Question

F=3x^2-2x+1 In this region an object is displaced from
x =20cm to x,=40cm by the given force. Calculate
the amount of workdone.​

Answer 1

Answer:

$\bullet \: Force \: (F) = 3x^2 - 2x + 1$

Work Done by the variable force is given by :

$=> \displaystyle W = \int\limits_{x_B}^{x_A} F \, dx$

$=> \displaystyle W = \int\limits_{20}^{40} ( {3x}^{2} - 2x + 1) \, dx$

$=> \displaystyle W = \Bigg[\dfrac{3x^{2 + 1}}{2 + 1} -\dfrac{2x^{1+ 1}}{1 + 1} + 1x\Bigg]^{40}_{20}$

$=> \displaystyle W = \Bigg[\dfrac{3x^{3}}{3} -\dfrac{2x^{2}}{2} + 1x\Bigg]^{40}_{20}$

$=> \displaystyle W = \Bigg[x^{3}-x^{2} + 1x\Bigg]^{40}_{20}$

$=> \displaystyle W = \Bigg[(40)^{3}-(40)^{2} + 40\Bigg] - \Bigg[(20)^{3}-(20)^{2} + 20\Bigg]$

$=> \displaystyle W = \Bigg[64000-1600 + 40\Bigg] - \Bigg[8000-400 + 20\Bigg]$

$=> \displaystyle W = 62440- 7620$

$=> \displaystyle \underline{ \boxed{ W = 54,820 \: J }}$