Answer:
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:
[tex]IMA=\frac{d_i}{d_o}[/tex]
where [tex]d_i[/tex] is the distance of the input force while [tex]d_o[/tex] 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
[tex]AMA=\frac{F_o}{F_i}[/tex]
where [tex]F_o[/tex] is the output force and [tex]F_i[/tex] 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:
[tex]W_i = W_o\\F_i d_i = F_o d_o[/tex]
Re-arranging this equation, we get
[tex]\frac{d_i}{d_o} = \frac{F_o}{F_i}[/tex]
which is equivalent to
[tex]IMA=AMA[/tex]
So, the AMA is equal to the IMA for a frictionless machine.
