# What is the speed of the lighter fragment?

1. Mar 30, 2009

### dherm56

1. The problem statement, all variables and given/known data

A projectile of mass M is moving in the -x direction with speed V when it explodes into two fragments: a lighter one having mass M/4 and a heavier one having mass 3M/4. The heavier fragment moves in the -y direction with speed V.

1) What is the speed of the lighter fragment? (Assume there are no external forces acting on the system).

V
2V
3V
4V
5V

A box of mass M initially sliding on a frictionless horizontal surface collides and sticks to a second box of mass 2M which is initially at rest.

2) What is the ratio of the initial kinetic energy before the collision to the final kinetic energy of the system after the collision?

1
2
3

3) A cart of mass M and a second cart of mass 2M collide head on elastically and bounce apart. Which cart experiences a larger magnitude of acceleration during the collision?

The more massive cart.
The less massive cart.
(Both carts experience the same acceleration)

4) Rain falls vertically into an open boxcar coasting freely on a horizontal frictionless track. As a result the momentum of the system consisting of the boxcar plus accumulated water increases.

True
False

5) In any collision between one object initially moving with velocity vector v1 and another object initially moving with velocity vector v2, the vector (v1 + v2) must be conserved, since momentum is conserved during the collision and the total mass of the system is also conserved.

True
False

6) It is not possible for a system to lose all of its kinetic energy in a collision.

True
False

2. Relevant equations

conservation of momentum, mv=mv

3. The attempt at a solution

1) MV= (m/4)v + 3Mv2. It only wants the lighter particle so MV=(m/4)v. so velocity = 4

2) mv1i = (3m)v2 but it asks for a ratio, momentum is conserved therefore, therefore the ratio is 1:1

3) The less massive cart experiences the larger magnitude. I imagined a golf ball being hit by a bowling like a demo I saw in lecture. The golf ball went further when the bowling struck it as compared to the golf ball hitting the bowling ball with the same velocity.

4) False, the momentum is conserved. As more rain accumulates, the mass increases while velocity decreases.

5) False, the vectors can be in opposite directions

6) False, imagine a cue ball transferring all of its KE to another upon a near perfact elastic collision