The tendons in a kangaroo\'s leg weigh 12.6 g, are 15 cm long, and have a densit

Question

The tendons in a kangaroo's leg weigh 12.6 g, are 15 cm long, and have a density of 1.12 g/cm^3. They have a coefficient of resilience of 0.93, meaning that 93% of the stored energy is recovered when the tension is released. Suppose the kangaroo weighs 20 kg, and is dropped from a height of 1 m. Assume that the tendons stretch, and the kangaroo then bounces up again without using its muscles to push off. Due to heating in the tendons the kangaroo will not bounce to the original height of 1 m. Calculate how high the kangaroo will bounce, and also by how much the kangaroo's tendons will stretch. You may assume that all of the heat produced in the tendons is produced during the release spring. (For this calculation just ignore braking action or forces generated by muscles.)

Explanation / Answer

Here, Initial energy = mgh

                                 = 20 * 9.8 * 1

                                  = 196 J

Thus, Final energy = 0.93 * 196 J

=>    0.93 * 196   = 20 * 9.8 * h

=> high kangaroo will bounce , h = 0.93 m

kangaroo tendons will stretch = 15 * (1 + 0.07)

                                                = 16.05 cm

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