Work, Power and Machines
Warm Up
• How would you define work and energy? Do
these words have the same meaning in science
and in everyday speech?
• What different types of energy do you know
about?
PSc. 3.1.3
• Explain scenarios in which work is done,
identifying the force, displacement, and energy
transfer.
• Compare scenarios in which work is done and
conceptually explain the differences in
magnitude of work done using the relationship
W=f x d
Energy
THERMAL
The ability to
cause change.
internal motion of
particles
MECHANICAL
NUCLEAR
ENERGY
motion of objects
changes in the nucleus
ELECTRICAL
CHEMICAL
bonding of atoms
joules (J)
motion of electric
charges
Energy
• Kinetic Energy (KE)
• energy in the form of motion
• depends on mass and velocity
• Which has the most KE?
80 km/h truck
• Which has the least KE?
50 km/h motorcycle
80 km/h
50 km/h
80 km/h
Energy
• Potential Energy (PE)
• stored energy
• depends on position or configuration of an object
• Which boulder has greater
gravitational PE?
• What other ways can an
object store energy?
Work
It’s not what you think!
Work is a transfer of energy to a body by the
application of a force that causes the body to move
in the direction of the force. Huh?
Work is using a force to change the position of an
object.
Work
Work is Force times distance where Force is the
force acting on the object (could be applied force,
could be gravitational force) and distance is how
far the object moved.
W = F•d
Units of work are Joules (J).
Examples
• A crane operator uses an average force of
5200N to lift a girder 25m. How much work does
the crane do on the girder?
• Given: F = 5200N
d = 25m
W=?
W = F•d
W = 5200N x 25m
W = 130,000J
Examples
• An apple weighing 1N falls a distance of 1m.
How much work is done on the apple by the
force of gravity?
Given: Fg = 1N
d = 1m
W=?
W = Fg•d
W = 1N x 1m
W = 1J
Examples
• The brakes of a bicycle apply 125N of frictional
force to the wheels as the bicycle travels 14m.
How much work have the brakes done on the
bike?
Given: F = 125N
d = 14m
W = F•d
W = 125N x 14m
W = 1750J
Examples
• A mechanic uses a hydraulic lift to raise a
1200kg car 0.5m off the ground. How much
work does the lift do on the car?
Given: m = 1200kg
d = 0.5m
W=?
W = F•d but… we have a mass, not a force.
So, we go back to Fg = mg (g = 9.8m/s/s)
F = 1200kg x 9.8m/s/s = 11,760N
Now, W = 11,760N x 0.5m = 5880J
Warm up
• A father is playing with his baby by lifting her into
the air repeatedly. How much work does he do
with each lift, assuming he lifts her 2m and
exerts an average force of 190N? How much
work does he do when he holds her and walks
her to her crib?
PSc.3.1.4
• Infer the Work-Power relationship:
P = W = FΔd = F x vave
Power
• You have to mow 30 lawns in a month. You can
mow 6 lawns per day and be done in 5 days or
you can mow one lawn per day and take all 30
days to finish.
What is analogous to the total number of lawns
mowed?
Work
What is analogous to the rate of mowing?
Power
Power
• Power is the rate at which work is done.
QuickLab: What is your power output when
climbing the stairs?
Question: Running up a flight of stairs takes the
same amount of work as slowly walking up a flight
of stairs. Why is it more tiring?
Power
• Power = Work = W
time
t
Units: Watts (W) or commonly kW (1kW = 1000W)
1W is the amount of power required to do 1J of
work in 1 second.
Example
• It takes 100kJ of work to lift an elevator 18m. If
this is done in 20s, what is the average power of
the elevator during this process?
Given: W = 100kJ d = 18 m t = 20s
100kJ x 1000J = 100,000J
1kJ
P = Work = 100,000J = 5000W
time
20s
5000W x 1kW = 5kW
1000W
Power
• You may be familiar with horsepower as a
measure of power. This originally referred to the
average output of a draft horse. 1hp = 746W
Power
• While rowing across the lake in a race, John
does 3960J of work on the oars in 60s. What is
the power output in watts?
Given: W = 3960J
t = 60s
P = W = 3960 = 66W
t 60s
Problems
• Suppose you are moving a 300N box of books.
Calculate your power output if…
a. You exert a force of 60N to push the box
across the floor 12m in 20s.
b. You lift the box 1m onto a truck in 3s.
For a. W = Fxd = 60N x 12m = 720J
P = W/t = 720J/20s = 36W
For b. W = Fxd = 300N x 1m = 300J
P = W/t = 300J x 3s = 900W
Problems
• A student lifts a 12N textbook 1.5m on 1.5s and
carries the book 5m across the room in 7s.
a. How much work does the student do on the book?
W = Fxd = 12N x 1.5m = 18J to lift the book
Note: No work is done to carry the book across
the room because the force on the book (vertical) is in
a different direction than the applied force (horizontal).
b. What is the power output of the student?
P = W/t = 18J/1.5s = 12W
Problems
• Compare the work and power used in the
following situations:
a. A 43N force is exerted through a distance of
2.0m over a time of 3s.
b. A 43N force is exerted through a distance of 3m
over a time of 2s.
Problems (cont.)
a. Given: F = 43N d = 2m t = 3s
W = F x d = 43N x 2m = 86J
P = W/t = 86J/3s = 29W
b. Given: F = 43N d = 3m t = 2s
W = F x d = 43N x 3m = 129J
P = W/t = 129J/2s = 65W
Energy transformation
• http://youtu.be/i6e-KrNCe_E
C. Conservation of Energy
• Law of Conservation of Energy
• Energy may change forms, but it cannot be created or
destroyed under ordinary conditions.
• EX:
• PE  KE
• mechanical  thermal
• chemical  thermal
C. Conservation of Energy
PE  KE
Conservation of Energy
Check Your Understanding
Energy
Includes
includes
Is the ability to do
can be
a.
which measures
b.
Kinetic
energy
transformed
c.
Which is energy
Associated with
which is energy
of
but never
acting over a
e.
distance
position
d.
or
destroyed
Warm Up
1. A force of 15N is used to push a box along the
floor a distance of 3m. How much work was
done?
2. What is the power of a kitchen blender if it can
perform 3,750J of work in 15s?
Warm Up Answers
1. Given: F = 15N d = 3m W = F x d
W = 15N x 3m = 45J
2. Given: W = 3,750J t = 15s P = W/t
P = 3,750J/15s = 250W
PSc. 3.1.4
• Determine the component simple machines
present in complex machines
• Define and determine Ideal Mechanical
Advantage
• Define and determine the efficiency of machines
• Explain why no machine can be 100% efficient
Machines and Mechanical Advantage
• Changing a car tire – the jack lets you lift a car
you otherwise couldn’t lift
• Machines redistribute work – they can change
the direction of the input force or they can
increase or decrease a force by changing the
distance. (W = F x d)
Machines and Mechanical Advantage
• Work with and without a machine:
You lift a 225N box 1m onto the back of a truck.
W = F x d = 225N x 1m = 225J
You push the box up a 3m ramp with 75N of force.
W = F x d = 75N x 3m = 225J
Same amount of work, but the machine (inclined
plane) lets you exert much less force.
Machines and Mechanical Advantage
• Mechanical advantage tells how much the
machine multiplies the force or increases the
distance traveled.
• Mechanical advantage is the ratio between the
output force and the input force or the input
distance and the output distance.
• AMA = output force IMA = input distance
input force
output distance
Machines & Mechanical Advantage
In the example of lifting a 225N box 1m on to the
back of a truck by itself and with a 3m ramp using
75N of force, determine the input and output
distances and forces.
With ramp:
Without ramp:
Input F = 75N
Input F = 225N
Input d = 3m
Input d = 1m
Output F = 225N
Output F = 225N
Output d = 1m
Output d = 1m
Machines and Mechanical Advantage
• No machine can increase force and distance at
the same time: W=fxd  if one increases the
other must decrease. (See example above)
• Said another way, you can’t get more work out of
a machine than you put into it.
• Machines don’t increase the amount of work
being done; they make the work easier to do.
Problems
• A mover uses a pulley system with a mechanical
advantage of 10.0 to lift a piano 3.5m.
Disregarding friction, how far must the mover
pull the rope?
MA = input dist
output dist
10.0 = input dist/3.5m
Input dist = 10.0 x 3.5m = 35m
Problems
• A person pushes a 950N box up an incline. If
the person exerts a force of 350N along the
incline, what is the mechanical advantage of the
incline?
• MA = output force = 950N = 2.7
input force 350N
What are the units of mechanical advantage?
None, it is a ratio. The units cancel out.
Problems
1. Calculate the MA of a ramp that is 6m long and 1.5m
high.
2. A sailor uses a rope and pulley to lift a 140N sail. The
sailor pulls down with a force of 140N on the rope.
What is the MA of the pulley?
3. Alex pulls on the handle of a claw hammer with a force
of 15N. If the hammer has a MA of 5.2, how much
force is exerted on the nail in the claw?
4. A rower pulls an oar back a distance of 0.8m on each
stroke. If the oar has a MA of 1.5, how far does the
blade of the oar move through the water on each
stroke?
1. MA = input dist/output dist = 6.0m/1.5m = 4.0
2. MA = output force/input force = 140N/140N = 1
3. Output force = MA x input force = 5.2 x 15N =
78N
4. Output dist = input dist/MA = 0.8m/1.5 = 0.53m
Warm Up
1. Put your phones in your backpacks and get out your
notes and a pencil.
2. Write the term with its correct definition. Then write its
equation and its units.
1. Work
2. Power
3. Mechanical advantage
a. The amount that a machine multiplies a force or a
distance
b. The rate at which work is done
c. What is done when a force makes an object move
Simple Machines
6 types of simple machines classified in 2 groups:
The Lever Family
The Inclined Plane Family
Simple lever
Simple inclined plane
Wheel & Axle
Wedge
Pulley
Screw
The Lever Family
1st Class Lever
Fulcrum is between points of
application of input and output forces.
Fulcrum – point on which the lever balances
Input Force – the force you apply to the lever
(effort)
Output Force – the force the lever exerts on
the object (load)
Ex: claw hammer, teeter totter
The Lever Family
2nd Class Lever
Fulcrum is at one end of the arm and input force is
applied to the other end.
Ex: wheelbarrow –
wheel is fulcrum
nutcrackers
hinged doors
The Lever Family
3rd Class Levers
Multiply distance rather than force.
Ex: many in human body – bicep contracts a small
distance and the hand moves a large distance
Which is the bicep?
Which is the hand?
Which is the fulcrum?
The Lever Family
• 1st Class Levers – can either multiply force OR
increase distance (not both)
claw hammer
• 2nd Class Lever – always multiplies force
hinged door
• 3rd Class Lever – always increases distance
broom
The Lever Family
Pulleys
Ex: flag pole, sail on boat
Can have different set ups of fixed and free pulleys
that change the input force required.
Pulleys
Lifting a 150N weight with
a single fixed pulley, the
weight must be fully
supported by the rope on
each side of the pulley.
(MA=1)
Mechanical Advantage in
pulley systems is found by
counting the number of
weight supporting ropes.
Input
Force =
150N
Output
Force =
150N
Pulleys
Output
force =
150N
Input
force =
75N
The 150N force is shared by two sections of
rope both pulling upward. (MA=2)
Pulleys
All of the sections
of rope pull up
against the
downward force of
the weight. This
gives it an even
larger mechanical
advantage.
(MA=3)
Input
force =
50N
Output
force =
150N
The Inclined Plane Family
Simple Inclined Plane – multiplies and redirects the
force.
Output
force
Input force
The output force is the force needed to lift the box
straight up to the top of the ramp. The inclined
plane spreads that force out over a longer distance
so it takes less input force to do the same amount
of work.
The Inclined Plane Family
Wedge
• modified inclined plane
• acts like two inclined planes back-to-back
Input Force
• takes 1 downward force and turns
it into 2 forces directed out and
towards the sides
Output Forces
The Inclined Plane Family
Screw
• Inclined plane wrapped around a cylinder
• Small force acting over large distance
• Ex: jar lids, spiral staircase
The Inclined Plane Family
Ex: The Great Pyramid at Giza was built by ancient
Egyptians as tombs for their royalty. It is made up
of over 2 million blocks of stone. The largest is 15
tons. The average stone weighs 2.5 tons. The
pyramid is 140M high.
Q: How did they get these stones onto the
pyramid? (2.5 tons = 22,000N)
Giza Problem cont’d
Given: ave. Weight = 2.5 tons = 22,000N
height = 140m
W = F•d
W = 22,000N x 140m
W = 3,100,000J (3.1MJ) so it takes 3.1MJ of work
to lift one block of stone to the top of the pyramid.
The Inclined Plane Family
If they used ramps with MA = 3, the average block
could be lifted by 7300N. If one person can pull
with an input force of 525N, how many people did it
take to pull an average block up a ramp?
Given:
MA = 3
Input force = 525N/1 person
Output force = 7300N
output force/input force
7300N
= 14 people
525N/1person
Compound Machines
• A machine made of more than one simple
machine
• Ex: scissors = 2 1st class levers joined at a
fulcrum
• Ex: car jack = lever and screw
• Q: ID all of the simple machines on a bicycle that
you can.
• A: brake = lever
pedal = wheel & axle
Efficiency of Machines
Just like us, machine can be more or less efficient
at what they do. The amount of work obtained
from a machine is always less than the amount of
work put into it. Machines can lose work to friction.
Efficiency is calculated as:
Work output x 100%
Work input
Engineers’ jobs are to design machines that are as
close to 100% efficient as possible.
Efficiency of Machines
Try this: A man expends 100J of work to move a
box up an inclined plane. The amount of work
produced is 80J. What is the efficiency of the
inclined plane?
Eff = work output/work input x 100%
Eff = 80J/100J x 100%
Eff = 0.8 x 100%
Eff = 80%
Note that efficiency does not have units. The units cancel
out in the calculation and you wind up with just a percent.
Review
List the 2 families of simple machines and the
types of simple machines that belong in each
family. Then describe what a compound machine
is.
Quiz
1. List 6 types of simple machines.
2. Identify the kind of simple machine:
1. A drill bit
2. Skateboard ramp
3. Boat oar
3. Describe how a lever can increase force without
changing the amount of work being done.
4. Choose a compound machine you use everyday and
identify the simple machines it contains. Draw a
sketch.