Simple Machines
WHEEL AND AXLE
PULLEYS
The Wheel and Axle
The wheel and axle is another type of simple machine
that moves objects across distances.
Wheels help move objects along the ground by
decreasing the amount of friction between what is
being moved and the surface.
The work of this simple machine can result from the
larger wheel being utilized to turn a smaller axle
wheel.
The bigger the wheel, the greater the twisting force
(torque) that can be applied to the axle.
The Wheel and Axle
Work can also result when an axle is used to rotate wheels, such as the example of a rear axle
and wheels of a truck.
The effort (force) is applied to the axle at a point close to where the axle turns.
This can be equated as the effort (force) distance.
When effort (force) is applied to the axle, the mechanical advantage will be less than one but
the speed is enhanced.
The distance between the point where the wheel touches the ground and the point where the
wheel turns can be called the resistance force (load) distance.
These two distances are equal to the radius of the axle and the radius of the wheel, respectively.
The Wheel and Axle
To calculate the mechanical
advantage of a wheel and axle
assembly divide the radius of the
wheel by the radius of the axle.
Example: What is the mechanical
advantage provided by a car's
steering wheel assembly when
the radius of the steering wheel
is 6 inches and the radius of the
axle is 1 inch?
The Wheel and Axle
Effort (force) is being applied to the steering wheel and therefore
multiplied, providing torque on the axle six times greater than the
effort (force) applied to the wheel.
The trade-off, however, is that the steering wheel travels six times
farther than the axle does during one full rotation.
Use the formula below to calculate the amount of effort (force)
required when using this simple machine.
Effort × Circumference = Resistance Force × Circumference
(Force) × (Wheel) = (Load) × (Axle)
In the drawing below of a well crank (windlass), the handle is attached
to a 2-inch radius axle. The turning circumference of the crank is 16
inches. How much effort (force) is required to lift a bucket of water
weighing 40 pounds?
The Pulley
A pulley can be considered as a circular lever.
◦ It is a wheel with a grooved rim and axle with a rope, belt,
or chain attached to it in order to change the direction of
the pull and lift a load.
Mechanical advantage for pulley systems
can be found using the following formulas:
The effort (force) distance is the radius of the pulley
(length from the axle to the side of the rope being
pulled).
The resistance force (load) distance is the radius of the
pulley from the axle to the load-carrying side of the
rope.
Pulleys are used to lift heavy loads and can be found in
block and tackles, cranes, hydraulic systems, and chain
hoists.
They change the direction of effort (force) making it
easier to lift the object or they enhance the effort
(force).
Or
Types of Pulleys
There are three types of pulleys:
fixed
moveable
compound
The mechanical advantage of pulley systems depends on the number
of ropes, chains, etc. supporting the load.
For example, using two supporting ropes to lift a resistance force
(load) of 40 pounds would give you a mechanical advantage of 2.
Fixed (Single)Pulley
A fixed (single) pulley is attached to a stationary object like a
wall or ceiling.
It acts as a first-class lever having the fulcrum at the axis and
the rope acting as the bar.
Fixed (single) pulleys only change effort (force) direction
(you can pull down on the rope to lift the load instead of
pushing up on it).
They do not enhance the effort (force).
◦ Effort (force) distance equals resistance force (load) distance
and, therefore, each foot of pull on the rope will lift the load one
foot.
It provides no mechanical advantage (MA = 1).
◦ Example: The fixed (single) pulley has a resistance force (load) at
one end of the rope. The other end must have effort (force)
applied downward to raise the load. The effort (force) is equal to
the load in this pulley system and there is no mechanical
advantage, with the MA equal to 1.
Movable Pulley
A movable pulley moves up and down with the effort (force).
It acts as a second-class lever having the resistance force
(load) between the fulcrum and the effort (force).
Unlike the fixed (single) pulley, it cannot change the direction
of the effort (force).
Moveable pulleys, however, enhance effort (force). Their
mechanical advantage is greater than 1.
The trade-off is that the effort (force) distance is greater than
the resistance force (load) distance.
The moveable pulley has the resistance force (load)
supported by both the rope ends (the rope end attached to
the upper bar and the rope end to be pulled effort [force] in
the upward direction).
The two upward tensions are equal and opposite in direction
to the load. The mechanical advantage is 2.
Compound Pulley
A compound pulley utilizes both a fixed (single) pulley and a movable
pulley.
Compound pulleys provide both a change in the direction of the effort
(force) as well as dramatically decreasing the effort (force) required to
lift the resistance force (load).
The mechanical advantage of this type of pulley is 2. The effort (force)
distance, however, like with the moveable pulley, will be greater than
the resistance force (load) distance.
Note: The mechanical advantage of pulley systems can also be
calculated visually by counting the number of ropes, chains, etc.
supporting the load.
For example, in the illustration of the compound pulley, there are two
supporting ropes to lift the resistance force (load), giving the pulley
system a mechanical advantage of 2.
Compound Pulley
Block and Tackle
A T of several fixed and moveable pulleys
is known as a block and tackle.
Archimedes showed that by using multiple
pulleys, a large ship fully loaded with men
could be pulled by a single man's effort.
Efficiency of a Pulley System
1. To calculate the efficiency of a
pulley system, first determine the
mechanical advantage.
2. Next, determine the velocity ratio
by dividing the distance moved by
effort (force) by the distance moved
by the resistance force (load).
3. Finally, divide the mechanical
advantage by the velocity ratio and
multiply this number by 100
percent.
Example:
A pulley system can lift an object weighing 50 N
with an effort (force) of 10 N.
The input distance is 5 m and the output
distance is 0.5 m.
What is the efficiency of the pulley system?