Question

You push a heavy crate out of a carpeted room and down a hallway with a waxed linoleum floor. While pushing the crate 2.3mout of the room you exert a force of 30N; while pushing it 8mdown the hallway you exert a force of 15N. How much work do you do in all?

Short answer

The total work done after pushing the heavy crate is W = 189 N - m

Step-by-step solution

Definition of Work

The work is a unit of measurement for the amount of energy transferred when an object is moved over a distance or displaced by an external force.

Explanation of given question

The magnitude of the force changes here, hence we could not determine the work done for a constant force. Therefore, the total work done equals the summation of the work done for each path and it will be given by

$W=\sum F-∆r$

Determine total work done after pushing heavy crate

They gave two paths in the question, hence the total work done in equation (1) will be calculated by

$\begin{array}{rcl}W& =& \sum Fr\\ & =& \left(30N\right)\left(2.3m\right)+\left(15N\right)\left(8m\right)\\ & =& 189N-m\end{array}$

Therefore, Total work done after pushing the heavy crate is W = 189 N - m