Question

Two asteroids bump in space. The larger one has a mass of 3000 kg and the smaller one has a mass of 100 kg. f the force of the collision is 10,000 newtons on each asteroid, what are their accelerations?

Answer 1

The larger one accelerates at `3.33 m/s^2` and the other accelerates at `100 m/s^2`

Explanation:

The acceleration is obtained thru use of Newton's 2nd Law:
`F = m*a`.
Rearranging this to yield acceleration gives us:
`a = F/m`

Each asteroid experiences a force of 10,000 N. Note, the Newton was defined to be equivalent to `(kg*m)/s^2`.

The 3000 kg asteroid:
`a = F/m = (10,000 N)/(3000 kg) = 3.33 ((kg*m)/s^2)/(kg) = 3.33 m/s^2`

The 100 kg asteroid:
`a = F/m = (10,000 N)/(100 kg) = 100 ((kg*m)/s^2)/(kg) = 100 m/s^2`

Since acceleration is a vector and since the 2 accelerations will be in opposite directions, one of them needs to be negative. Either could be negative depending on assignment of a reference system. The larger one would probably insist on saying his direction is positive, so the smaller asteroid's acceleration would be negative.

I hope this helps,
Steve