Question

A 2 kg object is given a displacement ∆~s = (5 m)ˆı + (3 m) ˆ + (−4 m) ˆk along a straight line. During the displacement, a constant force of F~ = (3 N)ˆı + (−1 N) ˆ + (7 N) ˆk acts on the object. Find the work done by F~ for this displacement.

Answer 1

Answer: 15Nm

Explanation:

Work is said to be done when a force cause a body to move through a distance. Mathematically,

Work = Force (F) × distance (s)

If F = F~ = (3 N)ˆı + (−1 N) ˆj + (7 N) ˆk

S = (5 m)ˆı + (3 m) ˆ + (−4 m) ˆk

According to vector notation,

i.I = j.j =k.k = 1

Multiplication of different component will give 'zero'

F×s = (3 N)ˆi × (5 m)ˆı

Work done = 15Nm