Question

The inventor of a new machine claims that its actual mechanical advantage is 4. Literature on the machine reports its input distance is 81 meters and its output distance is 27 meters. Find the machine's ideal mechanical advantage, and determine whether the developer's claim could be true.

Answer 1

To solve this we are going to use the formula for ideal mechanical advantage: $IMA= \frac{D_{I} }{D_{O}}$
where 
$IMA$ is the machine mechanical advantage 
$D_{I}$ is the input distance 
$D_{O}$ is the output distance

We know for our problem that $D_{I}=81$ and $D_{O}=27$. Lets replace those values in our formula to find $IMA$:
$IMA= \frac{D_{I} }{D_{O}}$
$IMA= \frac{81}{27}$
$IMA=3$

The ideal machine advantage of the machine is 3. The inventor is claiming that the actual mechanical advantage of the machine is 4. Since the actual mechanical advantage takes into account energy losses, it is always less than the ideal mechanical advantage. We can conclude that the developer's claim is false.