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 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

3rd Class Levers - “Tweezers”

Mechanical Advantage

What do simple machines do for

us anyway?

Bill Nye – Mechanical

Advantage

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…

Input Arm = 2 Output arm = 0 MA = 4

Set-up: 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