The work done by a force vec{F} = (-6x^3 hat{ | vedclass

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(B) The work done $W$ by a variable force $\vec{F}$ is given by the integral $W = \int_{x_i}^{x_f} F_x \, dx$.Given $\vec{F} = (-6x^3 \hat{i}) \, N$,t

Vedclass · Accepted Answer

$360$

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(B) The work done $W$ by a variable force $\vec{F}$ is given by the integral $W = \int_{x_i}^{x_f} F_x \, dx$.Given $\vec{F} = (-6x^3 \hat{i}) \, N$,the force component is $F_x = -6x^3$.The limits of integration are from $x_i = 4 \, m$ to $x_f = -2 \, m$.$W = \int_{4}^{-2} (-6x^3) \, dx$$W = -6 \left[ \frac{x^4}{4} \right]_{4}^{-2}$$W = -6 \left( \frac{(-2)^4}{4} - \frac{4^4}{4} \right)$$W = -6 \left( \frac{16}{4} - \frac{256}{4} \right)$$W = -6 \left( 4 - 64 \right)$$W = -6 \left( -60 \right) = 360 \, J$.

The work done by a force $\vec{F} = (-6x^3 \hat{i}) \, N$ in displacing a particle from $x = 4 \, m$ to $x = -2 \, m$ is ............... $J$.

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