Question

Calculating Work

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

$\mathbf{F}=-4\mathbf{i}+20\mathbf{j};P(0,10),Q(5,25)$

Short answer

The work done by force is $280$

Step-by-step solution

Step 1. Given information

Vectors are given as-

$\mathbf{F}=-4\mathbf{i}+20\mathbf{j};P(0,10),Q(5,25)$

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,

$\begin{array}{l}D=⟨5-0,25-10⟩\\ =⟨5,15⟩\\ W=F\cdot D\\ =⟨-4,20⟩\cdot ⟨5,15⟩\\ =(-4)\times 5+20\times 15\\ =-20+300\\ =280\end{array}$