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Work & Energy Lesson 1
3.1 Work It!
1. Force exerted in the direction of the motion.
a. From right above the piece of chalk, lift a heavy object.
b. Push a cart towards the piece of chalk.
Direction
Force Exerted
Direction of
Displacement
Angle between the force
and displacement.
Gained/Lost/Neither Gained Nor Lost
Ability to Smash Chalk.
2. Force exerted in the opposite direction of the motion.
a. With the heavy object already above the piece of chalk, catch the heavy
object as it is falling.
b. With the cart already moving towards the piece of chalk, catch the cart.
Direction
Force Exerted
Direction of
Displacement
Angle between the force
and displacement.
Gained/Lost/Neither Gained Nor Lost
Ability to Smash Chalk.
3. Force exerted perpendicular to the motion.
a. Holding up a heavy object above a piece of chalk then moving across the
room above another piece of chalk.
Direction
Force Exerted
Direction of
Displacement
Angle between the force
and displacement.
Gained/Lost/Neither Gained Nor Lost
Ability to Smash Chalk.
4. Force exerted and there is no displacement?
a. Force is exerted on a very massive object. The object does not move.
5. Force exerted at different angles.
a. Modified Atwood Machine with a cart initially at rest on a table at
different angles.
Direction
Force Exerted
Direction of
Displacement
Angle between the force
and displacement.
Gained/Lost/Neither Gained Nor Lost
Ability to Smash Chalk.
What about if I add a pulley going the other way?
SUMMARY OF OBSERVATIONS:
Experiment Direction
Direction of
Force
Displacement
Exerted
Angle between
the force arrow
and the
displacement
arrow
Gained/Lost/Neither
Gained Nor Lost
Ability to Smash
Chalk.
1.
2.
3.
4.
5.
Work, W, is the product of the magnitude of the average force FEX ON O that an external
environmental object exerts on a system object, the magnitude of the system object’s
displacement, d, and the cosine of the angle between FEX ON O and d.
W = ( FEX ON O cos  ) d
Energy, E, is that which the system gains when positive work is done on the system and
loses when negative work is done on the system. There are many forms of energy.
Practice:
1. Jeff did 573 J of work on a sled. He exerted a force on the sled over 30 m at an
angle 45o above the displacement of the system.
a. Draw a picture of the scenario.
b. Draw a force diagram for the sled. (up and to right)
c. Draw the direction of the displacement of the sled. (Right)
d. What is the angle between the force exerted by the sled and the
displacement of the sled? (45o)
e. What is the average force that he exerted on the system? (27N)
2. Steve slowly lifts a 20 kg barbell 0.8 m vertically.
a. Draw a motion diagram for the barbell.
b. Draw a force diagram for the barbell.
c. How much force did Steve exert on the barbell? (200N)
d. How much work did Steve do on the barbell? (160 J)
3. Jessica at a constant slow speed, moved a 1 kg book from a 2 m high shelf to the
floor.
a. Draw a motion diagram for the book.
b. Draw a force diagram for the book.
c. How much force did she exert on the book? (10N)
d. How much work did she do on the book? (-20J)
4. Suzzanne is pulling a sled up a hill that makes a 24o angle with the horizontal. She
keeps the rope parallel to the hill and exerts a 150- N force on it. How much work
did she do if she pulled the sled 150 m?
a. Draw the displacement arrow for the sled.
b. Draw a force diagram for the sled.
c. What is the angle between the displacement arrow and the force Suzzanne
exerted? (0o)
d. How much work did she do if she pulled the sled 150 m? (22,500J)
3.2 Types Energy & Energy Transformation
3.3 Keep Track of Your Money: An Analogy with Energy
3.4 Energy Skate Park
Explore phet.colorado.edu
1. What is happening to the bars as the skater skates up and down the half pipe?
What does this mean?
2. Where is the kinetic energy the highest? Lowest?
3. Where is the gravitational potential energy highest? Lowest?
4. What happens to the height of the bars when the mass of the skater increases?
5. What happens to the height of the bars when the skater is on a planet where the
pull due to gravity is greater? Weaker?
6. What happens to the height of the bars when the skater is dropped from a higher
position?
7. What happens to the height of the bars when I move the reference level to a
higher level? Lower level?
8. What do you think is the reference level?
3.5 Problem Solving
Problem Solving Strategy
1. Draw Picture
a. Identify the initial and finals states and draw a picture of each. Include
important information given
b. Identify the system and reference level
c. Decide if there is work and what types of energy the system has in each
the initial and final states
1. Ask yourself…
1. Is there an external
object exerting a
force on the system?
2. Does it have a
height?
3. Is it moving?
4. Is anything
stretching or being
compressed?
2.
4. If yes, which direction
is the force exerted?
Which direction is the
object moving? Find the
angle,  between them.
8. If no
10. If yes
12. If no
14. If yes
16. If not
18. If yes
20. If no
3.
5. W is + if  is < 90o
6. W is 0 if  = 90o
7. W is – if 90 <  < 180o
9. W = 0
11. Then Ug is + or –
(positive if above the
reference level, negative
for below)
13. Ug = 0J
15. K = +
17. K = 0J
19. Us = +
21. Us = 0J
2. DRAW BAR CHART – keep track of the energy
3. MATH – use bar chart to and the law of conservation of energy to represent the
scenario mathematically. Substitute the respective energy equations into the
general equation.
4. SOLVE – use all your representations to solve the problem
5. EVALUATE
a. Make sure all your representations (picture, bar chart, math and verbal) are
consistent
b. Make sure your answer makes sense (correct units, correct orders of
magnitude)
Energy Equations
 Work, W
W = FEX ON O cos  d
 Gravitational Potential
energy, Ug
Ug = mgh
 Kinetic Energy, KE
KE = ½ mv2
 Elastic Potential Energy,
Us
Us = ½ kx2
Law of Conservation of Energy
EI + W = E F
 F is the magnitude of
the force exerted by an
external object.
  is the angle between
the direction of the
force and direction of
the displacement
 d is the magnitude of
the displacement
(distance)
 m is the mass of the
object in kg
 g is 9.8 m/s2 or 10 m/s2
 h is the height of the
object with respect to
the reference level
 m is the mass of the
object in kg
 v is the velocity of the
object in m/s
 k is the spring constant
AKA force constant of
a spring. It is measured
in N/m
 x is the distance that a
spring is stretched
from its relaxed
position.
Practice: Follow all the steps of problem solving strategy to solve these problems.
1. If you drop a baseball from a window 20 m above the ground, how fast will the
ball be moving the instant before it hits the ground? Draw a bar chart representing
this process. Disregard the force exerted by the air on the ball. (20 m/s)
Side Note: What if I dropped a bowling ball instead of a baseball from the same height?
What would be its velocity the instant before it hits the ground?
Galileo’s Pisa Experiment
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
HW8
1. If a stretched slingshot has 100 J of potential energy, how fast will a 0.5 kg
softball be moving right after the launcher fires it? Specify the system, its initial
and final states, and any assumptions you made. Explain how these assumptions
affect your answer. (20 m/s)
2. A crane lifts a 50 g crate so that the crate’s speed increases from 0 m/s to 5.0 m/s
over a vertical distance of 10.0 m. Draw a bar chart representing this process.
What is the force that the crane exerts on the crate? (0.563 N)
3. A man throws a 0.4 kg softball vertically into the air and with an initial speed of
10 m/s. How fast will it be traveling when it passes 1/3 of its maximum elevation?
(8.2 m/s)
4. A man throws a 0.4 kg softball vertically into the air and with an initial speed of
10 m/s. How fast will it be traveling when it passes 1/3 of its maximum elevation?
(8.2 m/s)
5. University Physics 6.15 (answers in back)
6. University Physics 6.26 (3 m/s)
7. University Physics 6.77 (answers in back)
8. University Physics 6.82 (4.74m/s)
Read and outline 6.1, 6.2, & 6.3 – pg 194
Sample Solution
3.