4. An Olympic high jumper can jump from rest to a height of 1m (This is called s

Question

4. An Olympic high jumper can jump from rest to a height of 1m (This is called standing high jump). I am trying to say that his center of mass is lm higher during the jump than when he is in a normal standing position. His mass is 80kg. The legs of the jumper extend during this jump from a crouched position to total extended position by 1/2 m. Assume that during the phase of the jump when he is straightening his legs that the jumper pushes with a constant force against the ground while the legs straighten. a. What is the kinetic energy at the moment of lift-off, so that he can soar up the lm? b. What is his kinetic energy at the top of the jump? What about energy conservation? c. What is the magnitude of his leg force while he is pushing off (please also include the work needed to lift the center of mass by the extra 1/2m from the crouched position) ?

Explanation / Answer

Height of jump = h = 1 m

mass = m = 80 kg

a) The kinetic energy at the moment of lift-off is same as the potential energy at the top:

so Kinetic energy = potential energy = mgh = 80 kg x 9.8 x 1 = 784 J

b) At the top of jump , the kinetic energy becomes 0. this is due to conservation of energy. the kinetic energy at the surface is converted into potential energy at the top of jump.

c) Using work-kinetic energy theorem ::

Work done = change in kinetic energy

F d = 784 J

F ( 0.5 m) = 784 J

F = 1568 N

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