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Question

A particle moves from a point r1=2^i+3^j(m) to another point r2=3^i+2^j(m) during which a certain force F=5^i+5^j acts on it. Find the work done by the force on the particle during the displacement.

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Solution

r1 = 2^i + 3^j (m)

r2 = 3^i + 2^j (m)

Particle moves from position 1 to position 2 whose position vectors are given above we know displacement is change in position.

s = r2 r1

= (3^i + 2^j) (2^i + 3^j)

s = ^i . ^j

Also F = 5^i + 5^j (N)

w = F . s

= (5^i + 5^j) . (^i ^j)

W = 5 - 5 = 0 Joules


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