Question

1) A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system?

(2) A bowling ball and a Ping-Pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest?

(3) A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kgcannonball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?

Answer 1

1) First remember that the kinetic energy

of a particle i, cannot be negative.

If the total kinetic energy of a system is zero

Like every kinetic energy cannot be negative

  For every particle in the system

Therefore the total momentum

The total momentum of the system of particle is zero

2) By the second Newton's law

for a constant force

In our case the final momentum is zero

Taking only the maginutde of the force

and clearing for t

That is the time that take stop an object with initial momentum p₁ with a constant force F .

In our case the initial momentum of the bowlling ball and the Ping-Pong ball are the same, and so the force to stop it. Therefore the time to stop the two balls is the same.

I could gladly answer the other questions, but you need to repost for each question, specifying the question you want.