Question

A ball of mass 5 kg experiences a force of 2x2 +x work done by the ball to displace 2m is

Answer 1

GiveN :

• Mass of ball (m) = 5 kg
• Force (F) = 2x² + x
• Ball is displaced from 0m to 2m

To FinD :

• Work Done by ball to displaced

SolutioN :

As we know that,

$\longrightarrow \boxed{\sf{W\ =\ \int F .dx}}$

Where,

• F is Force
• W is work done
• dx is the displacement
• And limit lies between 0 to 2

$\displaystyle \longrightarrow \sf{W\ =\ \int _0 ^2 (2x^2 \: + \: x)dx} \\ \\ \longrightarrow \sf{W \: = \: \bigg[ \dfrac{2x^3}{3} \: + \: \dfrac{x^2}{2} \bigg]_0 ^2 } \\ \\ \longrightarrow \sf{W \: = \: \bigg[ \bigg( \dfrac{2 \: \times \: 2^3}{3} \bigg) \: + \: \bigg( \dfrac{2^2}{2} \bigg) \bigg] \: - \: \bigg[ \dfrac{2 \: \times \: 0^3}{3} \: + \: \dfrac{0^2}{2} \bigg] } \\ \\ \longrightarrow \sf{W \: = \: \bigg( \dfrac{2 \: \times \: 8}{3} \: + \: \dfrac{4}{2} \bigg) - \: 0 } \\ \\ \longrightarrow \sf{W \: = \: \dfrac{16}{3} \: + \: 2} \\ \\ \longrightarrow \sf{W \: = \: \dfrac{16 \: + \: 6}{3}} \\ \\ \longrightarrow \sf{W \: = \: \dfrac{22}{3}} \\ \\ \underline{\sf{\therefore \: Work\ done\ by\ ball\ is\ \dfrac{22}{3}\ J}}$