- Lever:
MA = length of effort arm ÷ length of resistance arm.
- Wheel
and axle: A wheel is essentially a lever with one arm the distance between
the axle and the outer point of the wheel, and the other the radius of the axle.
Typically this is a fairly large difference, leading to a proportionately large
mechanical advantage. This allows even simple wheels with wooden axles running
in wooden blocks to still turn freely, because their friction is overwhelmed by
the rotational force of the wheel multiplied by the mechanical advantage.
- Pulley:
Pulleys change the direction of a tension force on a flexible material, e.g. a
rope or cable. In addition, pulleys can be "added together" to create mechanical
advantage, by having the flexible material looped over several pulleys in turn.
More loops and pulleys increases the mechanical advantage.
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)
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; Workin will be greater than Workout
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:
- Ideal
mechanical advantage (IMA)
- 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
= DE / DR
where
DE equals the effort distance and DR 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 / Eactual
where
- R is the resistance
force,
- Eactual
is the actual effort force.
