A Princeton prof. (mass = 61.0 kg), surprised by the large stopping force he cal
ID: 1443947 • Letter: A
Question
A Princeton prof. (mass = 61.0 kg), surprised by the large stopping force he calculates for jumping flat footed from a height of 0.13 m, decides to try the experiment. Calculate he deceleration (in g's) if he stops in a distance of 0.50 cm. (Do not try this. You could easily break an ankle!)
Work (=Force times distance along the force) is the energy that has to be spent to exactly counter the kinetic energy gained through the free fall Equate the work done by gravity with the work while decelerating then find the deceleration. The prof. ended up limping for the rest of the week, having tried this from an even smaller height
Explanation / Answer
From work energy theorem, work done is,
F d = (1/2)mv^2
F d = mgh
F = mgh / d
F = 61*9.80*0.13 / 0.005
F = 15.5 *10 ^ 3 N
F = 15.5 kN
acceleration a = F / m = 215.5 *1000 / 61*9.8 = 26 g