Question

Calculating Work

Find the work done by the force F in moving an object from $P$to $Q$

$\mathbf{F}=4\mathbf{i}-5\mathbf{j};P(0,0),Q(3,8)$

Short answer

The work done by force is $-28$

Step-by-step solution

Step 1. Given information

Vectors are given as-

$\text{F}=4\text{i}-5\text{j};P(0,0),Q(3,8)$

Step 2. Concept used

Scalar product or Dot product:

$a·b=\left|a\right|\left|b\right|\cos \theta$

The work W done by a force F in moving along a vector D is-

$W=F·D$

Use formula to find the work done.

Step 3. Calculation

Distance D form P to Q is given by,

$\begin{array}{l}D=⟨Q-P⟩\\ D=⟨3-0,8-0⟩\\ =⟨3,8⟩\\ W=F\cdot D\\ W=⟨4,-5⟩\cdot ⟨3,8⟩\\ =12-40\\ =-28\end{array}$