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?

please explain and answer all 3

Answer 1

1. Total kinetic energy = where i represents different particles.

For the total Kinetic energy to be 0, each particle has to be 0 velocity (As the term of v is in square)

Total momentum = , Since velocity of all the particles is 0 as shown above, the momentum will be 0

So total momentum of the system = 0

2) Force is defined as rate of change of momentum

=>

=>

We know that the initial momentum of bowling ball and ping pong ball ate the same. Since we need to stop both of the, the change in momentum for both is same. Also the Force, F applied on both is same

So the amount of time requied to stop both is same,

3) Initial velocity of railroad as well as cannon = 0

total mass = 1000 kg

mass of cannon ball = 10 kg

velocity of cannonball = 50 m/s ( to left is assumed to be positive)

let the recoil speed of flatcar be v

mass of flatcar = 1000-10 = 990 kg

By conservation of momentum

1000 * 0 = 10*50 + 990*v

=> v = - 500/990 = - 0.505 m/s (negative sign imples the direction is towards right)

So recoil speed of the flat car = 0.505 m/s to right