1. UNIT 4
Work and Energy

2. Energy Considerations

Energy cannot be created, nor can it be
destroyed, but it can change from one form
into another.
It is essential to the study of physics and then it is
applied to chemistry, biology, geology, astronomy

In some cases it is easier to solve problems
with energy then Newton’s laws

3. Forms of Energy

Mechanical
 focus





for now
chemical
electromagnetic
Nuclear
Heat
Sound

4. Consider the following
situations …


A student holds a heavy chair at arm’s length
for several minutes.
A student carries a bucket of water along a
horizontal path while walking at constant
velocity.
Do you think that these situations require a lot of
“work”?

5. Work


Provides a link between force and energy
The work, W, done by a constant force on an
object is defined as the product of the
component of the force along the direction of
displacement and the magnitude of the
displacement

6. Work, cont

F cos θ is the component of the force in the direction
of the displacement


Process Called the Dot Product (we will get to the Dot
Product in AP Physics)
Δ x is the displacement
Units of Work
• SI
▫
Newton • meter = Joule

N•m=J

7. More about Work

This gives no information about
 the
time it took for the displacement to occur
 the velocity or acceleration of the object


Scalar quantity
The work done by a force is zero when the
force is perpendicular to the displacement


cos 90° = 0
If there are multiple forces acting on an object,
the total work done is the algebraic sum of the
amount of work done by each force

8. More About Work, continued

Work can be positive or negative
 Positive
if the force and the displacement are in
the same direction
 Negative if the force and the displacement are in
the opposite direction
Work is positive when lifting the box
• Work would be negative if lowering the
box
•

9. When Work is Zero
•
•
•
Displacement is horizontal
Force is vertical
cos 90° = 0

10. Example (pg 169)

How much work is done on a vacuum cleaner
pulled 3.0 m by a force of 50.0 N at an angle of
30.0o above the horizontal?

11. YOU TRY! (pg 170 #1)
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 if it moves a distance of 3.00
km?

12. Kinetic Energy

Once again Energy associated with the motion
of an object
Kinetic Energy: The energy of an object due to
its motion
The equation is:

The unit for KE is JOULES (J).


1 2
K E = mv
2

13. Example (pg 173)
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?

14. Work-Kinetic Energy Theorem

The theorem stating that the net work done on
an object is equal to the change in the kinetic
energy of the object.
Wnet=ΔKE
Wnet = KE f - KEi = DKE

15. Example (pg. 175)
On a frozen pond, a person kicks a 10 kg sled,
giving it an initial speed of 2.2 m/s. How far
does the sled move if the coefficient of kinetic
friction between the sled and the ice is .10?

16. Potential Energy

Potential energy is associated with the position
of the object within some system
 Potential
energy is a property of the system, not
the object
 A system is a collection of objects or particles
interacting via forces or processes that are
internal to the system

17. Gravitational Potential Energy

Gravitational Potential Energy is the energy
associated with the relative position of an
object in space near the Earth’s surface
 Objects
interact with the Earth through the
gravitational force
 Actually the potential energy of the earth-object
system
PEg = mgy

18. Example (pg. 180 #5)
A spoon is raised 21.0 cm above a table. If the
spoon and its content have a mass of 30.0 g,
what is the gravitational potential energy
associated with the spoon at that height relative
to the surface of the table?

19. 5.3: Conservation of Energy


Conserved quantities: conserved means that it
remains constant.
If we have a certain amount of a conserved
quantity at some instant of time, we will have
the same amount of that quantity at a later
time.
 This
does not mean that the quantity cannot
change form during that time.
 EXAMPLE: Money

20. Mechanical Energy


Mechanical Energy: the sum of kinetic energy
and all forms of potential energy associated
with an object or group of objects.
Mechanical Energy is CONSERVED (in the
absence of friction)
MEi = MEf
KEi + PEi = KEf + PEf

21. Energy Tables


To simplify our method of analyzing these
situations, we will use an energy table. Each
variable has to be found at each point.
Remember:
v
= 0 means zero KE
 h = 0 means zero PEg

22. Example 1

Starting from rest, a child zooms down a
frictionless slide from an initial height of 3.00
m. What is the speed at the bottom of the
slide? Assume she has a mass of 25 kg.

23. Example 2
Assume no friction.
Solve for each blank.
“ME” just is the total
energy (ET). At position
3, assume the skater is
not moving.

24. Power



The rate at which energy changes (specifically
work) is called power.
We designate power in equations with a P.
Power is measured in Watts (W).
P = W/t
P = Power (W)
W= Work (J)
t= time (sec)

25. Power (another equation)

We can also define power in the following way
…
P = Fv
P=Power (W)
F= Force (N)
v= velocity (m/s)

26. Power

Machines with different power ratings do the
same work in different time intervals.
 So,
work is the same but the time it takes to do
that work is either longer or shorter depending
upon the power.
 While
the SI Unit for Power is WATTS (W),
sometimes power will be measured in
horsepower.
 One
horsepower (hp) = 746 watts

27. Example 1

A 193 kg curtain needs to be raised 7.5 m, at
constant speed, in as close to 5.0 s as
possible. The power ratings for three motors
are listed as 1.0 kW, 3.5 kW and 5.5 kW.
Which motor is best for the job?

28. Example 2

A 1.0 x 103 kg elevator carries a maximum
load of 800 kg. A constant frictional force of
4.0 x 102 N retards the elevators motion
upward. What minimum power, in kilowatts,
must the motor deliver to lift the fully loaded
elevator at a constant speed of 3.00 m/s?

29. Conservation of Energy Review
Solve for all the blanks using an Energy
Table

30. Hooke’s Law

Fs = - k x
Fs is the spring force
 k is the spring constant


It is a measure of the stiffness of the spring

A large k indicates a stiff spring and a small k indicates a soft
spring
x is the displacement of the object from its
equilibrium position
 The negative sign indicates that the force is always
directed opposite to the displacement


31. Hooke’s Law Force

The force always acts toward the equilibrium
position
 It
is called the restoring force
The direction of the restoring force is such that
the object is being either pushed or pulled
toward the equilibrium position
 F is in the opposite direction of x


32. Hooke’s Law – Spring/Mass
System



When x is positive (to
the right), F is negative
(to the left)
When x = 0 (at
equilibrium), F is 0
When x is negative (to
the left), F is positive
(to the right)

33. Elastic Potential Energy

A compressed spring has potential energy
 The
compressed spring, when allowed to expand,
can apply a force to an object
 The potential energy of the spring can be
transformed into kinetic energy of the object

34. Elastic Potential Energy

The energy stored in a stretched or
compressed spring or other elastic material is
called elastic potential energy
Pes = ½kx2


The energy is stored only when the spring is
stretched or compressed
Elastic potential energy can be added to the
statements of Conservation of Energy and
Work-Energy

35. PEs Example 1

If you compress as spring with spring constant 4
N/M, 50 cm how much energy is stored?

36. Fs Example 1

If a mass of .55 kg attached to a vertical spring
stretches the spring 2.0 cm from its original
equilibrium position, what is the spring
constant?

37. Nonconservative Forces


A force is nonconservative if the work it does
on an object depends on the path taken by the
object between its final and starting points.
Examples of nonconservative forces
 kinetic
friction, air drag, propulsive forces

38. Friction and Energy

The friction force is transformed from the
kinetic energy of the object into a type of
energy associated with temperature
 the
objects are warmer than they were before the
movement
 Internal Energy is the term used for the energy
associated with an object’s temperature

39. Nonconservative Forces w/
Energy


When nonconservative forces are present, the
total mechanical energy of the system is not
constant
The work done by all nonconservative forces
acting on parts of a system equals the change
in the mechanical energy of the system
W
n o n c o n s e r v a t iv e
E n e rg y

40. Problem Solving w/ Nonconservative Forces




Define the system
Write expressions for the total initial and final
energies
Set the Wnct equal to the difference between
the final and initial total energy
Follow the general rules for solving
Conservation of Energy problems