P = Work
=
W
time interval
Δt
 P = Fd
Δt
 P = Fv (Force x speed)
 Power is measured in Watts (W).
Horsepower (hp) is another unit of power
that is sometimes used; 1 hp = 746 watts
