A2 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.

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

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