Unit 4
Work &
Power
1
2
Information: The Meaning of Work
“I’m going to work.”
“This job is hard work.”
“I worked hard to study for this test.”
In general, the word “work” refers to the effort it takes to get things done. Manual labor is seen as
work and so is mental labor.
Activities that may seem like work to you might NOT seem like work to a scientist. For example, if
you sit quietly and study for a long time, a scientist would say that you’re not doing any work at all!
And you could push against a car until you were exhausted, but if
the car doesn’t move, the scientist would say you had done no work
on the car. As you can see, there is a big difference between the
everyday use and the scientific use of the word “work.”
Two things must happen for a force to do work on an object. First,
the force must push or pull on the object. Second, the object must
move a distance. Both must happen; otherwise, no work is done.
For example, if you pick up a book bag and put it on your desk, a
scientist would say that you have done work on the book bag.
Critical Thinking Questions
1. What two things does work depend on?
2. If an object is pushed on, but does not move, is there any work being done to the object?
Why?
Teacher Initials
3
Information: Calculating Work
In the scientific community, work is only done if a force is applied to an object and that object
moves a distance. To calculate the work done on an object, the force that pushes or pulls on the
object is multiplied by the distance the object moves. Work involves both force and distance.
So, how much work did you do on that book bag you lifted onto the desk? It’s not hard to figure
out. Multiply the force needed to lift the bag by the distance the object as lifted. That’s it! In other
words: Work = Force x Distance
Force is measured in Newtons (N) and distance in measured in meters (m). When multiplying the
two to find Work, we end up with a Newton-meter (N*m). A Newton-meter is also called a Joule
(J). Work is measured in Joules (J), for James Joule, who made important discoveries about work
and energy.
Here’s an example of how to calculate work:
Michael lifts his book bag, which weighs 25 N, from the floor to a desktop that is 0.80 m above the
floor. How much work does Michael do on the bag?
Work = Force x Distance
Work = 25 N x 0.80 m
Work = 20.0 J
Michael does 20.0 J of work on the book bag.
Critical Thinking Questions
1. What units is work measured in?
2. If a pencil drops from a desk, is work being done? Why?
3. What is doing the work on the pencil from question 2?
4. What is the equation for work?
5. What would the triangle for work look like?
Teacher Initials
4
Put it to Use: Work Mini Lab
Problem: To investigate the scientific definition of work.
Background Information: WORK is done when a force causes an object to move in the direction of
force. For work to be done, two things must occur. First, you must apply a force to an
object. Second, the object must move in the same direction as the force you apply. If there
is no motion, there is no work. This is very different from the way we use the word work in
everyday life.
Work can be calculated with this formula:
Work = Force x Distance
W=F d
The units of force are Newtons and the units of distance are meters. Therefore, work is
measured in Newton-Meters. These units are referred to as Joules.
Materials:
4 Books
Spring Scale
Meter Stick
5 different objects
Part A:
1. Stand with your arms out in front of you at waist level, palms up.
2. Have your partner put a book on each of your hands.
3. Lift the books to about shoulder level, then lower them.
4. From waist height, lift the books over your head, and then lower the books.
Critical Thinking Questions:
1. When did you do more work: when lifting the books from waist to shoulder height or when
lifting the books from waist height to over your head? Explain using what you’ve learned
about work.
5
Part B:
1. Stand with your arms out in front of you at waist level, palms up.
2. Have your partner put 2 books on each of your hands.
3. Lift the books to about shoulder level, then lower them.
4. From waist height, lift the books over your head, and then lower the books.
Critical Thinking Questions:
1. Are you using more force when lifting 2 books than when you were holding only one book?
Explain using what you know about force and weight.
Part C:
1. Stand with your arms stretched out to the sides (like you’re showing your wing span).
2. Have your partner put 2 books on each hand.
3. Hold the books at shoulder level until your arms get tired.
Critical Thinking Questions:
1. Are you exerting a force on the books?
2. Are you doing work in this situation? Explain.
6
Part D:
1. Attach one of the objects to the spring scale.
2. Record the object’s name in the data table below.
3. Hold the meter stick straight up in the air next to the object.
4. Slowly pull the object straight up along the meter stick.
5. Looking at the spring scale, determine how much force you used to pull the object
(Newtons).
6. Record the force in the data table below.
7. Using the meter stick, measure the distance you moved the object.
8. Record the distance in meters in the data table below.
9. Calculate the work you did.
10. Record the work you did in the data table below.
11. Repeat steps 1-10 with the other objects.
Data:
Calculation of Work
Object
Force (N)
Distance (m)
Work (J)
7
Analysis Questions:
1. Using a force of 50 N, you push a cart 10m across a classroom floor. How much work did
you do?
Givens
Equation
Solving For
Substitution
Answer with Units
2. What is a Joule?
______________________________________________________________________________
3. Were you doing work when you were holding the books? Explain your answer.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Were you doing work when you were lifting the objects with the spring scale? Explain your
answer.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. In Greek mythology, Atlas held the world on his shoulders. Did he do any work? Explain
your answer.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
8
Work Problems
Directions: Use your knowledge of power and work to answer the following problems. Make sure
to show all work and include all units.
1. A person pushes a block 4 m with a force of 24 N. How much work was done?
Givens
Solving For
Equation
Substitution
Answer with Units
2. A person does 15 J of work moving a couch 1.3 m. How much force was used?
Givens
Solving For
Equation
Substitution
Answer with Units
3. Paul Konerko hit a 125 m grand slam in Game 2 of the World Series. He did 3000 J of
work. With what force did he hit the ball?
Givens
Solving For
Equation
Substitution
Answer with Units
4. You lift a box that weighs 50 N to a height of 1.7 m. How much work did you do on the box?
Givens
Solving For
Equation
Substitution
Answer with Units
9
5. A 750 N skydiver jumps out of an airplane that is flying at an altitude of 2800 m. By the time
the skydiver reaches the ground, how much work was done on her by gravity?
Givens
Solving For
Equation
Substitution
Answer with Units
6. A bulldozer performs 75,000 J of work pushing dirt 18 m. What is the force exerted?
Givens
Solving For
Equation
Substitution
Answer with Units
7. Mr. Z holds 200 kg above his head for 5 seconds. What is the work done on the weights?
Givens
Solving For
Equation
Substitution
Answer with Units
8. If Ms. Oldham has a mass of 55 kilograms and climbs up stairs that are 30 meters tall then
how much work was done?
Givens
Solving For
Equation
Substitution
Givens
Equation
Answer with Units
Solving For
Substitution
Answer with Units
10
9. If 100 J of work are done by lifting a box 1.5 m, then how much mass was the box?
Givens
Solving For
Equation
Substitution
Givens
Equation
Answer with Units
Solving For
Substitution
Answer with Units
10. You hurry to your physics class after a yummy meal in the cafeteria. In your arms you carry
books that include your highly valued EMP binder. All together the food and the binder
weigh 22 N. How much work is done on the books when you walk 80 m along the hall, go
up stairs 12 m high, and then turn right for an additional 15 m to class?
Givens
Solving For
Equation
Substitution
Answer with Units
11
Information: The Meaning of Power
“I have the power!”
“She is in a powerful position.”
“How much power do you have to make a change?”
In general, the word “power” refers to strength, authority, control or influence. But in science, the
word “power” like the word “work” has a very specific meaning.
Power is the rate at which work is done or how quickly work is done. Power takes into
consideration how much work is done on an object AND how quickly the work was done.
Two things must happen for a force to do work on an object. First, the force must push or pull on
the object. Second, the object must move a distance. Both must happen; otherwise, no work is
done. Power also takes into consideration how much time it took for the force to move the object.
For example, if you pick up a book bag and put it on your desk, a scientist would say that you have
done work on the book bag. If you time how long it takes you to lift the book to the desk, then you
can figure out how much power you used!
Critical Thinking Questions
1. What two things does power depend on?
2. If an object is pushed on, but does not move, is there any power being used? Explain.
3. If an object is pushed on, moves 10 m and does so in 1 minute, is there any power used?
Explain.
Teacher Initials
12
Information: Calculating Power
In the scientific community, power is only used if work is done on an object in a certain amount of
time. To calculate the power used on an object, the work done on the object is divided by the
time it took to do the work. Power involves both work and time.
So, how much power did you do on that book bag you lifted onto the desk? It’s not hard to figure
out. First find the work you did on the book bag. Multiply the force needed to lift the bag by the
distance the object as lifted.
Here’s an example of how to calculate power:
Michael lifts his book bag, which weighs 25 N, from the floor to a desktop that is 0.80 m above the
floor. It takes him 5 s to lift the book bag. How much power does Michael use?
Work = Force x Distance
Work = 25 N x 0.80 m
Work = 20.0 J
Michael does 20.0 J of work on the book bag.
Then divide the work by the time it took to lift the book bag.
Power =
Work
time
Power =
20.0 J
5s
Power = 4 J/s or W
Work is measured in Joules (J) and time is in measured in seconds (s). When dividing the two to
find Power, we end up with Joules per second (J/s). A Joule per second (J/s) is also called a Watt
(W). Power is measured in Watts (W).
Critical Thinking Questions
1. What units is power measured in?
2. What is the equation for power?
3. What would the triangle for power look like?
Teacher Initials
13
Power Problems
Directions: Use your knowledge of power and work to answer the following problems. Make sure
to show all work and include all units.
1. Dante uses 14 J of work to lift a weight for 30 seconds. How much power did he use?
Givens
Solving For
Equation
Substitution
Answer with Units
2. A machine produces 4000 Joules of work in 5 seconds. How much power does the machine
produce?
Givens
Solving For
Equation
Substitution
Answer with Units
3. Ms. Johnson can bench press 150 kg from 0.7 m from the ground to 1.5 m above the
ground.
a. How much weight (not mass) did Ms. Johnson lift?
Givens
Solving For
Equation
Substitution
Answer with Units
b. How much power did she use if she lifts the weights in 10s?
Givens
Solving For
Equation
Substitution
Answer with Units
14
4. If it took Ms. Oldham 37 seconds to lift a 400 N student up 15 m, how much power did she
use?
Givens
Solving For
Equation
Substitution
Answer with Units
5. Darth Vader unleashed the power of the dark side (1225 W) on the unsuspecting Jedi. If he
did 727 J of work, how much time did it take?
Givens
Solving For
Equation
Substitution
Answer with Units
6. While playing 17 straight hours of the Wii, Mr. Wallaby successfully raised his arm to scratch
his head 187 times. If he raised his hand 1 m and his arm had a mass of 2.3 kg, how much
power was used?
Givens
Solving For
Equation
Substitution
Givens
Equation
Answer with Units
Solving For
Substitution
Answer with Units
15
7. Superman moves a car 2700 N on a track of 500 m. If the car takes 32 seconds to move
the entire distance, how much (super)power is exerted by Superman?
Givens
Solving For
Equation
Substitution
Givens
Equation
Answer with Units
Solving For
Substitution
Answer with Units
8. Superman is unhappy with his time in the above problem, so he attempts to lift the same
car. This time, it takes 18.1 seconds. How much does his power increase?
Givens
Solving For
Equation
Substitution
Answer with Units
9. If a man slowly lifts a 20 kg bucket from a well and does 6.00 kilojoules of work (1000 Joules
= 1 kilojoule), how deep is the well?
Givens
Solving For
Equation
Substitution
Givens
Equation
Answer with Units
Solving For
Substitution
Answer with Units
16
10. Hulky and Bulky are two workers being considered for a job at the UPS loading dock. Hulky
boasts that he can lift 100 kg box 2.0 m vertically in 3.0 seconds. Bulky counters with his
claim of lifting a 200 kg box 5.0 m vertically in 20 seconds.
Which worker has a greater power rating? __________________________________________
Hulky (3 steps)
Givens
Equation
Solving For
Substitution
Givens
Equation
Solving For
Substitution
Givens
Equation
Substitution
Substitution
Answer with Units
Solving For
Substitution
Givens
Equation
Answer with Units
Solving For
Givens
Equation
Answer with Units
Solving For
Bulky (3 steps)
Givens
Equation
Answer with Units
Answer with Units
Solving For
Substitution
Answer with Units
17
11. You and a friend run up stairs that are 30 m high. Both of you reach the top in 12 seconds.
You weigh 570 N and your friend weighs 620 N.
Which of you has more power? _____________
Why? _______________________________________________
You
Givens
Equation
Solving For
Substitution
Givens
Equation
Solving For
Substitution
Your Friend
Givens
Equation
Answer with Units
Solving For
Substitution
Givens
Equation
Answer with Units
Answer with Units
Solving For
Substitution
Answer with Units
18
How Many Horses?
It was the late 1800’s, and engineer James Watt was stumped. He’d just figured out a way
to make steam engines operate much more efficiently. He wanted to start manufacturing and
selling his new invention. But how could he describe how powerful these amazing engines were?
Watt’s answer? Compare the power of the steam engine with something that people were
very familiar with: the power of a horse.
In Watt’s day, ponies (small horses) were used to pull ropes attached to platforms that lifted
coal to the surface of the earth from the mine below. Watt measured how much these loads
weighed (force). Then he determined how far the ponies could raise them (distance) in one minute
(time). Using these measurements, he calculated how much work a pony could do in a minute –
he calculated the power of a pony – ponypower!
At that time, the unit of work used by British scientists was the foot-pound (ft-lb). On the
basis of his observations and calculations, Watt found that a pony could do 22,000 ft-lb of work a
minute. Because he figured that the average horse was as powerful as 1.5 ponies, he multiplied
the power of one pony (22,000 ft-lb of work per minute) by 1.5 and called it 1 horsepower (hp).
In other words, 1 hp is equal to 33,000 ft-lb of work per minute, or 550 ft-lb of work per
second. This means that an average horse can lift a 550-lb load a distance of 1 foot in 1 second.
Horsepower can be translated into watts (W): 1 hp equals 750 W. A 350-hp engine,
therefore, has the same power as a 262,500-W engine. But when numbers get as big as this, you
can see that watts aren’t a convenient way of expressing the power of engines. So, the term
“horsepower” stuck around. Using the word “horsepower” also probably makes drivers feel closer
to the old days – when people were pioneers and mustangs were horses!!
1. Why do you think James Watt used a horse as a measure of a unit of power?
______________________________________________________________________________
______________________________________________________________________________
2. How did Watt decide the value of 1 horsepower?
______________________________________________________________________________
______________________________________________________________________________
3. Why is “horsepower” still a useful unit of power?
______________________________________________________________________________
______________________________________________________________________________
4. How many Watts make up 1 hp? ______________________________________________
5. How long did it take a horse to lift 550 lb a distance of 1 ft, according to Watt? ___________
19
Put it to Use: Power Up
Background Information:
• You are doing WORK when you use force to cause motion in the direction of force.
• Work can be calculated mathematically.
• The formula for work is:
Work = force x distance
• Time is not considered when calculating work
• Force (or weight) is measured in Newtons. Distance is measured in meters. The unit
for work is a Newton-meter.
• A Newton-meter is called a Joule.
•
•
•
POWER is the rate at which work is done. It is the amount to work per unit of time.
The formula for Power is:
Power = work / time
Another way to calculate it is:
Power = (force x distance) / time
Pre-lab Questions:
1. Do you do more work climbing stairs quickly or climbing stairs slowly? ________________
2. Does it take more power to climb stairs quickly or climb stairs slowly? ________________
Materials:
Calculator
Meter stick
Staircase
Bathroom Scale
Stopwatch
Procedure:
1. Calculate the DISTANCE you will move:
•
Count the number of steps.
______________
•
Use the meter stick to measure the height of one step
______________ cm
•
Convert the height of one step from cm to m
______________m
•
Calculate the total height of the staircase and record in Data Table 1.
(Hint: Height of the staircase = height of one step x number of steps.)
2. Calculate the FORCE you will use to climb the stairs
•
Use the scale to find your mass
•
Convert your mass into weight in Newtons and record in Data Table 1.
______________kg
______________N
(This weight is your FORCE needed to climb the stairs.)
20
3. One partner will now climb the stairs SLOWLY.
4. The other partner will use the stopwatch to time how long it takes to climb the stairs.
5. Record your data in Data Table 2.
6. Repeat two more times.
7. Calculate the average time to climb the stairs slowly.
8. The same partner will now climb the stairs QUICKLY.
9. The other partner will use the stopwatch to time how long it takes to climb the stairs.
10. Record your data in Data Table 3.
11. Repeat two more times.
12. Calculate the average time to climb the stairs quickly.
13. Calculate the amount of work and power that you did as you walked SLOWLY up the stairs.
14. Calculate the amount of work and power that you did as you walked QUICKLY up the stairs.
15. Record these values in Data Table 4.
21
Data:
Data Table 1: Background Data
Height of Staircase (m)
Force to climb stairs (N)
Data Table 2: Time to Climb the Stairs Slowly
Time to Climb Slowly (s)
Trial 1
Trial 2
Trial 3
Average
Data Table 3: Time to Climb the Stairs Quickly
Time to Climb Stairs Quickly (s)
Trial 1
Trial 2
Trial 3
Average
Data Table 4: Work & Power to Climb Stairs
Work done climbing stairs (J)
Slowly
Power to climb stairs (J/sec)
Quickly
22
Analyze the Data:
1. Make a bar graph comparing the amount of WORK done when climbing the stairs slowly
and quickly.
Title: _______________________________________________________________
2. Make a bar graph comparing the amount of POWER done when climbing the stairs slowly
and quickly.
Title: _______________________________________________________________
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3. What do the graphs tell you about work and power?
______________________________________________________________________________
______________________________________________________________________________
Post-lab Questions:
1. When did you do the most work, when you climbed the stairs slowly or quickly?
______________________________________________________________________________
2. What two things could be changed to change the amount of work done?
______________________________________________________________________________
3. When did you use the most power, when you climbed the stairs slowly or quickly?
______________________________________________________________________________
4. If the amount of Work done stays the same, what must change in order to change the
amount of power used?
______________________________________________________________________________
24
WORK READING GUIDE
Directions: Read pages 406 - 411 in your book, and answer the following
questions.
1. What is work?
2. What two conditions need to exist in order to do work?
3. What is power?
4. What is the equation for Work?
5. What do work and power depend on? (What are the variables in the equation?)
6. What is the unit for work?
7. How are force and direction of motion related when talking about work?
25
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27
Bill Nye “Simple Machines”
Directions: Answer the following questions as you watch Bill Nye.
1. Simple machines let us change the _________________________ and
_______________________ of force.
2. What simple machine is in a catapult, and how does it work?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. What is the fulcrum of a lever?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Which object shot by a catapult do you like best? Why?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. How are wheels and levers related?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
6. What parts of a bicycle are simple machines?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7. How does a ramp make work easier?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
28
8. Why doesn’t the rope break when a large book is pulled on a ramp?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
9. How is a screw related to a ramp?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
10. What does a pulley do to require less force?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
11. What simple machines can be seen on a sailboat, and what do they do?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
29
Simple Machines Internet Review
Purpose: To review simple & compound machines
Part 1:
1. Go to this website: http://edheads.org/activities/simple-machines
2. Click on the start button
3. A new window will open up. You can bounce between the two windows as necessary.
4. Choose your first activity from THE HOUSE (the second window)
a. There are four locations in the house: the garage, the bedroom, the bathroom, and
the kitchen.
5. Click on each location and do the activity as it is directed. MAKE SURE TO USE YOUR
HEADPHONES!!!
30
31
6. Go back to the original screen and click on the TOOLSHED.
6. Following the directions in the intro, click on each compound machine and figure out what
simple machines make up the compound machine.
7. List the simple machines found in each compound machine.
Part 2
Go to the following website http://edheads.org/activities/odd_machine/index.htm
Click on the start button and play THE ODD MACHINE GAME
32
Going Up!!
It was May 1854. The World’s Fair was being held in New York City. On display were the
newest inventions from many countries. The crowds were amazed by the promise of technology.
A crowd gathered around a tall, dignified man in a top hat. He
mounted a platform. As people looked on, the platform was slowly
raised by a rope that was wrapped around a motor-driven drum.
When the platform had ascended well above the crowd, another
figure standing on a landing above the platform suddenly reached out
and slashed the heavy rope by which the platform was suspended. The
crowd gasped.
The platform dropped, but only by a few centimeters. Then it
came to a stop. “All safe, ladies and gentlemen, all safe!” the man on
the platform proclaimed.
The man on the platform was Elisha Otis, and he’d just proudly
demonstrated his invention – the safety elevator. His device would become the first public
passenger elevator. Just three years after this dramatic demonstration, the first public passenger
elevator was put into service at a New York City department store. By 1873, more than 2000 Otis
elevators were being used in office buildings, hotels, and department stores.
An Elevator Fit for a King
The earliest elevators were little more than lifting platforms. More than 2000 years ago, the
Romans described lifting platforms that featured pulleys and rotating drums. The power for these
devices was supplied by humans or animals. In 1742, France’s King Louis XV had a private
elevator built in his palace at Versailles. It was operated using human power. Servants pulled on
ropes to lift and lower the king. Counterweights helped balance the weight of the king as he
moved from floor to floor.
These early elevators had a simple design. The car was suspended by a rope or cable that
ran over a pulley at the top of the elevator shaft. At the other end of the cable was a counterweight
that balanced with the weight of the car plus the average
weight of the load the elevator carried. The car and the
counterweight were guided between rails to keep from
swinging freely.
Putting on the Brakes
Beginning in 1830 or so, freight elevators were in common use. But all these elevators,
including the one used by King Louis XV, had a big drawback: if the rope from which they were
suspended snapped, the elevator went crashing to the ground. There was nothing to cushion or
stop its descent.
That’s why Otis’s invention was so important. His safety elevator had something that none
of the earlier models did – a brake. If the rope broke, a large spring forced two large latches to
lock into ratchets on the guide rails. These latches kept the elevator from falling.
New Forms of Power
33
The earliest passenger elevators were powered by steam engines. As years passed, other
power sources were used. Water pressure was tried. The invention of electric-powered elevators,
like Otis’s safety device, was an important advance in elevator technology.
The invention of the electric-powered elevator for passengers had a strong effect on city
living. Before it came into use, most buildings were no more than four stories high. People just
couldn’t huff and puff their way up any more flights of stairs!
The lack of appropriate building materials was another
drawback to the growth of tall buildings.
Changing the Landscape – And People’s Lives
By the beginning of the 20th century, the word
“skyscraper” had entered the English language. Buildings
were built taller and taller – and thanks to elevators, people
could make their way easily to the top. Additional refinements
included self-opening doors, an automatic leveling feature,
and faster speeds. Modern elevators travel up to 600 meters
a minute.
Today, you can zoom to the top of the Washington
Monument or the Empire State Building and back in minutes,
thanks to electric-powered elevators. And, thanks to Elisha
Otis, you can be assured of a safe trip in both directions.
1. How are pulleys used in elevators?
______________________________________________________________________________
______________________________________________________________________________
2. What is the purpose of the counterweight in an elevator?
______________________________________________________________________________
______________________________________________________________________________
3. What has been the impact of elevators on building design?
______________________________________________________________________________
______________________________________________________________________________
34