If a simple machine could be frictionless, how would its ima and ama compare?

They would be equal

Explanation:

The IMA (Ideal Mechanical Advantage) of a machine is equal to the maximum mechanical advantage of a machine, and it is given by:

where is the distance of the input force while is the distance of the output force.

The AMA (Actual Mechanical Advantage) is equal to the mechanical advantage of the machine when including energy lost due to friction, and it is given by

where is the output force and the input force.

In a simple machine which is frictionless, as in this problem, there is no loss of energy, so the work in input is equal to the work in output:

Re-arranging this equation, we get

which is equivalent to

So, the AMA is equal to the IMA for a frictionless machine.

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