3. +
What do you think?
List five examples of things you have done in the
last year that you would consider work.
Based on these examples, how do you define
work?
4. +
Work
Inphysics, work is the magnitude of the force (F)
times the magnitude of the displacement (d) in
the same direction as the force.
W = Fd
What are the SI units for work?
Force units (N) distance units (m)
N•m are also called joules (J).
How much work is 1 joule?
Liftan apple weighing about 1 N from the floor to
the desk, a distance of about 1 m.
5. +
Work
Ifwe lift two loads, we do twice as much
work as lifting one load the same
distance, because the force needed is
twice as great.
Ifwe lift one load twice as far, we do twice
as much work because the distance is
twice as great.
6. +
Work
Work is done in lifting
the barbell. If the barbell
could be lifted twice as
high, the weight lifter
would have to do twice
as much work.
7. +
Work
Whilethe weight lifter is holding a barbell
over his head, he may get really tired, but
he does no work on the barbell.
Work may be done on the muscles by
stretching and squeezing them, but this
work is not done on the barbell.
When the weight lifter raises the barbell,
he is doing work on it.
8. +
Classroom Practice Problem
A 20.0kg suitcase is raised 3.0 m above a
platform. How much work is done on the
suitcase?
Answer: 600 J
Suppose that you apply a 60-N horizontal
force to a 32-kg package, which pushes it
4 meters across a mailroom floor. How
much work do you do on the package?
W = Fd = 60 N × 4 m = 240 J
9. +
Work is a Scalar
Work can be
positive or
negative but does
not have a
direction.
10. +
Sign of Work is Important
Work is positive
Force is in the same direction as the displacement
Work is negative
Forceis in a different direction as the
displacement
Sing of the net work lets you know if the object
is speeding up or down
+ for speeding up and work is being on object
- for slowing down and work is done by object
12. +
Kinetic Energy
Energy associated with an object in
motion Wnet = Fd = mad
Since v2f = v2i + 2ad
v2
f vi2
Then
2 2 Wnet m( )
v f v
i 2
ad
2
Finally 1 2 1 2
Wnet mv f mvi
2 2
13. +
Kinetic Energy
Kinetic energy depends on speed and
mass
The net work done on a body equals its
change in kinetic energy
SI units for KE
kg•m2/s2 or N•m or Joule (J)
14. +
Example
A 7.0 Kg bowling ball moves at 3.0 m/s. How
fast must a 2.45g ping pong ball move in order
to have the same kinetic energy as the bowling
ball? Is the speed reasonable for the ping
pong ball?
Given:
Bowling ball: m- 7.0 kg v= 3.0m/s
Ping pong: m= 2.45 g (this= 0.00245kg) v-??
15. +
Example
2KE
KE= ½ mv2 v
m
KE= ½ (7)(32)
KE= 31.5 J 2(31.5)
v
0.00245
Rearrange Equation
to get v by itself v = 160.36 m/s
16. +
Classroom Practice Problems
A 6.00
kg cat runs after a mouse at 10.0
m/s. What is the cat’s kinetic energy?
Answer: 3.00 x 102 J or 300 J
Suppose the above cat accelerated to a
speed of 12.0 m/s while chasing the
mouse. How much work was done on the
cat to produce this change in speed?
Answer: 1.32 x 102 J or 132 J
17. +
Work and Kinetic Energy
KEis the work an object can do if the speed
changes.
Wnet
is positive if the speed increases, and
negative is speeds decrease
You must include all the forces that do work
on the object in calculating the net work done
18. +
Potential Energy
Energyassociated with an object’s potential
to move due to an interaction with its
environment basically its stored energy
A book held above the desk
An arrow ready to be released from the bow
Some types of PE are listed below.
Gravitational
Elastic
Electromagnetic
19. +
Gravitational Potential Energy
Energy associated with an object due to the
object’s position relative to a gravitational
source
SI unit is still a Joule
Theheight (h) depends on the “zero level”
chosen where PEg= 0.
20. +
Elastic Potential Energy
Theenergy available for use in deformed elastic
objects
Rubber bands, springs in trampolines, pole-vault poles,
muscles
For springs, the distance compressed or stretched =
x
21. +
Elastic Potential Energy
The spring constant (k) depends on the
stiffness of the spring.
Stiffer
springs have higher k values.
Measured in N/m
Force in newtons needed to stretch a spring 1.0
meters
22. +
Example
A 70.0kg stuntman is attached to a bungee
cord with an unstretched length of 15m. He
jumps off a bridge from a height of 50m.
When he finally stops the cord has a
stretched length of 44m. Assuming the spring
constant is 71.8 N/m, what is the total PE
relative to the water when the man stops
falling?
24. +
Example
PEg= mgh PEelastic = ½ k x2
PEg= (70)(10)(6) PEelastic= ½ (71.8)(292)
PEg= 4200 J PEelastic= 30191.9J
PEtotal= PEg + PEelastic
PEtotal= 4200 + 30191.9
PEtotal= 34391.9J
25. +
Classroom Practice Problems
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.
What is the gravitational potential energy
associated with the mass relative to the table?
Answer: 9.81 J
What is the spring’s elastic potential energy if
the spring constant is 400.0 N/m?
Answer: 2.00 J
27. +
Mechanical Energy (ME)
ME = KE + PEg + PEelastic
Doesnot include the many other types of
energy, such as thermal energy, chemical
potential energy, and others
ME is not a new form of energy.
Just a combination of KE and PE
28. +
Conservation of Mechanical Energy
The sum of KE and PE remains constant.
One type of energy changes into another
type.
For the falling book, the PE of the book changed
into KE as it fell.
As a ball rolls up a hill, KE is changed into PE.
29. +
Example
Starting from rest, a child zooms down a
frictionless slide from an initial height of
3.0m. What is her speed at the bottom of
the slide? Her mass is 25kg.
Given:
vi= 0m/s hi= 3m m=25kg
vf= ?? hf=0m
30. +
Example
*Choose your equations
PE= mgh KE= ½ mv2
PEf= (25)(10)(0) KEf= ½ (25)v2
PEf= 0J KEf= ??
PEi= (25)(10)(3) KEi= ½ (25)(02)
PEi= 750J KEi= 0J
31. +
Example
*Put together
PEi+ KEi= PEf+ KEf
750 + 0 = 0 + ½ (25)vf2
750= 12.5 vf2
vf2 = √60
vf= 7.75m/s
32. +
Classroom Practice Problems
Suppose a 1.00 kg book is dropped from a height
of 2.00 m. Assume no air resistance.
Calculate the PE and the KE at the instant the book
is released.
Answer: PE = 19.6 J, KE = 0 J
Calculate the KE and PE when the book has fallen
1.0 m. (Hint: you will need an equation from Chapter
2.)
Answer: PE = 9.81 J, KE = 9.81 J
Calculate the PE and the KE just as the book
reaches the floor.
Answer: PE = 0 J, KE = 19.6 J
33. +
Table of Values for the Falling Book
h (m) PE(J) KE(J) ME(J)
0 19.6 0 19.6
0.5 14.7 4.9 19.6
1.0 9.8 9.8 19.6
1.5 4.9 14.7 19.6
2.0 0 19.6 19.6
34. +
Conservation of Energy
Acceleration does not have to be constant.
ME is not conserved if friction is present.
If friction is negligible, conservation of ME is reasonably
accurate.
A pendulum as it swings back and forth a few times
Consider a child going down a slide with friction.
What happens to the ME as he slides down?
Answer: It is not conserved but, instead, becomes less
and less.
The “lost” energy? is converted into nonmechanical
energy (thermal energy).
35. +
Classroom Practice Problems
A small 10.0 g ball is held to a slingshot that
is stretched 6.0 cm. The spring constant is
2.0 102 N/m.
What is the elastic potential energy of the
slingshot before release?
What is the kinetic energy of the ball right after
the slingshot is released?
What is the ball’s speed at the instant it leaves
the slingshot?
How high does the ball rise if it is shot directly
upward?
37. +
What do you think?
Twocars are identical with one exception.
One of the cars has a more powerful engine.
How does having more power make the car
behave differently?
What does power mean?
What units are used to measure power?
38. +
Power
Therate at which work is done or
energy is transferred
Energy used or work done per second
If we substitute W for Fd then Fd
P
t
39. +
Power
The unit of power is the joule per second,
also known as the watt.
One watt (W) of power is expended when
one joule of work is done in one second.
One kilowatt (kW) equals 1000 watts.
One megawatt (MW) equals one million
watts.
40. +
Power
SI units for power are J/s.
Calledwatts (W)
Equivalent to kg•m2/s3
Horsepower (hp) is a unit used in the
Avoirdupois system.
1.00 hp = 746 W
41. +
Watts
These bulbs all consume
different amounts of power.
A 100watt bulb consumes
100 joules of energy every
second.
42. +
Example
A 193kg curtain need to be raised 7.5m, at a
constant speed, in as close to 5 sec as
possible. Unsure which motor would be the
best 3 motors were bought. Power ratings are
1.0kW, 3.5kW, and 5.5kW. Which motor is
best for the job?
Given:
m= 193kg d= 7.5m t= 5 sec P=??
43. +
Example
P=2895 W or 2.895kW
So
the best motor would be the 3.5kW
motor
44. +
Classroom Practice Problems
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.
Calculate the power delivered by the
horses.
How much work is done by the two horses?
Answers: 1.0 x 103 W and 6.0 x 105 J
45. +
Now what do you think?
Twocars are identical with one exception.
One of the cars has a more powerful engine.
How does having more power make the car
behave differently?
What does power mean?
What units are used to measure power?
