Part 5 Mechanical Advantage

Mechanical advantage

• Mechanical advantage is the ratio of output force to input force.

Mechanical advantage

• If the mechanical advantage is greater than 1, the output force is bigger than the input force.

• A mechanical advantage less than 1 means the output force is smaller than the input force.

• All levers include a stiff structure that rotates around a fulcrum.

• The side of the lever where the input force is applied is called the input arm.

• The output arm is the end of the lever that applies the output force.

Parts of the lever

Mechanical advantage of a Lever• By changing the position of the fulcrum, you can alter

the amount of input force needed compared to output force desired.

• The length of the lever arm is indirectly related to the corresponding force.

• Using the length of the lever arms, mechanical advantage can also be calculated by dividing the length of the input arm by the length of the output arm.

The Three Classes of Levers• Pliers, a wheelbarrow,

and your arm represent each of three classes of levers.

• Each class of levers is defined by the location of the input and output forces relative to the fulcrum.

The Three Classes of Levers

Class of Lever Fulcrum Force Length of Arms

1st Between input and output

forces

Vary in magnitude

Vary in length

2nd One end of lever

Output > input Input > output

3rd One end of lever

Input > output Output > input

Gears transfer motion and force• Gears can transfer motion and force

when the teeth of one gear press on the teeth of another gear as each gear rotates around a shaft.

• Connected in this way, the two gears turn in different directions.

• You can think of a gear as a rotating lever.

• The tip of a tooth of a gear is like the end of a lever and the shaft of the gear is like the fulcrum.

• This means that forces are applied where the teeth press against each other.

Gears change force and speed• The input gear is the one you

turn, or apply forces to. • The output gear is the one that is

connected to the output of the machine.

• Force is multiplied when the input gear in a pair is smaller and has fewer teeth than the output gear.

How gears work• Because the teeth don’t slip, moving 36

teeth on one gear means that 36 teeth have to move on any connected gear.

• If the output gear has 36 teeth, it turns once to move 36 teeth.

• If the input gear has only 12 teeth, it has to turn 3 times to move 36 teeth.3 x 12 = 36.

• In this example, the output gear is larger so force is multiplied.

Gear ratio and mechanical advantage

• The gear ratio is the ratio of output turns to input turns.

• The gear ratio can also be calculated as the ratio of the number of teeth on the input gear versus the number on the output gear.

• The mechanical advantage of a pair of gears is the inverse of the gear ratio.

Tension in ropes and strings• Ropes and strings carry tension forces along their length.

• The tension is the same at every point in a rope.

• If the rope is not moving, its tension is equal to the force pulling on each end (below).

• Ropes or strings do not carry pushing forces.

The forces in a rope and pulley system

• Imagine pulling with an input force of 5 newtons.

• In case A, the load feels a force equal to your input force.

• In case B, there are two strands of rope supporting the load, so the load feels two times your input force.

• In case C, there are three strands, so the output force is three times your input force.

Mechanical Advantage of Ropes and Pulleys

• The mechanical advantage of a pulley system depends on the number of strands of rope directly supporting the load.

Mechanical Advantage and work

• To raise the load 1 meter in case C, the input end of the rope must be pulled for 3 meters.

• This is because each of the three supporting strands must shorten by 1 meter.

• The mechanical advantage is 3, but the input force must be applied for three times the distance as the output force.

• In other words, to compensate for multiplying force, you need to apply the input force over a greater distance than when the output work is done.