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.
