Question

A block is constrained to move along x-axis under a force F = 2x+3x2. Here, F is in newton and x is in
meter. The work done by this force when block is displaced from x= 1 m to x=2 m, is :
(1) 105
(2) 15 J
(3) 20 J
(4) 40 J​

Answer 1

Answer:

(2) 15 J

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Answer 2

The work done by this force when block is displaced from x= 1 m to x=2 m is 10 Joules.

Explanation:

Force is given by :

$F = 2x+3x^2$

It is required to find the work done by this force when block is displaced from x= 1 m to x=2 m. Work done is given by :

$W=\int\limits^2_1 {F{\cdot} dx}\\\\W=\int\limits^2_1 {(2x+3x^2){\cdot} dx}\\\\W=x^2+x^3|_1^2$

Using upper and lower limits :

$W=2^2+2^3-(1^2+1^2)=10\ J$

So, the work done by this force when block is displaced from x= 1 m to x=2 m is 10 Joules.

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