Question

Five ramps lead from the ground to the second floor of a workshop, as sketched below. All five ramps have the same height; ramps B, C, D and E have the same length; ramp A is longer than the other four. You need to push a heavy cart up to the second floor and you may choose any one of the five ramps.Assuming no frictional forces on the cart, which ramp would require you to do the least work?

Answer 1

The mechanical advantage of ramp A is greater than others and it will require the least force to move the load to greater distance.

• Let the height of the ramp = h
• Let the length of ramp B, C, D and E = L
• Let the length of the ramp A = 2L

The mechanical advantage of the ramp is calculated as follows;

$M.A = \frac{L}{h}$

The mechanical advantage of the ramp B, C, D and E is calculated as;

$M.A = \frac{L}{h}$

The mechanical advantage of the ramp A is calculated as follows;

$M.A = \frac{2L}{h} \\\\M.A = 2(\frac{L}{h} )$

Since the length of the ramp A is greater than other ramps, the mechanical advantage will be greater and it will require the least force to move the load to greater distance.

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