Chapter 4: Machines, Work, and Energy

Chapter 4: Machines,
Work, and Energy
“Reserve your right to think, for even to think
wrongly is better than not to think at all.”
HYPATIA, Natural Philosopher (355? - 415 CE) She
taught mathematics and natural philosophy. She is
credited with the authorship of three major treatises
on geometry and algebra and one on astronomy.
4.1 Work and Power
• Define work in terms of force and distance
and in terms of energy.
• Calculate the work done when moving an
• Explain the relationship between work and
Reviewing the Definition of Work
• We say work is done on an object when a force acts
to move that object in the direction of the force.
• Work done on an object transfers energy to that
• An object (or system) with energy has the ability to
do work.
• Work, like energy, is measured in Joules (J).
Work and Energy
• When a force does work on an
object, it could:
– Increase the kinetic energy of the
object (make it speed up)
– Increase the potential energy of the
object (so the object gains the
ability to do work on something
else later
– Or, if friction is involved, perhaps
just heat up the surroundings.
• Remember only forces acting in
the direction of motion will do
Force A does no work
Force B does some work
Force C does the most work
Work Done Against Gravity
• The work done while
lifting an object against
gravity is equal to its
change in potential
energy of the object.
• This is true whether you
lift the object straight
up or use a (frictionless)
ramp and lift it
• Power is the rate at which work is done.
• The quicker work is being done (or
energy transferred) the more power
• The metric unit for power is the Watt
which is equal to one joule per second
(1 horsepower = 746 watts).
Michael and Jim do the same
amount of work but Michael
is more powerful!
• How much energy does a
typical light bulb give off in 1
second? 10 seconds? 1
• The maximum power output of
a person is typically around a
few hundred watts.
• Highly trained athletes can
keep up a power of 350 watts
for about an hour.
60 Joules in 1 second
600 Joules in 10 seconds
3600 Joules in 1 minute
Calculate this amount of
energy and compare to lifting
an average person in the air!
4.2 Simple Machines
• Describe how a machine works in terms of
input and output.
• Define simple machines and name some
• Calculate the mechanical advantage of a
simple machine given the input and output
Simple Machines
• Below are some examples of simple machines. Most of
these machines were known in ancient times.
• Simple machines are “force multipliers” – they allow you
to exert a small “input” force and get a larger “output”
force? For free?
• Many modern machines are combinations of simple
machines – the textbook cites bicycles and VCRs.
Mechanical Advantage
• The ratio of the “output”
force to the “input” force is
called the mechanical
• Generally simple machines
have a MA > 1; that’s why
we use them, we can exert
a smaller “input” force and
get a larger “output” force!
• Usually the “output” force is
just the weight of the object
we are trying to move.
Work and Machines
• A simple machine has no source of energy except the
immediate forces you apply. That means the only way to get
output work from a simple machine is to do input work on the
• The output work of a machine can never be greater than the
input work. So how do we get a larger output force? What is
the trade off?
Work and Machines
• The force and distance are
related by the amount of work
done. Remember W = Fd.
• You can exert less force only if
you do so over a longer distance.
That is the trade off!
• This pulley ideally has a
Mechanical Advantage of 2.
Mechanical Advantage of Pulleys
The Mechanical Advantage of a pulley will simply be the number of strands of rope
directly supporting the weight (load).
Block and Tackle
• A block and tackle is a system of
two or more pulleys with a rope
threaded between them.
• What is the mechanical
advantage of the block and tackle
shown to the right?
• If you wanted to lift a 600 lbs
crate onto the boat, how much
force would you need to exert?
• If you needed to lift the crate 5
feet off the ground, how much
rope would you have to pull in?
MA = 6, 100 lbs, 30 feet
Count the number of strands
Mechanical Advantage of Ramps
• If the mechanical advantage
is 10, how much input force
do you have to exert to pull
the 500 N cart up the ramp?
• Instead of just lifting the
cart 1 meter off the ground
(this is want you want to
accomplish after all), what
distance do you have to
exert the input force?
1/10th of the force: 50 N, but…
10 times the distance, 10 m!
Less force, but…
More distance – that is the tradeoff
Levers rotate about a pivot point called
a fulcrum.
There are three classes of levers
discussed in the textbook. An example
of each diagram below would be: (1) a
see-saw, (2) a wheelbarrow, (3) the
human arm.
What class of lever is Archimedes
“Give me a place to stand and with
a lever I will move the whole world.”
- Archimedes (c. 287 BC – c. 212 BC)
Mechanical Advantage of Levers
• What is the mechanical
advantage of the lever
shown if the input force
“effect” is applied 5 feet
from the fulcrum, while
the load is 1 foot from
the fulcrum?
• How much work, in ftlbs, do you input into
the machine?
• How much work does
the machine output?
Screws and Gears
• Gears: When you force a larger
“input” gear, the smaller “output”
gear’s speed will be increased, but
not it’s force.
• Archimedes' screw is a machine
historically used for transferring
water from a low-lying body of
water into irrigation ditches.
4.3 Work, Energy, and Efficiency
• Describe the relationship between work and
energy in a simple machine.
• Use energy conservation to calculate input or
output force or distance.
• Explain why a machine’s input and output
work can differ.
• No machine is 100% perfectly
efficient. Some of the input
work is lost to useless energy,
such as heat, or wear & tear on
the parts.
• Bicycles may be up to 95%
efficient, but automobiles are
about 15% - most of the
chemical energy stored in the
gasoline goes into overcoming
frictional forces of all kinds!
• If the input work = the output
work, the machine is 100%
efficient, but generally which
is greater? The input work
• The efficiency can be
calculated using the following
Output _ Work
Efficiency 
Input _ Work
How efficient is the 8 foot long
ramp, if the man pushes the
200 lbs dresser 2 feet off the
ground with 62.5 lbs of force?
Time’s Arrow
• Systems tend to go from a more organized
state to a less organized state.
• For example the Kinetic Energy of a
moving bullet is more “organized” than
the random motion and heat generated
after the bullet hits an apple.
• An irreversible process, one that is less
than 100% efficient, is what we encounter
in nature. Nature seems to have a
direction in time!
• What do some say is the ultimate fate of
the universe? A heat death!
How a sandcastle reveals the end of all things
Chapter 4 Review
1) What is the usual purpose of a simple machine?
2) What is the tradeoff to using less force?
3) In what way is a machine subject to the law of energy
conservation? Is it possible for a machine to produce more
output work compared to the the input work?