Finding speed of particle after collision

In summary, the speed of a particle after a collision can be calculated using the conservation of momentum and the conservation of kinetic energy equations. The speed of a particle can increase after a collision if the collision is inelastic. Factors such as mass, initial velocity, and type of collision can affect the final velocity. The angle of collision also plays a role and can be calculated using the law of cosines. There is a difference in calculating the final velocity for a head-on collision and an oblique collision.
  • #1
StaryNight
1
0
I'm having problem with the following special relativity question:

An object with energy E and momentum p collides with a mass m at rest and coalesces with it to form a single body without loss of energy. Show that the speed of the composite body is p/(m+E/c^2).

I've tried using the mass-energy invariant but can't seem to derive the above. Any help would be much appreciated.
 
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  • #2
Have you tried momentum and energy conservation?
 

1. How do you calculate the speed of a particle after a collision?

The speed of a particle after a collision can be calculated using the conservation of momentum and the conservation of kinetic energy equations. The formula is: v = (m1u1 + m2u2) / (m1 + m2), where v is the final velocity, m1 and m2 are the masses of the colliding particles, and u1 and u2 are the initial velocities.

2. Can the speed of a particle increase after a collision?

Yes, the speed of a particle can increase after a collision. This can happen if the collision is inelastic, meaning that some of the kinetic energy is lost during the collision. In this case, the final velocity will be lower than the initial velocity, but still higher than the velocity of either particle before the collision.

3. What factors can affect the speed of a particle after a collision?

The speed of a particle after a collision can be affected by the masses of the colliding particles, the initial velocities of the particles, and the type of collision (elastic or inelastic). Other factors such as external forces or friction may also play a role in the final velocity.

4. How does the angle of collision affect the speed of a particle after a collision?

The angle of collision can affect the speed of a particle after a collision. If two particles collide at an angle, the final velocity will not only depend on the initial velocities and masses, but also on the angle of collision. This can be calculated using the law of cosines.

5. Is there a difference in calculating the speed of a particle after a head-on collision and an oblique collision?

Yes, there is a difference in calculating the speed of a particle after a head-on collision and an oblique collision. In a head-on collision, the angle of collision is 180 degrees, so the final velocity can be calculated using the conservation of momentum equation. In an oblique collision, the angle of collision is not 180 degrees, so the law of cosines must be used to calculate the final velocity.

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