1. WORK
chapter 6
work and energy
Has a different meaning in PHYSICS

2. (don’t write this down yet)
WORK
(don’t write this down yet)
Work = Force x displacement
Force
Displacement

3. WORK W = F d In physics work is: The force times displacement
displacement traveled by the object (m)
Dx or Dy or …
Component of force
parallel to the direction motion (N)

4. Work = F d For work this is called a Joule (J) N m N m Or kg m2 s2
If you prefer

5. How much work is done on the box?
A person drags a crate horizontally across a floor with a force of N for a distance of 5.0 m. (watch signs)
How much work is done on the box?
What if it was pulled for Twice the distance??
What if it was pulled with TWICE the FORCE for TWICE the DISTANCE??

6. What if the crate is traveling to the left for 5
What if the crate is traveling to the left for 5.0 m and the person exerts a force to the right of 30.0 N (he is slowing it down). (watch signs)
How much work does he do on the box?

7. + W = (+F) (+d) + W = (–F) (-d)
If the force and displacement are pointed the same way the work is positive
+ W = (+F) (+d)
+ W = (–F) (-d)
Work itself is not a vector, but its sign does mean something

8. - W = (+F) (-d) - W = (–F) (+d)
If the force and displacement are pointed in opposite directions the work is negative
- W = (+F) (-d)
- W = (–F) (+d)

9. How much work does a weightlifter do on a a 150 kg barbell lifting set of weight it 1.8 m from the ground (at a constant velocity)
W = F d

10. How much work does a weightlifter do holding a 150 kg set of weights motionless over his head for 10 seconds?
Is he exerting a force?
W = F d

11. How much work is done on a golf ball flying through space at a constant 220 m/s if it travels 10 m?
W = F d

12. In order for work to be done, there must be force AND distance!!

13. Lastly in order to count as “work”,
Work = Force x Distance
Lastly in order to count as “work”,
the force has to be in the parallel with the displacement of the object
The force does work on the box
Force
displacement

14. Does this force do work on the box?
Work = Force x Distance
Does this force do work on the box?
Force
displacement

15. Work is not done by the force
Work = Force x Distance
Work is not done by the force
Force

16. Only Part of this force will do work
distance

17. A crate is pulled at a constant velocity with a force of 130 N by a rope which is 25o above the horizontal for 8.0 m. How much work is done.
130 N
25o
8.0 m

18. How much work is do you do carrying a 20 kg box across a level floor for 10 m at a constant velocity?
Force
Displacement

19. In order for work to be done, there must be force AND distance!!
AND the force has to be in the same direction as the movement

20. How much work does Sisyphus do pushing a 540 kg boulder 1100 m along the slope of a a mountain with a 65 degree grade? The boulder moves with a constant velocity up the hill. Ignore friction here
Direction of motion?
Forces in same direction?
How much force does Sisyphus have to exert?
1100 m Fg
Fgx FN
540 kg
65o

21. Force and displacement are in the same direction
Positive work
Force and displacement have opposite directions
Negative work
Force and displacement are perpendicular
zero work
Object is not moving
zero work

22. Not all forces remain constant as an object moves.
Such as….
Lifting a rocket into space
Pushing on a spring
Pulling two magnets apart etc…..

23. Here force applied to an object increases linearly
as it moves. The distance is .050 m.
What force would be used.
THE AVERGE FORCE
22 N
Force
0 N
0 m
Distance
.050 m

24. W = F d = ½ * 22 *.05 22 N The AREA under the curve Force 0 N 0 m
Distance
.050 m

25. If the force was non-linear, you can break it up into a bunch of small pieces to find the area under the curve.
22 N
Force
0 N
0 m
Distance
.050 m

26. A ball with a mass of 1 kg rotates in a horizontal circle due to a string with a length of 12 cm exerting a force of 58 N . How much work does the string do one the ball in one rotation?

27. Honors Physics
WS 6-1

28. What is the common theme

29. ENERGY
is the ability to do work.

30. ENERGY has many forms

31. 2 Main types of ENERGY Kinetic Energy (KE) – motion
Potential Energy(PE) – position
Both kinetic and potential energy are considered Mechanical Energy

32. ENERGY The ability to do work J kg m2 s2 It has the same units as work
Joule

33. Work = DENERGY
BIG IDEA!!!!!

34. Objects with kinetic energy can do work!
When the car hits the wagon, it exerts a force on the crate
force
distance

35. Objects with kinetic energy can do work!
force
distance

36. Which has a bigger impact on KE,
mass of object (kg)
velocity of object (m/s)
mv2
K = 2
Kinetic Energy
of the object
Which has a bigger impact on KE,
Mass or velocity?

37. What is the kinetic energy of a 750 kg car,
traveling at 10 m/s?

38. Compare KE between
1 kg object moving at 1 m/s
2 kg object moving at 1 m/s?
Compare KE between
1 kg object moving at 1 m/s
1 kg object moving at 2 m/s?

39. Force Displacement It requires work to give an object kinetic energy.
The more work that is done on the car, the faster it goes and the more kinetic energy it has
Force
Displacement

40. How much work is done to speed up a car mass = m. In the scenario belowV1 V2
Force
Displacement

41. F = m a W = F d W = m a d mass = m Initial Velocity = v1
Final Velocity = v2
distance of acceleration = d
W = ?
F = m a
W = F d
plugging in gives
W = m a d

42. W = m a d v2 = v1 + 2ad mass = m Initial Velocity = v1
Final Velocity = v2
distance of acceleration = d
W = ?
W = m a d
Notice that
What equation relates a,d, v1, v2 ,
v2 = v1 + 2ad 2

43. W = mad
v2 = v1 + 2ad 2 2
Solving for ad
ad = v2 – v1 2

44. W = mad ad = v2 – v1 2 W = mad = m(v2 – v1) W = mv2 – mv1 2 2
Multiply both sides by m
W = mad = m(v2 – v1) 2
W = mv2 – mv1 2

45. mv2 – mv1 W = 2 2 mv KE = 2 W = DKE = KE2-KE1
Work is the change in Kinetic Energy mv 2
KE = 2
W = DKE = KE2-KE1

46. mv 2
KE = 2
W = DKE = KE2-KE1
Work done on an object is equal to its change in KE
Either to speed it up or slow it down.
(disclaimer --if no friction or PE stored)

47. What is the change in kinetic energy for a 5 kg car which speeds up from 10 m/s to 20 m/s?
How much work was done on the car?

48. Change in Kinetic Energy from 0 to 1 m/s
and from 1 to 2 m/s
Kinetic Energy
Velocity

49. Force Displacement Will the work be positive or negative?
Will the cars KE increase or decrease?
Force
Displacement
POSITIVE WORK Increases an objects KE

50. Force Displacement Will the work be positive or negative?
Will the cars KE increase or decrease?
Force
Displacement
Negative WORK Decreases an objects KE

51. A 100 N force is applied over 5 m to a: 1 kg car at rest &
Afterwards which car has more KE
Afterwards which car is moving faster?

52. An object is initially at rest
An object is initially at rest. If a 250 N force propels it forward and a 110 N force pushes it backward, how much kinetic energy does the object possesses after moving forward for 10.0 m?

53. A car has 450 J of kinetic energy
A car has 450 J of kinetic energy. How far would the car continue to travel if a force of 310 N was applied opposing its motion?

54. If the object is has twice as much KE,
Twice as much work must be done to stop it.
So the car with twice as much KE skids for twice as long
(if equal braking force)
1 kg
1 m
2 m
2 kg

55. Compare the stopping distances for cars of equal mass, but different speeds
(hint: think KE)
10 m/s
1 m
20 m/s
4 m
16 m
40 m/s

56. What is the kinetic energy of a person
who is sitting at their desk?
They are stationary compared to the floor.
Are they stationary?
Velocity is relative and so is Kinetic Energy,
you can not really say how much energy an object has because it is not really something an object “has”. It is a comparison

57. Energy an object has “stored” due to position
Potential Energy:
Energy an object has “stored” due to position
Because a position is relative
( or compared to something else)
Potential Energy is always a comparison
(not absolute measurement)

58. Potential Energy

59. UG= m g h mass height (kg) (m) 9.8 m/s2 This compares the PE
to another height really
9.8 m/s2

60. The boulder has potential energy due to gravity
Potential Energy-- is a comparison between 2 positions
-- there must be a force on the object
The boulder has potential energy due to gravity

61. HOW much PE does the boulder have?

62. Work = Fd Fg = mg = 2 kg * 9.8 m/s2 = 19.6 N
A 2.0 kg rock is lifted 3.0 m.
How much work was done on it?
What is its potential energy?
2kg 3m
Work = Fd
Fg = mg = 2 kg * 9.8 m/s2 = 19.6 N
Work = m g d = 19.6 N 3.0 m = 59 J
Its potential energy increased because work was done on it

63. Just mass, height, and gravity
Gravitation PE does not depend on the path!!!!
PE = mgh m m m h
Just mass, height, and gravity

64. Work = DPE m m m
The work done on each rock is the same as the left one. (if no friction)
How can this be?

65. Elastic Potential Energy
Many materials will resist changing shape (deforming)
Archery bow, spring, rubber band
To change them from there “natural” state you must apply a force over a distance.
In other words you do work on them. d
Natural State
Stretched

66. BUT…If you go beyond the ELASTIC LIMIT
If deformed a little objects will store that energy as PE.
BUT…If you go beyond the ELASTIC LIMIT
Rubber breaks
Springs Stretch
Archery bows snap

67. Most objects (within their elastic limit) act like springs and obey Hooke’s Law:
Fs = - k x
Force exerted by the “spring” (N)
How far the spring is stretched from it “natural” position (m)
Spring Constant
How “stiff” the spring is (N/m)
WHY THE NEGATIVE

68. Direction spring will pullx y
Force
(+ or -)
Direction spring will pull
Displacement
(+ or -) + -
Stretched
Natural
State + -
Compressed
A spring will always exert a force in the direction opposite the way is was moved from the natural state
Fs = - k x

69. Fs = - k x Fs = 0 Fs Fs Natural State x Stretched x Stretched further
The further the spring is stretched the harder it will pull back!!!!
Fs = - k x
The negative means the spring is pulling the opposite of the way it is stretched

70. A spring is naturally. 50 m long, when stretched to
A spring is naturally .50 m long, when stretched to .80 m what force will the spring exert (on whatever is holding) if the spring constant if 2.6 N/m

71. kx Force (N) x Distance (m) Work = F*d average
The AREA under the curve W= F*d
Distance (m) x

72. W = F d W = d = = average F = kx 2 kx 2 x kx 2 kx2
The work done to compress or stretch a spring is
W = F d
x is also the distance the force was exerted
average F = kx 2
W = d kx 2 = x kx 2
kx2 =

73. WS = US = kx2 2 kx2 2 Since the work done on a spring is
This is also how much energy was put into it SO
kx2
US = 2

74. Work = F*d kx
Force
(N)
The AREA under the curve W= F*d
Distance (m) x

75. The FORCE on a spring goes up with a linearly when it is stretched
The FORCE on a spring goes up with a linearly when it is stretched. This is why the scale on a spring scale is not logarithmic.
The Energy required to stretch a spring is exponential, because the force increases as it is stretched or compressed.

76. What if it was stretched twice as far?
When a spring is stretched 0.30 m from its natural state it takes a force of 18 N to keep it there.
What is its spring constant?
How much PE does it have?
What if it was stretched twice as far?

77. How much force was exerted? NONE
How much PE does a 150 kg rock gain if it moves up 2 meters on a planet with no gravity? m
How much force was exerted?
NONE
NONE
How much work was done?
How much energy did it gain?
NONE

78. If gravity were “turned off” this rock would have NO potential energy due to its height!!

79. An object only gains PE if:
1.) work was done against a force
&
2.) if that energy stored in a way that it can be used

80. Which has more potential energy a 100 kg mass which is lifted up 5 meters above the ground on earth or the moon.
Earth
Moon
Same

81. How much work is done to push a 35 kg object up the frictionless ramp below (on earth)?

82. What if one is switched so that they both attract?
Two magnets repel each other how would you increase their potential energy?
What if one is switched so that they both attract?

83. What type of energy does Temperature indicate (KE or PE)
Some times when energy is added to a substance it gets hotter (temperature goes up)
What type of energy does Temperature indicate (KE or PE)
Atoms at different temperatures applet

84. KE & PE LAB

85. The rate at which work can be done
POWER
The rate at which work can be done
What does rate mean here?

86. Work POWER = Time Which is more powerful a motor which can do:
100 J of work in 2 seconds or
100 J of work in 1 seconds

87. Work (J) POWER = Time (s) POWER has units of J/s
Also called a watt (W) Or
kg m2 s3
If you prefer

88. 1 J
1 Watt =
1 s
1,000 J
1 kW =
1000 W =
1 s

89. An electric device like a heater or light bulb is rated in watts.
This tells you the rate at which it uses electrical energy to do work.

90. Running up a set of stairs
Walking up a set of stairs
Both do the same work
BUT one needs more power!!!

91. 1 kg
1 kg
Both motors do the same amount of work but one can do it faster because it has more power

92. What’s the same & different?
1 kg
10 kg
What about here?
What’s the same & different?

93. 1 kg
1 kg
What about here?

94. A 35 kg box is lifted from the floor to a height of 2. 3 m in 3
A 35 kg box is lifted from the floor to a height of 2.3 m in 3.0 seconds by a forklift. What is the power of the forklift?
One that is twice as powerful would have done it in….
Half as powerful…

95. What power would be required to accelerate a 2700 kg car from 0 to 15 m/s in 10 seconds?

96. If a motor rated for 60 W were to lift a 50 kg student vertically
If a motor rated for 60 W were to lift a 50 kg student vertically. What would there upward velocity be?

97. POWER In the SI system, power is rated in Watts or KW
The power of your car is rated in:
Hp (horsepower)

98. 1 hp = 746 W

99. W P = t SKIP 232 HP 1360 Kg W = DK = K2-K1 mv K =
The mazda RX-8 has the following
specifications.
How long would it take to reach a speed of 27 m/s (60 mph) from rest
What is its theoretical acceleration?
How many g’s?
232 HP
1360 Kg
work done here is changing KE
W = DK = K2-K1 W
P = t
K = mv 2
SKIP

100. Power Lab

101. NO ENERGY is conserved Uh Like, quit wasting electricity
What does it mean in science when something is conserved?
Uh Like, quit wasting electricity

102. Energy is conserved means:
Initial Energy = Final Energy

103. Energy is conserved means:
Energy doesn’t get “produced” or destroyed it just changes forms between types PE & KE
(often moving from 1 object to another)

104. Force x distance

105. changes energy from 1 type to another
Work
moves energy around
&
changes energy from 1 type to another

106. Work is like spending it
Energy is like money J J J J
Work is like spending it

107. Gravitational PE Heat Kinetic Energy
Gravity does work on the mass and changes the form of the energy
Just before it hits the ground it is all in the form of kinetic energy
Heat
Kinetic
Energy

108. the mass does work on the ground
Gravitational PE
When it hits the ground,
the mass does work on the ground
Heat
Kinetic
Energy

109. Even though the energy changes we always have the same amount
Gravitational PE
Even though the energy changes we always have the same amount
Heat
Kinetic
Energy

110. Conversion of energy in happy / sad balls
Where does the energy go?

111. Energy changing form

112. Total Energy is Conserved

113. Energy changes in a pendulum

114. The total energy at any time is the same
For a swinging Pendulum h h
start PE PE
75 J KE KE
100 J
100 J
100 J
25 J PE KE
The total energy at any time is the same
(if no friction)

115. Which ball will have the faster velocity when it reaches the bottom?
If there is no friction
The same!!!
What if the red ball was twice as heavy?
Still the same!!!

116. Each Rock has the same Initial PE
So each rock would have the same KE when it reached the bottom.

117. THE TOTAL ENERGY IS CONSTANT

118. THE TOTAL ENERGY IS CONSTANTPE PE PE PE KE KE KE KE KE

119. Where will the car be moving the slowest?KE PE PE KE

120. Where will the car be moving the FASTEST?PE KE KE

121. Anytime it is at the same height?
At what spots on the ride will the car have the same speed as it does now?
Anytime it is at the same height? PE KE

122. Uh oh Let’s go Why might this rollercoaster designer be fired? KE PE

123. The total energy of a system doesn’t change
(if there is no friction, this is a non-conservative force)
Total Energy(initial) = Total Energy(Final)
U1 + K1 = U2 + K2
Gravitational and Elastic are the big ones

124. A pendulum (with a mass of m kg) is attached to a 25 cm string
A pendulum (with a mass of m kg) is attached to a 25 cm string. If released from rest how fast is it traveling at the bottom of its swing in the picture below?
.11 m

125. Compare the speeds of the two rocks when they reach the bottom of a frictionless ramp?

126. Does the answer depend on the mass?
A 150 kg rollercoaster car. A C
20 m
15 m
15 m B
0 m
If the car started at from rest at the top how fast is it moving at points A, B, and C?
Does the answer depend on the mass?

127. A cannon ball is fired from a cliff at 35 m/s at 60o above the horizontal. If the cliff is 130 m tall, how fast is it going when it hits the ground below?

128. A 5 kg rock is compressed into a spring such that the spring is
A 5 kg rock is compressed into a spring such that the spring is .25 meters shorter than its natural state.
The spring constant is k = 1,500 N/m
How fast is the rock moving when it just leaves the spring.
How high does it go compared to its original height?
5kg
? m
5kg
? m/s
5kg
0.25 m
initial
State 2
State 3

129. Back to our bungee jumper (mass of 75 kg), if he falls 15 m before the cord starts to stretch, how high does the bridge need to be if the spring constant of the cord is 50 N/m?
15 m
? m
15 m
y m
Quadratic solver

130. Conservation of Energy Lab

131. FRICTION Energy is conserved if there is no friction.
Does friction destroy energy?
FRICTION
Energy

132. The forces we have looked at currently are called CONSERVATIVE FORCES.
Like gravity, a push, springs, etc...
Because the work that they do is conserved in the system.
Friction is a non-conservative force because the work allows energy to leave the system.

133. No Friction converts PE & KE into heat.
The total amount of energy is the same
PE1 + KE1 = PE2 + KE2 + Energy Lost

134. Energy converted to heat in red
Friction does not destroy the energy, it just converts it to heat so will not go as high PE PE PE KE KE PE KE
Energy converted to heat in red KE
This energy is no longer available to help the car go up the hill.

135. Because of friction the hills must be lower as the ride goes on
Because of friction the hills must be lower as the ride goes on. (unless energy is added)
Let’s go

136. If the rollercoaster gets hot due to friction,
that energy won’t stay in the rollercoaster.
It will warm up surrounding objects.

137. Total Energy in the Universe is always CONSERVED

138. No energy is lost, where would it go?
Universe (initial)
Universe (Final) =
No energy is lost, where would it go?
The total “units” of energy is constant but
it changes form and location

139. When we make measurements we have to define a system, because we can’t measure the whole universe!!!
A “system” just includes objects of interest.
Such as:
a rollercoaster
a ball dropping
a box sliding

140. The total energy of the universe is constant
Universe -initial (6 units)
Universe -Final (6 units)
the system
the system
(3 units)
The total energy of the universe is constant
But your “system” can lose or gain energy to the
universe

141. WFRICTION = FFd = ELOST Work done against FRICTION IS “LOST”
(from the system).
WFRICTION = FFd = ELOST

142. ---Did the system lose energy?
A 2.4 kg ball starts from rest and rolls down the ramp below. Its velocity at the bottom of the ramp is 11 m/s.
---What is the system?
---Did the system lose energy?
12 m
19 m

143. A 2.4 kg crate starts from rest and is pushed up the ramp a distance of 22.5 m with a force of N and comes to a stop at the top.
---What is the system?
---How much work was done?
---How much energy did the crate gain?
---How much energy was lost?
--- What was the FF
12 m
22.5 m
19 m

144. A 2.4 kg crate starts from rest and is pushed at a constant velocity along the ground a distance of 19 m with a force of 15.0 N. After 19 m the crate immediately stops.
---What is the system?
---How much work was done?
---How much KE & PE did the crate gain?
---How much energy was lost?
--- What was the FF
15.0 N
19 m