Question

A meteor with a mass of 1 kg moving at 20 km/s collides with Jupiter's atmosphere. The meteor penetrates 100 km into the atmosphere and disintegrates. What is the average force on the meteor once it enters Jupiter's atmosphere (Ignore gravity).

*The answer is 2 x 10^3 N but I have no idea why.

Answer 1

They want you to assume that its initial velocity is 20 km/sec, and 100km later, it's undergone a constant deceleration and its velocity is now zero. The problem is that when a meteor disinigrates, it's almost always still moving at a large fraction of its original speed (once it slows to a low speed, the stresses that cause disintigration aren't being created anymore. So to solve the problem *as written*, they'd have to give you the speed at breakup. But assume it's zero even though that never happens. ;)

So figure out the time and deceleration it takes to decelerate from 20km/sec to zero in 100 km. Hint - it's exactly the same formula as "start from zero, accelerate to 20 km/sec and cover 100km, except with an opposite sign. So use v=a*t and d=(1/2)a t^2 to solve for a and t.

You should find that it takes 10 seconds at an average deceleration of 2km/sec/sec. Now you know the mass, and the acceleration, you can compute the newtons.

F = 2 *100 * 10= 2000N = 2 * 10³ N