Mechanisms_2b_mechanical_advantage_S.pdf

Mechanical advantage

Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter,

and attached to the weight is called a single fixed pulley. It has a MA = 1, meaning no mechanical advantage (or disadvantage)

however advantageous the change in direction may be.

A single moveable pulley has a Mechanical Advantage = 2. Consider a pulley attached to a weight being lifted. A rope passes

around it, with one end attached to a fixed point above, e.g. a barn roof rafter, and a pulling force is applied upward to the

other end with the two lengths parallel. In this situation the distance the lifter must pull the rope becomes twice the distance

the weight travels, allowing the force applied to be halved. Note: if an additional pulley is used to change the direction of the

rope, e.g. the person doing the work wants to stand on the ground instead of on a rafter, the mechanical advantage is not

increased.

By looping more ropes around more pulleys we can continue to increase the mechanical advantage. For example if we have two

pulleys attached to the rafter, two pulleys attached to the weight, one end attached to the rafter, and someone standing on the

rafter pulling the rope, we have a mechanical advantage of four. Again note: if we add another pulley so that someone may

stand on the ground and pull down, we still have a mechanical advantage of four.

Here are examples where the fixed point is not obvious:

A man sits on seat that hangs from a rope that is looped through a pulley attached to a roof rafter above. The man pulls down

on the rope to lift himself and the seat. The pulley is considered a movable pulley and the man and the seat are considered as

fixed points; MA = 2.

A velcro strap on a shoe passes through a slot and folds over on itself. The slot is a movable pulley and the Mechanical

Advantage =2.

Two ropes laid down a ramp attached to a raised platform. A barrel is rolled onto the ropes and the ropes are passed over the

barrel and handed to two workers at the top of the ramp. The workers pull the ropes together to get the barrel to the top. The

barrel is a movable pulley and the MA = 2. If the there is enough friction where the rope is pinched between the barrel and the

ramp, the pinch point becomes the attachment point. This is considered a fixed attachment point because the rope above the

barrel does not move relative to the ramp. Alternatively the ends of the rope can be attached to the platform.

• Inclined plane: MA = length of slope ÷ height of slope

Generally, the mechanical advantage is calculated thus:

• MA = (the distance over which force is applied) ÷ (the distance over which the load is moved)

also, the Force exerted IN to the machine × the distance moved IN will always be equal to the force exerted OUT of the

machine × the distance moved OUT. For example; using a block and tackle with 6 ropes, and a 600 pound load, the operator

would be required to pull the rope 6 feet, and exert 100 pounds of force to lift the load 1 foot, therefore:

• (force IN 100 × distance IN 6 ) = (force OUT 600 × distance OUT 1 )

• or, WORK in = WORK out

This requires an ideal simple machine, meaning that there are no losses due to friction or elasticity. If friction or elasticity exist

in the system efficiency will be lower; Work in will be greater than Work out

Mechanical advantage also applies to torque. A simple gearset is able to multiply torque.

Type of mechanical advantage

There are two types of mechanical advantage:

1. Ideal mechanical advantage (IMA)

2. Actual mechanical advantage (AMA)

Ideal mechanical advantage

The ideal mechanical advantage is the mechanical advantage of an ideal machine. It is usually calculated using physics

principles because we have no ideal machine. It is 'theoretical'.

The IMA of a machine can be found with the following formula:

IMA = D E / D R

where D E equals the effort distance and D R equals the resistance distance.

Actual mechanical advantage

The actual mechanical advantage is the mechanical advantage of a real machine. Actual mechanical advantage takes into

consideration real world factors such as energy lost in friction. In this way, it differs from the ideal mechanical advantage,

which, is a sort of 'theoretical limit' to the efficiency.

The AMA of a machine is calculated with the following formula:

AMA = R / E actual

where

R is the resistance force,

E actual is the actual effort force.

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