An elastic bungee cord can be modeled as an ideal spring with spring constant

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

k=150\,\text{N}\,\text{m}^{-1}

. The unstretched length of the cord is defined as

\Delta x=0

. A

70\,\text{kg}

jumper steps off a platform and, at the lowest point of the jump, the cord is stretched downward by

1.80\,\text{m}

. Air resistance is negligible. (a) Calculate the elastic potential energy stored in the cord when it is stretched by

1.80\,\text{m}

. (b) On the axes below, sketch a graph of the cord’s elastic potential energy

U

(vertical axis) versus stretch

\Delta x

(horizontal axis) for

0 \le \Delta x \le 2.0\,\text{m}

. Label the value of

U

\Delta x=1.80\,\text{m}

calculated in part (a). (Provide a clear verbal description of your sketch in your response.) (c) Using your graph, determine the additional amount of elastic potential energy stored as the stretch increases from

1.40\,\text{m}

1.80\,\text{m}

. Show how the graphical representation supports your numerical result.

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