Question

An electric scooter has a battery capable of supplying $\mathbf{120}\mathbf{}\mathbf{}\mathit{w}\mathit{h}$ of energy. If friction forces and other losses account for$\mathbf{60}\mathbf{.}\mathbf{0}\mathbf{\%}$ of the energy usage, what altitude change can a rider achieve when driving in hilly terrain if the rider and scooter have a combined weight of $\mathbf{890}\mathbf{}\mathbf{}\mathit{N}$?

Short answer

The altitude change can a rider achieve when driving in hilly terrain if the rider and scooter have a combined weight of$890N$ is $\Delta y=194m$.

Step-by-step solution

Defining the energy formula

The energy E is defined as

$E=F\Delta y$

where

$E=$Energy transfer

$\Delta y=$Change in altitude

$F=$Normal force.

Determining the altitude

From step (1) the useful output energy is

$$\begin{gathered} E=mg\left(y_f-y_i\right) \\ =F\Delta y\left(\because F=mg\right) \\ \Delta y=\frac{120W\left(3600s\right)0.40}{890N}\left(\frac{J}{W.s}\right)\left(\frac{N.m}{J}\right) \\ \Delta y=194m \end{gathered}$$

Thus, the altitude change can a rider achieve when driving in hilly terrain if the rider and scooter have a combined weight of$890N$ is $\Delta y=194m$.