## Using Pulleys to Change the Size and Direction of a Force

At its simplest, a pulley can be using to lift something up by pulling down on a piece of string.

The massabove will be pulled up if

We can modify the contraption by adding more rollers to reduce the forceneeded to pull the mass up. This will reduce the force needed because the tension in each section of the rope isso if the mass is pulled up by n sections of rope, we only need

In the diagram above the masswill be pulled up if

We can change the direction of the force in more subtle ways, to be directed at any angle of our choosing.

The diagram above shows a three pulley system with a block connected directly to two pulleys and indirectly to a third. The tension in the string isResolving horizontally for the force on pulley 1 due to the tension in the string gives

Resolving vertically for the force on pulley 1 gives

The force on pulley 1 dues to the tensions is then

Resolving horizontally for the force on the block:

Resolving vertically for the force on the block:

The resultant force then makes an anglewith the horizontal.

The magnitude of the resultant force is

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