LEVERS
~ Archimedes
Introducing… The Lever
• A lever includes a stiff structure (the lever) that
rotates around a fixed point called the fulcrum.
fulcrum
• Lever – A bar that is free to move about a
fixed point
– Parts of a lever
• Fulcrum – The fixed point of a lever
• Effort Arm – The part of the lever that the effort
force is applied to (measured from the fulcrum to
the point at which the force is applied)
• Resistance Arm – The part of the lever that applies
the resistance force (measured from the fulcrum to
the center of the resistance force)
Anatomy of the lever
• Fulcrum – point around which the lever
rotates
• Input Force – Force exerted ON the lever
• Output Force – Force exerted BY the lever
Levers and the human body
• Your body contains
muscles attached to
bones in ways that
act as levers.
• Here the biceps
muscle attached in
front of the elbow
opposes the
muscles in the
forearm.
Can you think of other muscle
levers in your body?
Eureka - Levers
Three Classes of Levers
• First Class - fulcrum
between Input and output
 Second Class – output
between fulcrum and input
 Third Class – input
between fulcrum and
output
First Class Levers – “See-Saw” Levers
• 1st Class Lever - The fulcrum is located between the
effort arm and the resistance arm.
• First class levers can multiply force and distance.
– Examples: scissors, see-saw, hammer’s claws, pliers, etc…
2nd Class Levers – “Wheelbarrow Levers”
• 2nd Class Lever - resistance is located
between the effort arm and the fulcrum.
These levers multiply the force but the
direction stays the same.
– Example: wheelbarrow, stapler, bottle
opener, finger nail clippers, nut cracker
3rd Class Levers - “Tweezers”
• 3rd Class Lever - The effort force is located
between the fulcrum and the resistance.
The effort arm is always shorter than the
resistance arm so it cannot multiply the
force and the MA is always less than 1.
– Examples: rake, hockey stick, broom, shovel,
fishing pole, tweezers, tongs
Mechanical Advantage
What do simple machines do for
us anyway?
There are four ways that a machine
helps us to do work.
• Transfers our effort force from one
place to another.
Ex: seesaw
• Multiplies your effort force.
Ex: crowbar
• Magnifies speed and distance.
Ex: baseball bat
• Changes the direction of the force.
Ex: pulley on the flagpole
Mechanical Advantage
• The number of times a machine multiplies
your effort force.
– Example: If you push on the handle of a car
jack with a force of 30 lbs and the jack lifts a
3000 lb car, what is the jack’s mechanical
advantage?
– The jack multiplies your effort force by 100
times.
There are 2 types of mechanical advantage.
• IMA – Ideal mechanical
advantage.
• This is the number of
times a machine is
designed to multiply your
effort force.
• It is based on
measurements of the
machine.
• Ignores friction
• AMA – Actual mechanical
advantage
• This is the number of
times the machine
actually multiplies your
effort force.
• AMA = resistance
force/effort force.
• Includes the effects of
friction
IMA is always greater than AMA.
• By using the length of the effort arm and
the resistance arm you can find the ideal
mechanical advantage.
– Ideal Mechanical Advantage (IMA) – What the
mechanical advantage of a machine would be
if there were no energy lost due to friction
• IMA = length of effort arm = le
length of resist arm lr
.
Lever
1
ft.
MA=Fulcrum to Effort / Fulcrum to Load
MA=3 / 1
MA=3
Solve…
A construction worker uses a board and log as
a lever to lift a
heavy rock. If the input arm is 3 meters long
and the output arm is 0.75 meters long, what is
the mechanical advantage of the lever?
Answer…
MA = 3 / 0.75
MA = 4
Solve…
Sometimes levers are used
to multiply distance. For a
broom, your upper hand is
the fulcrum and your lower
hand provides the input
force.
The mechanical advantage
of this
broom is:
Answer…
MA = 0.3 / 1.2
MA = 0.25
Explain…
A mechanical advantage less than one doesn’t
mean a machine isn’t useful. It just means that
instead of multiplying force, the machine
multiplies distance.
A broom doesn’t push the dust with as much
force as you use to push the broom, but a small
movement of your arm pushes the dust a large
distance.
Solve…
What is the mechanical advantage of a
lever that has an input arm of 3 meters
and an output arm of 2 meters?
Solve…
A lever with an input arm of 2 meters
has a mechanical advantage of 4.
What is the output arm’s length?
Answer…
Set-up:
Input Arm = 2
Output arm = 0
MA = 4
2/x=4
Solve for x by multiplying
both sides by the
denominator which is x.
You get: 2 = 4x
Divide each side by 4 you
get: 2 / 4 which is equal
to .5