Question

Variable force F= 4x^2+8x+2 displace an object from x= 2m to x=4m. Calculate the amount of work done.

Answer 1

Answer: 126.67 J

Explanation:see attachment..

Answer 2

The amount of work done is 126.6 J.

Explanation:

Given that,

Force $F=4x^2+8x+2$

We need to calculate the work done

Using formula of work done

$dW= F(x) dx$

Put the value into the formula

$dW=(4x^2+8x+2)dx$

On integration w.r.t x

$\int_{0}^{W}{dW}=\int_{2}^{4}{(4x^2+8x+2)dx}$

$W=(4\dfrac{x^3}{3}+8\dfrac{x^2}{2}+2x)_{2}^{4}$

$W=4\times\dfrac{4^3}{3}+8\times\dfrac{4^2}{2}+2\times4-4\times\dfrac{2^3}{3}-8\times\dfrac{2^2}{2}-2\times2$

$W=126.6\ J$

Hence, The amount of work done is 126.6 J.

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Topic : work done

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