Q. A position dependent force `F= 7-2x + 3x^2 N`acts on a small body of mass 2 kg and displaces it from `x=0 ` to `x=5 m.`The work done by this force on the body is (in Joules) :- A) 70 B) 270 C) 35 D) 135

Expert Answers

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By definition the work done by a constant force F acting on a body that have a displacement is

W = F*R 

where F and R are vectors and * is the scalar product.

In the text the force is variable with the displacement x therefore the infinitesimal work done is (assuming the force acts along the x axis):

`dW = F*dx = (7 -2x +3x^2)*dx`

the total work of force F between x =0 m and x= 5 m is

`W = int_0^5F(x)*dx =int_0^5(7-2x +3x^2)*dx =`

`=(x^3 -x^2 +7x) "(taken from 0 to 5)" =`

`=5^3 -5^2 +7*5 = 135 J`

The correct answer choice is D) 135

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