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

W = ∫ F d x = ∫ ax + bx 2 dx = a 2 x 2 0 L + b 3 x 3 0 L = a L 2 2 + b L 3 3

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PhysicsW.E.P.Calculation of workEasy2 minQB

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When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude
F = ax + bx²where a and b are constants. The work done in stretching the unstretched rubber-band by L is :

Options:

Answer:

Solution:

$W = \int F d x$

$= \int (ax + {bx}^{2}) dx$

$= \frac{a}{2} {[x^{2}]}_{0}^{L} + \frac{b}{3} {[x^{3}]}_{0}^{L}$

$= \frac{a L^{2}}{2} + \frac{b L^{3}}{3}$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Calculation of work

⏱ 2mℹ️ Source: QB

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