Question 176: Work, Energy and Power & Circular Motion

Question

When a rubber-band is stretched by a distance $x$, it exerts restoring force of magnitude $F = ax + b{x^2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is :

Accepted Answer

Given Restoring force, F = ax + bx
2
Work done in stretching the rubber-band by a distance $dx$ is
$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,dW = F\,dx = \left( {ax + b{x^2}} \right)dx$
Intergrating both sides,
$W = \int\limits_0^L {axdx + \int\limits_0^L {b{x^2}dx}}$
= $\left[ {a{{{x^2}} \over 2} + b{{{x^3}} \over 3}} \right]_0^L$
= ${{a{L^2}} \over 2} + {{b{L^3}} \over 3}$

Answer

$a{L^2} + b{L^3}$

Answer

${1 \over 2}\left( {a{L^2} + b{L^3}} \right)$

Answer

${{a{L^2}} \over 2} + {{b{L^3}} \over 3}$

Answer

${1 \over 2}\left( {{{a{L^2}} \over 2} + {{b{L^3}} \over 3}} \right)$

Work, Energy and Power & Circular Motion

When a rubber-band is stretched by a distance x, it exerts restoring force of magnitude F = ax + b{x^2} where a and b are constants. The work done in stretching the unstretched rubber-band by L is :

Choose the correct answer: