Pulleys

The theoretical mechanical advantage of a system is the ratio of the force that performs the useful work to the force applied, assuming there is no friction in the system.

Velocity ratio is defined as the ratio of the distance moved by effort and load, in the same time interval.

 

The work (W) done by a constant force of magnitude F on a point which undergoes a displacement (s) in a straight line in the direction of the force is

 

One wheel

 

A one wheel pulley allows the direction of force to be changed.

The force required - and work done - remains the same.

 

Pulling down 1m of rope raises the load by 1m.

The velocity ratio is 1.

 

Looking at a loaded pulley

The tension, T, remains the same throughout the string.

 

What happens next depends on the values of M₁ and M₂

If M₁ > M₂

M₁ moves down, causing M₂ to rise.  

This causes downwards acceleration of load M₁
and upwards acceleration of load M₂

and

 

 

If M₂ > M₁

M₂ moves down, causing M₁ to rise.  

This causes downwards acceleration a₂
and upwards acceleration a₁

 

 

Example

Find the downwards acceleration of the block:

Alternatively, from the diagram

 

Two wheels

 

Pulling down 1m of rope raises the load by 0.5m

 

Effort = 1/2 the load!

Youtube example

 

If a pulley system is perfectly efficient the mechanical advantage and the velocity ratio are both equal to the number of pulleys.

Example

Calculate the acceleration of the load and the tension in the system.

 

Three wheels

 

Example

Calculate the acceleration of the moveable pulley and the tension in the rope.

 

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