Question

Work

The force $\mathbf{F}=4\mathbf{i}-7\mathbf{j}$moves an object $4$ft along the x-axis in the positive direction. Find the work done if the unit of force is the pound.

Short answer

Work done is $W=16\text{ftlb}$

Step-by-step solution

Step 1. Given information

A force is given as $\mathbf{F}=4\mathbf{i}-7\mathbf{j}$ and displacement of body is 4

Step 2. Concept used

The work done by a force in moving an object in the direction of displacement is

$W=F·d$

Where

$F$is the force applied, d is the displacement in the direction of force

Apply the dot product formula of work done which is the dot product of force and displacement.

Step 3. Calculation

Apply formula and simplify,

$\begin{array}{l}W=F.d\\ W=(4i-5j).4i\\ i.i=1\\ i.j=0\\ W=16i^2\\ W=16\text{ftlb}\end{array}$