An object with a mass of #1 kg# is hanging from an axle with a radius of #16 m#. If the wheel attached to the axle has a radius of #64 m#, how much force must be applied to the wheel to keep the object from falling?
This is a moment arm question. It uses the principle that all moment must be equal for 'equilibrium' to exist. The values are determined by the magnitude of force time its moment arm about a point.
Example of 'equalization': Let clockwise be positive and anticlockwise be negative. Then:
The apposing moment to give equilibrium could be:
The sum of moments is 0. If they are not then the system will be in motion.
The moments are:
Axil edge to centre
Wheel edge to centre
Let the unknown load be
Then the system is:
Divide both sides by
However, the question askes for 'Force'. This is quite often presented in the units of 'Newtons'
There are 9.81 Newtons for each Kg
So in Newtons we have
The manipulation of units trick can be very useful if you know the units need in an answer but are not sure how to conduct a calculation.
What you do to the available units to obtain your objective you also do to their related numbers.