Download Unit Seven Work Energy

Work and Energy
Preview
Section 1 Work
Section 2 Energy
Section 3 Conservation of Energy
Section 4 Power
Section 5 Extra questions
Section 1
Work and Energy
Section 1
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?
Work and Energy
Section 1
Work
• In physics, 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?
– Lift an apple weighing about 1 N from the floor to the
desk, a distance of about 1 m.
Work and Energy
Section 1
Work
• Pushing this car is work because
F and d are in the same direction.
• Why aren’t the following tasks
considered work?
– 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 a constant velocity.
Work and Energy
Work
• How would you calculate the
work in this case?
– What is the component of F in
the direction of d?
• F cos 
– If the angle is 90°, what is the
component of F in the direction
of d?
• F cos 90° = 0
– If the angle is 0°, what is the
component of F in the direction
of d?
• F cos 0° = F
Section 1
Work and Energy
Work
Section 1
Work and Energy
Section 1
Work is a Scalar
• Work can be
positive or
negative but
does not have
a direction.
• What is the
angle between
F and d in
each case?
Work and Energy
Section 1
Classroom Practice Problem
• A 20.0 kg suitcase is raised 3.0 m above a
platform. How much work is done on the
suitcase?
• Answer: 5.9 x 102 J or 590 J
Work and Energy
Section 1
Now what do you think?
• Based on the physics definition, list five examples of
things you have done in the last year that you would
consider work.
Work and Energy
Section 2
What do you think?
• You have no doubt heard the term kinetic
energy.
– What is it?
– What factors affect the kinetic energy of an object and
in what way?
• You have no doubt heard the term potential
energy.
– What is it?
– What factors affect the potential energy of an object
and in what way?
Work and Energy
Section 2
Kinetic Energy
Wnet  F x  max
Since
then
or
v  v  2ax
2
f
2
i
Wnet  m(
Wnet
v v
2
f
2
i
2
)
1 2 1 2
 mv f  mvi
2
2
Work and Energy
Kinetic Energy
• What are the SI units for KE?
– kg•m2/s2 or N•m or J
Section 2
Work and Energy
Section 2
Work and Kinetic Energy
• KE is the work an object can do if the speed changes.
• Wnet is positive if the speed increases.
Work and Energy
Section 2
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
Work and Energy
Section 2
Potential Energy
• Energy associated with an object’s potential to
move due to an interaction with its environment
– 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
Work and Energy
Section 2
Gravitational Potential Energy
• What are the SI units?
– kg•m2/s2 or N•m or J
• The height (h) depends on the “zero level” chosen where
PEg = 0.
Work and Energy
Section 2
Elastic Potential Energy
• The energy available for use in deformed elastic objects
– Rubber bands, springs in trampolines, pole-vault poles, muscles
• For springs, the distance compressed or stretched = x
Work and Energy
Section 2
Spring Constant(k)
Click below to watch the Visual Concept.
Visual Concept
Work and Energy
Section 2
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
• What are the SI Units for PEelastic?
Work and Energy
Section 2
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
Work and Energy
Section 2
Now what do you think?
• What is kinetic energy?
– What factors affect the kinetic energy of an object and
in what way?
– How are work and kinetic energy related?
• What is potential energy?
– What factors affect the gravitational potential energy
of an object and in what way?
– What factors affect the elastic potential energy of an
object and in what way?
Work and Energy
Section 3
What do you think?
• Imagine two students standing side by side at
the top of a water slide. One steps off of the
platform, falling directly into the water below.
The other student goes down the slide.
Assuming the slide is frictionless, which student
strikes the water with a greater speed?
– Explain your reasoning.
• Would your answer change if the slide were not
frictionless? If so, how?
Work and Energy
Section 3
What do you think?
• What is meant when scientists say a quantity is
conserved?
• Describe examples of quantities that are
conserved.
– Are they always conserved? If not, why?
Work and Energy
Section 3
Mechanical Energy (ME)
• ME = KE + PEg + PEelastic
– Does not 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
Work and Energy
Section 3
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
Work and Energy
Section 3
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
Work and Energy
Section 3
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.
Work and Energy
Section 3
Conservation of Mechanical Energy
Click below to watch the Visual Concept.
Visual Concept
Work and Energy
Section 3
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.
– What happens to the “lost” energy?
• Answer: It is converted into nonmechanical energy (thermal
energy).
Work and Energy
Section 3
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?
Work and Energy
Section 3
Now what do you think?
• Imagine two students standing side by side at
the top of a water slide. One steps off of the
platform, falling directly into the water below.
The other student goes down the slide.
Assuming the slide is frictionless, which student
strikes the water with a greater speed?
– Explain your reasoning.
• Would your answer change if the slide were not
frictionless? If so, how?
Work and Energy
Section 3
Now what do you think?
• What is meant when scientists say a quantity is
“conserved”?
• Describe examples of quantities that are
conserved.
– Are they always conserved? If not, why?
Work and Energy
Section 4
What do you think?
• Two cars 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?
Work and Energy
Power
• The rate of energy transfer
– Energy used or work done per second
Section 4
Work and Energy
Section 4
Power
• SI units for power are J/s.
– Called watts (W)
– Equivalent to kg•m2/s3
• Horsepower (hp) is a unit used in the Avoirdupois
system.
– 1.00 hp = 746 W
Work and Energy
Section 4
Watts
• These bulbs all consume
different amounts of
power.
• A 100 watt bulb
consumes 100 joules of
energy every second.
Work and Energy
Section 4
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
Work and Energy
Section 4
Now what do you think?
• Two cars 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?
Work and Energy
Preview
• Multiple Choice
• Short Response
• Extended Response
Section 4
Work and Energy
Section 4
Multiple Choice
1. In which of the following situations is work not
being done?
A. A chair is lifted vertically with respect to the
floor.
B. A bookcase is slid across carpeting.
C. A table is dropped onto the ground.
D. A stack of books is carried at waist level
across a room.
Work and Energy
Section 4
Multiple Choice, continued
Use the graph below to answer questions 3–5.
The graph shows the energy of a 75 g yo-yo at
different times as the yo-yo moves up and down
on its string.
Work and Energy
Section 4
Multiple Choice, continued
3. By what amount does the mechanical energy of
the yo-yo change after 6.0 s?
A. 500 mJ
B. 0 mJ
C. –100 mJ
D. –600 mJ
Work and Energy
Section 4
Multiple Choice, continued
4. What is the speed of the yo-yo after 4.5 s?
F. 3.1 m/s
G. 2.3 m/s
H. 3.6 m/s
J. 1.6 m/s
Work and Energy
Section 4
Multiple Choice, continued
5. What is the maximum height of the yo-yo?
A. 0.27 m
B. 0.54 m
C. 0.75 m
D. 0.82 m
Work and Energy
Section 4
Multiple Choice, continued
6. A car with mass m requires 5.0 kJ of work to move
from rest to a final speed v. If this same amount of
work is performed during the same amount of time
on a car with a mass of 2m, what is the final speed
of the second car? F. 2v
G.
2v
v
H.
2
v
J.
2
Work and Energy
Section 4
Multiple Choice, continued
Use the passage below to answer questions 7–8.
A 70.0 kg base runner moving at a speed of 4.0 m/s
begins his slide into second base. The coefficient of
friction between his clothes and Earth is 0.70. His
slide lowers his speed to zero just as he reaches the
base.
7. How much mechanical energy is lost because of
friction acting on the runner?
A. 1100 J
B. 560 J
C. 140 J
D. 0 J
Work and Energy
Section 4
Multiple Choice, continued
Use the passage below to answer questions 7–8.
A 70.0 kg base runner moving at a speed of 4.0 m/s
begins his slide into second base. The coefficient of
friction between his clothes and Earth is 0.70. His
slide lowers his speed to zero just as he reaches the
base.
8. How far does the runner slide?
F. 0.29 m
G. 0.57 m
H. 0.86 m
J. 1.2 m
Work and Energy
Section 4
Multiple Choice, continued
Use the passage below to answer questions 9–10.
A spring scale has a spring with a force constant
of 250 N/m and a weighing pan with a mass of
0.075 kg. During one weighing, the spring is
stretched a distance of 12 cm from equilibrium.
During a second weighing, the spring is
stretched a distance of 18 cm.
Work and Energy
Section 4
Extended Response
Base your answers to questions 14–16 on the
information below.
A projectile with a mass of 5.0 kg is shot
horizontally from a height of 25.0 m above a
flat desert surface. The projectile’s initial
speed is 17 m/s. Calculate the following for
the instant before the projectile hits the
surface:
14. The work done on the projectile by gravity.
Work and Energy
Section 4
Extended Response, continued
Base your answers to questions 14–16 on the
information below.
A projectile with a mass of 5.0 kg is shot horizontally
from a height of 25.0 m above a flat desert surface.
The projectile’s initial speed is 17 m/s. Calculate the
following for the instant before the projectile hits the
surface:
15. The change in kinetic energy since the projectile
was fired.
Work and Energy
Section 4
Extended Response, continued
Base your answers to questions 14–16 on the
information below.
A projectile with a mass of 5.0 kg is shot
horizontally from a height of 25.0 m above a
flat desert surface. The projectile’s initial
speed is 17 m/s. Calculate the following for
the instant before the projectile hits the
surface:
16. The final kinetic energy of the projectile.
Work and Energy
Section 4
Extended Response, continued
17. A skier starts from rest at the top of a hill that is
inclined at 10.5° with the horizontal. The hillside is
200.0 m long, and the coefficient of friction between
the snow and the skis is 0.075. At the bottom of the
hill, the snow is level and the coefficient of friction is
unchanged. How far does the skier move along the
horizontal portion of the snow before coming to rest?
Show all of your work.