Do These Solutions Accurately Solve Basic Momentum Problems?

[justagirl]

Hey, just want to double check on these:

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.

- I said true - since there is no friction, velocity would not decrease. However, mass increases and momentum increases.

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.

I said false, since the more massive cart would influence the final direction and change the initial vector.

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

- I said it's V, since it has to balance out the initial momentum.

Are those right??

Thanks!

 

[vsage]

1. Not sure if I agree quite yet. It is hard for me to imagine the boxcar would be moving at the same velocity if many times its weight in raindrops fell into the cart. Additionally, the nature of fluids is to move in a way that is not uniform so the momentum of particles jostling around tends to cancel the momentum of other particles.
2. You're right I think. Conservation of Momentum is sort of a "weighted average" of all the bodies involved.
3. Since the system was originally moving at the speed V on the +x direction and 0 in the +y direction, the y momentums must cancel after the projectile explodes.

 

[pmrazavi]

Hey, just want to double check on these:

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.

ONE OF THE PHYSICS LAW, CONSERVATION OF MOMENTUM:

Momentum in a system is always conserved: m1v1i+m2v2I=m1v1f+m2v2f

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.

No, not necessarily. B/c we have conservation of MOMENTUM, it means that sum of the products of mass and velocity in a system, containing any number of objects, is constant. Algebraically, it doesn't mean that the sum of the velocities are constant too.

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

The speed is 5V.
Notice that momentum is a vector quantity, not scalar. It means that you should take the directions (and angles) of the velocities into account.
For solving this question, you should write 2 equations, one for x direction and one for y direction, and solve them individually, than find the whole magnitude ( (a^2+b^2) ^ (1/2) )