Question

what is the input force needed to push a 1580 newton snowmobile up a 2.5 long board into the back of a pick-up truck. the bed of the pickup is 1.10 meters high and the board is 80% efficient?

Answer 1

869 Newtons.

Explanation

What's the gain in Gravitational Potential Energy in this process?

$\displaystyle \Delta \text{PE} = \underbrace{(m\cdot g)}_{1580\;\text N}} \cdot \Delta h = 1580\times 1.10\;\text{m} = 1738\;\text{J}$.

What's the energy input in this process?

The output of the board is the same as the gain in gravitational potential energy, 1738 Joules.

$\displaystyle W_\text{in} = \frac{W_\text{out}}{\text{Efficiency}} = \frac{1738}{0.8} = 2172.5\;\text{J}$.

$F = \dfrac{W_\text{in}}{d}= \dfrac{2172.5}{2.5} = 869\;\text{N}$.