# An object with a mass of #24 kg# is hanging from an axle with a radius of #16 m#. If the wheel attached to the axle has a radius of #48 m#, how much force must be applied to the wheel to keep the object from falling?

##### 2 Answers

The force is

#### Explanation:

The load is

The radius of the axle is

The radius of the wheel is

The effort is

The acceleration due to gravity is

Taking moments about the center of the axle

The force is

#### Explanation:

Did you know that units of measurement can be manipulated in the same way that numbers can. If you are ever not sure what to do with the numbers look at what you have to do to the units to give you your target.

The mass of 24 kg converted to downward force in Newtons is:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Presenting opposing forces about the shaft centre line of the shaft as if it is a fulcrum we have:

If this condition is not 'in equilibrium' (all balanced out) then the system would be in motion.

Taking moments about the fulcrum

But force is measure in Newtons by changing the units of measurement we have:

Divide both sides by

But