In one of his more flamboyant moments, Galileo wrote “Who does not know that a h

Question

In one of his more flamboyant moments, Galileo wrote “Who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height or a cat from a height of eight or ten cubits will suffer no injury? Equally harmless would be the fall of a grasshopper from a tower or the fall of an ant from the distance of the moon.” Find the speed of an ant that falls to earth from the distance of the moon at the moment when it is about to enter the atmosphere. Assume it is released from a point that is not actually near the moon, so the moon’s gravity is negligible. You will need the result of example 9 on p. 333.

Show your work!**

Example 9: Gravitational potential energy example 9 We have already found the equation PE = Fy for the gravitational potential energy when the change in height is not enough to cause a significant change in the gravitational force F. What if the change in height is enough so that this assumption is no longer valid? Use the equation W = GMm(1/r2 1/r1) derived in section 13.4 to find the potential energy, using r = as a reference point. The potential energy equals minus the work that would have to be done to bring the object from r1 = to r = r2, which is PE = GMm r . This is simpler than the equation for the work, which is an example of why it is advantageous to record an equation for potential energy relative to some reference point, rather than an equation for work.

Explanation / Answer

V=(2*G*Me/R)0.5

= 11160.355 m/sec

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