Question

A body of mass 2 kg is acted upon by two forces
2 N and 5 N in the direction of i+j and Î-k
respectively. If the body is displaced from
(3,-2, 1) to (-1, 2, 3) (Positions are in m), then
work done is
(1) 105
(3) 15 J
(2) 5/2 J
(4) 20J​

Answer 1

Explanation:

Given A body of mass 2 kg is acted upon by two forces

2 N and 5 N in the direction of i+j and Î-k

respectively. If the body is displaced from

(3,-2, 1) to (-1, 2, 3) (Positions are in m), then

work done is

• We know that F = F1 + F2
•                           = 2 (1/√2 , 1/√2, 0) + 5(0, 1/√2, - 1/√2)
•                      F = (√2 , 7/√2, 5/√2) N
•                      Δ r = (-1,2,3) – (3,- 2, 1) = (- 4, 4, 2) m
•       We know that W = F . Δ r
•                             W = √2. – 4 + 7/√2 4 – 5/√2 .2
•                                  = - 4 √2 + 28 / √2 - 10√2
•                                  = - 8 + 28 – 10 / √2
•                                    = 10 / √2 J
•                                     = 5 x √2 x √2 / √2
•                                    = 5 √2 J