Pulleys

A pulley is a wheel with a groove along its edge, for holding a rope or cable. Pulleys are usually used in sets designed to
reduce the amount of force needed to lift a load. However, the same amount of work is necessary for the load to reach the

same height as it would without the pulleys. The magnitude of the force is reduced, but it must act through a longer distance.
Pulleys are usually considered one of the simple machines.

Types of Pulleys

a

movable

pulley

a

fixed

pulley

* A fixed pulley has a fixed axle and is used to redirect the force in a rope (called a belt when it goes in a full circle).

- A fixed pulley has a mechanical advantage of 1.

* A movable pulley has a free axle, and is used to transform forces - when stationary the total force on the axle balances the

total force provided by the tension in the rope (which is constant in magnitude in each segment). As illustrated below, if one
end of a rope is attached to a fixed object, pulling on the other end will apply a doubled force to any object attached to the

axle.

- A movable pulley has a mechanical advantage of 2.
With one pulley, the

force you must pull with

is the

same

as the

weight of the object

. In order to raise the object a height of 1

metre, you must pull the rope 1 metre.
This simple setup does have one advantage. You don't have to be

above

the object; you can stand

beside it

to lift it.

Although you have to pull just as hard as without a pulley, being able to pull from the side is more convenient.

compound

pulley

tackle

•

A compound pulley is a system of movable pulleys. The mechanical advantage can be increased by using a block and

tackle, where there are several pulleys on each axle. Plutarch reported that Archimedes moved an entire warship, laden
with men, using compound pulleys and his own strength.

Here is another way that one pulley can be used to lift the object.

The rope is anchored on the ceiling on the right, and passes down

through the pulley, which is connected to the object. The rope then

continues back upwards.

The same 100 newton object is now being supported by two

segments of rope. Each segment of rope only has to support half

the weight ... they share the load.

Half of the load, 50 newtons, is supported by the ceiling.

The other 50 newtons is supported by you, pulling on the far end of

the rope.

You only have to pull half as hard

.

The disadvantages? You have to pull upwards. That isn't very

convenient. And since you only have to work half as hard, you must

pull twice as far! In order to lift the object a height of 1 metre, you

must pull the rope 2 metres.

Here is the same setup as above, with one more pulley.

This extra pulley doesn't make it easier to lift the object.

It is used to reverse the direction of the pull.

Now you can pull downwards, from the side.

This is much more convenient.

If you add more pulleys anchored to the ceiling, you can lessen the
work you have to do, even more. Every time you add another anchor,
you cut the work in half, because you are sharing the load between
two ropes.

In this set up we are supporting the object with an

additional

pulley.

There is still just one rope; it loops its way around each of the

pulleys, sometimes twice.

The rope is still anchored to the ceiling at the right.

It runs down to the lower pulley 1, which as before is supporting the

object. But now it takes a side trip.

It heads

up to pulley 2

, and then back down again.

Then it loops once more around pulley 1, and then heads over to

pulley 3, and down to where you are pulling.

By inserting the extra pulley, we have added two more segments of

rope that are directly supporting the object.

Now the weight of 100 newtons is supported by four rope

segments, and they

share the load

, so each only has to pull with a

force of 25 newtons.

The single segment passing over the final pulley (which, once again,

is there only to reverse the direction of the pull), is the one you pull

on, with a pulling force of just 25 newtons.

You only have to pull one quarter as hard.

Of course, this time you will have to pull the rope 4 metres, in order

to make the object lift 1 metre.

This is the principle used in a

block and tackle

, a device made from

pulleys for lifting or moving heavy objects.

Inclined plane

An inclined plane or a ramp is one of the basic machines. It reduces the force necessary to move a load a certain distance up

by providing a path for the load to move at a low angle to the ground. This lessens the needed force but increases the distance
involved, so that the amount of work stays the same.

Examples are ramps, sloping roads, chisels, hatchets, plows, air hammers, carpenter's planes and wedges. The most canonical
example of an inclined plane is a sloped surface; for example a roadway to bridge a height difference. The inclined plane is

used to reduce the force necessary to overcome the force of gravity when elevating or lowering a heavy object. The ramp

makes it easier to move a physical body vertically by extending the distance traveled horizontally (run) to achieve the desired

elevation change (rise).

In civil engineering the slope or ratio of rise/run is often referred to as a grade or gradient. Others may also call it tilt.

Ramps are used as an alternative for a stairway for wheelchairs, buggies and shopping carts. Ramps may zigzag. There are also

moving ramps.

By changing the angle of the ramp one can usefully vary the force necessary to raise or lower a load. For example:

A wagon trail on a steep hill will often traverse back and forth to reduce the gradient experienced by a team pulling a heavily

loaded wagon. This same techique is used today in modern freeways which travel through steep mountain passes. Some steep
passes have separate truck routes that reduce the grade by winding along a separate path to rejoin the main route after a

particularly steep section is past while smaller automobiles take the straighter steeper route with a resulting savings in time.

It is important in the history of science, engineering and technology for a variety of reasons:

The ramp or inclined plane was useful in building early stone edifices, in roads and aqueducts, and military assault of fortified

positions.

Experiments with inclined planes helped early physicists such as Galileo Galilei quantify the behavior of nature with respect to
gravity, mass, acceleration, etc.

Detailed understanding of inclined planes and their use helped lead to the understanding of how vector quantities such as
forces can be usefully decomposed and manipulated mathematically. This concept of superposition and decomposition is critical

in many modern fields of science, engineering, and technology.

Other simple machines based on the inclined plane include the blade, in which two inclined planes placed back to back allow
the two parts of the cut object to move apart using less force than would be needed to pull them apart in opposite directions.

MECHANICAL ADVANTAGE OF THE INCLINED PLANE

If an object is put on an inclined plane it
will move if the force of friction is smaller

than the combined force of gravity and
normal force. If the angle of the inclined

plane is 90 degrees (rectangle) the object

will free fall.
The term inclined plane is also used for a

funicular.

The wedge

A wedge is a simple machine used to separate two objects, or portions of objects, through the application of force. A wedge is
made up of two inclined planes. These planes meet and form a sharp edge. This edge can split things apart. Wedges are used

as either separating or holding devices. There are two major differences between inclined planes and wedges. First, in use, an
inclined plane remains stationary while the wedge moves. Second, the effort force is applied parallel to the slope of an inclined

plane, while the effort force is applied to the vertical edge (height) of the wedge. Force multiplication varies inversely with the

size of the wedge angle; a sharp wedge ( small inclined angle ) yields a large force.
Wedges are used as either separating or holding devices. A wedge can either be composed of one or two inclined planes. A

double wedge can be thought of as two inclined planes joined together with their sloping surfaces outward.
Examples of wedges are: knives, axes, forks and nails

The wheel and axle is a simple machine.
The wheel and axle consists of a handwheel (a disc or lever arm with a handle) which turns an axle around which a chord is

wound. A heavy weight attached to the chord can be lifted more easily because of mechanical advantage.
The mechanical advantage of a wheel and axle is the ratio of the radius of the wheel to the radius of the axle. If the radius of

the wheel is four times greater than the radius of the axle, every time you turn the wheel once, your force will be multiplied
four times.

Examples of wheel and axles are:

Bicycles, Ferris wheels, gears, wrenches, door-knobs and steering wheels.

The screw

A screw is a specialized application of the wedge or inclined plane. It contains a wedge, wound around an interior cylinder or

shaft, that either fits into a corresponding plane in a nut, or forms a corresponding plane in the wood or metal as it is inserted.
The technical analysis (see also statics, dynamics) to determine the pitch, thread shape or cross section, coefficient of friction

(static and dynamic), and holding power of the screw is very similar to that performed to predict wedge behavior. Wedges are
discussed in the article on simple machines.

Critical applications of screws and bolts will specify a torque that must be applied when tightening. The main concept is to

stretch the bolt, and compress the parts being held together, creating a spring like assembly. The stretch introduced to the bolt

is called a pre-load. When external forces try to separate the parts, the bolt sees no strain unless the pre-load force is exceeded
(this takes some effort to imagine).

As long as the pre-load is never exceeded, the bolt or nut will never come loose (assuming the full strength of the bolt is used).

If the full strength of the bolt is not used (e.g. a steel bolt into aluminum threads) then a thread locking adhesive may be used.

If the pre-load is exceeded during normal use the joint will eventually fail. The pre-load is calculated as a percentage of the

bolt's yield tensile strength, or the strength of the threads it goes into, whichever is less.