Question

the ball of mass 5kg experiences a forces f=2x^2+x.work done in displacing the ball by 2m is

Answer 1

Data:
Mass of ball = m = 5 kg
Force = F = 2x² + x
Displacement of the ball = 2 m
Work done = W = ?
Solution:
Since,
Work done = W = ∫(0,2) F dx
(∵ the ball is displaced from 0 to 2 m)
Work done = W = ∫(0,2) (2x² + x) dx
Work done = W = ∫(0,2) 2x² dx + ∫(0,2) x dx
Work done = W = 2. Ιx³/3Ι (0,2) + Ι x²/2 Ι (0,2)
Work done = W = 2 ( 0 - 2³/3 ) + ( 0 - 2²/2 )
Work done = W = 2 ( - 8/3 ) - 4/2
Work done = W = - 16/3 - 2
Work done = W = (-16 - 6) / 3
Work done = W = - 22/3
Work done = W = - 7.3 J
Which is the required answer.
Hopefully it helps.
Thanks.