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.

Question

Gwendolyn Francis

Physics

3 July, 03:26

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.

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Huerta · 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