............................................................................................................................................
EDinformatics.com
In physics and
engineering, mechanical advantage (MA) is the factor by which
a machine multiplies the force put into it.
The mechanical
advantage can be calculated for the following simple machines by
using the following formulas:
· 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 increase 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.
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, WORKin = WORKout
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 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:
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 = 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.
EDUCATION
FOR THE INFORMATION AGE
No comments:
Post a Comment