Simple machines

Simple machines
A simple machine is a device that requires only the force of a human to perform work. One of
the properties of a simple machine is that it can be used to increase the force that can be applied
to a task.
Law of Simple Machines
Resistance Force x resistance distance = effort force x effort distance
The Mechanical Advantage is the ratio of the resistance force to the effort force
resistance force
MA =
effort force
There are four types of simple machines: the lever, the inclined plane (the wedge and the screw
are special cases of the inclined plane), the pulley, the wheel and axle (including the gear).
The Lever
The lever is a simple machine consisting of a rigid bar that is free to pivot on a fulcrum.
Depending on the position of the force (F), the load or resistance (R) and the fulcrum, there are
three classes of levers:
First Class Lever
F
R
Fulcrum
Second Class Lever
R
Third Class Lever
F
Fulcrum
R
F
Fulcrum
Simple Machines1.doc
Physics ~ ASC 2005

First Class Level
Force
F
⋅ d
= R ⋅
1
d 2
(*)
Fulcrum
d
d
1
2
R
F
=
d
d
1
2
=
MA pulley
The fulcrum is between the force and the load. This is the most common arrangement. The
mechanical advantage of this lever depends upon where we place the fulcrum. If the fulcrum is
closer to the load, the mechanical advantage is higher.
Examples of this class are the seesaw, the rows in a boat, etc.
Second Class Level
Force
d
1
Fulcrum
d
2
R
F
F ⋅ d
d
=
d
1
d 2
1
2
= R ⋅
=
MA pulley
(*)
Here the load ( R ) is between the force and the fulcrum. The mechanical advantage of this type
of lever depends upon the placement of the load. It is greater when the load is closer to the
fulcrum. When the load is closer to the force, the mechanical advantage approaches to one, so no
mechanical advantage at all.
R
MA pulley
= = 1 ⇒ R = F
F
Examples of this class are: the wheelbarrow, the stapler, the nutcracker, etc
(*) Notice that the distance is always measured from the force (or load) to the fulcrum no matter where it
is located.
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Simple Machines1.doc
Physics ~ ASC 2005

Third Class Level
Load ( R )
2
Fulcrum
Force
R d
d
1
1
= = MA pulley
d
F d
2
2
Load(R)
Force
Load
Distance
Force Distance
d d 2 1
In this class the force is between the fulcrum and the load (R ). The human forearm is a third
class lever. The elbow is the fulcrum, and the forearm muscles apply the effort between the
elbow and hand. Tweezers, tongs, and the fishing rod are examples of this type. Levers of this
class are used less often because their mechanical advantage is less than one; this means that the
force needed to use them is greater than the force they can move.
The Inclined Plane
F ⋅ d
= R ⋅
1
d 2
lenght of
=
height of
plane
=
plane
MA inclined plane
The inclined plane is a simple machine, consisting of a sloping surface, which has some angle
above or below the horizontal used to raise objects that are too heavy to lift vertically.
Gangways, chutes, and ramps are all examples of the inclined plane.
Switchbacks on mountain roads are also examples of inclined planes that reduce the effort of an
automobile engine but increase the distance a car must travel to ascend the mountain.
R
F
F ⋅ d
1
= R ⋅ d
The inclined plane has been modified in many ways. The screw and wedge are applications
of the principle behind the inclined plane but do not require that the load be moved vertically
for their successful operation.
• The screw consists essentially of a solid cylinder, usually of metal, around which
an inclined plane winds spirally, either clockwise or counterclockwise. It is used
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Simple Machines1.doc
Physics ~ ASC 2005

to fasten one object to another, to lift a heavy object, or to move an object by a
precise amount.
• The wedge shape has a triangular cross-section. It may be used to lever, split, or
tighten.
The Pulley
The pulley is a simple machine, consisting of a wheel that rotates around a stationary axle. The
outer rim of the pulley is grooved to accommodate a rope or chain. Pulleys are used for lifting by
attaching one end of the rope to the object, threading the rope through the pulley (or system of
pulleys), and pulling on the other end of the rope.
A single, fixed pulley just changes the direction of the applied force and make it easier to lift the
load, since a person can pull down on a rope, rather than simply lifting the load. A common
example of a pulley can be found at the top of a flagpole. .
Pulleys reduce the effort needed to lift an object by increasing the distance over which the effort
is applied
Force
Force
F
Load
Load
R
The law of simple machines as applied to pulleys:
d F
d R
R . d R = F . d F
Where d refers to the distance moved, not the diameter of the pulley
So, we can say
R
F
d
=
d
F
R
= MA
pulley
When one continuous cord is used, this ratio reduces to the number of strands holding the
resistant in the pulley system,
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Simple Machines1.doc
Physics ~ ASC 2005

MA pulley = Number of strands holding the resistance
The resistance force (R) is spread equally among the supporting strands.
Therefore, R = n T, where n is the number of strands holding the resistance and T is the tension
in each supporting strand.
The effort force (F) is equal to the tension in each supporting strand , so
R nT
MA pulley
= = = n
F T
The wheel-and-axle
This simple machine is a wheel attached rigidly upon an axle or drum of smaller diameter; the
wheel and the axle have the same axis, so that both can turn together.
The law of simple machines as applied to wheel-and-axle is
r F
where:
R . r R = F . r F
r R
F
R = resistance force
r R = radius of resistance wheel
R
F = effort force
r F = radius of resistance wheel
radius of effort force
MA
wheel−and−axle
= =
=
radius of
resistance
force
r
r
F
R
Examples are the steering wheel of an automobile, the doorknob, the tires and the casters.
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Simple Machines1.doc
Physics ~ ASC 2005