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?

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

3 ft.

Solve…

A construction worker uses a board and log as a lever to lift aheavy 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 thisbroom 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