When a certain rubber band is stretched a distance of x, it exerts a restoring force of magnitude

  1. F = ax + bx2
  2. Where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is
  1. aL2 + bLx3
  2. aL + 2bL2
  3. a + 2bL
  4. bL
  5. aL2/2 + bL3/3


Answer:

The work done in stretching this rubber band from x = 0 to x = L is aL2/2 + bL3/3

Helping Concept:

  1. Work done is given by
  2. \dpi{80} \fn_jvn W = \int_{0}^{L} F dx
  3. \dpi{80} \fn_jvn W = \int_{0}^{L}(ax + bx^{2})dx
  4. \dpi{80} \fn_jvn W = \int_{O}^{L}(ax)dx + \int_{0}^{L}(bx^{2})dx
  5. \dpi{80} \fn_jvn W = a\left | \frac{x^{2}}{2} \right |_{0}^{L} + b\left | \frac{x^{3}}{3} \right |_{0}^{L}
  6. Substituting upper and lower limits
  7. \dpi{80} \fn_jvn W = \frac{aL^{2}}{2} + \frac{bL^{3}}{3}

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