How Is Momentum Conserved in a Glider Collision?

[paulsberardi]

Homework Statement

Gliders C and D, of masses 2kg and 4kg, respectively, collide on a frictionless track. Glider C initially moves to the right with a speed of .6 m/s relative to the track, while glider D is at rest. After the collision, glider C moves to the left with a speed of .2 m/s. System S consists of gliders C and D.

Homework Equations

What is the magnitudes and directions of the momentum vectors for glider C, glider D, and system S before and after the collision?

Is the momentum of system S before the collision the same as it is after the collision? Explain.

The Attempt at a Solution

I was able to find the momentum of glider C before and after the collision using p=mv. I also knew glider D would not have a momentum vector before the collision because it is at rest.

I could not find the momentum of glider D after the collision or the momentum vectors of system S.

 

[Kurdt]

You know momwntum is a conserved quantity. Therefore the momentum before should equal the momentum afterwards.

 

[kerimek]

I can provide a response to this problem by stating that the law of conservation of momentum applies in this scenario. Before the collision, the total momentum of the system (gliders C and D) is equal to the momentum of glider C, which is moving to the right with a speed of 0.6 m/s. This can be represented by the equation p = mC * vC, where mC is the mass of glider C and vC is its velocity.

After the collision, the total momentum of the system is still conserved, but now it is split between the two gliders. Glider C now has a momentum vector to the left with a magnitude of 0.2 m/s, while glider D has a momentum vector to the right with a magnitude of 0.4 m/s. This can be represented by the equation p = mC * vC + mD * vD, where mD is the mass of glider D and vD is its velocity.

Therefore, the total momentum of system S before the collision (0.6 kgm/s) is equal to the total momentum after the collision (0.6 kgm/s). This shows that momentum is conserved in this system, as expected. The direction of the momentum vectors for glider C and D also changed after the collision, as expected according to the law of conservation of momentum.

In terms of the homework question regarding the magnitudes and directions of the momentum vectors, I have provided the calculations and explanations above. Additionally, I have also shown that the momentum of system S is the same before and after the collision, as expected according to the law of conservation of momentum.

In conclusion, the law of conservation of momentum can be applied to this glider collision problem, and the momentum vectors for gliders C and D can be calculated using the equation p = mv. The momentum of system S is conserved, and the direction of the momentum vectors can change after the collision.