21. - Consider a completely elastic head-on collision...

21. - Consider a completely elastic head-on collision between two particles that have the same mass and the same speed. What are the velocities after the collision? A. Both are zero. B. The magnitudes of the velocities are the same, but the directions are reversed. C. One of the particles continues with the same velocity, and the other comes to rest. D. One of the particles continues with the same velocity, and the other reverses direction at twice the speed. E. More information is required to determine the final velocities.

21. - Consider a completely elastic head-on collision between two particles that have the same mass and the same speed. What are the velocities after the collision?
A. Both are zero.
B. The magnitudes of the velocities are the same, but the directions are reversed.
C. One of the particles continues with the same velocity, and the other comes to rest.
D. One of the particles continues with the same velocity, and the other reverses direction at twice the speed.
E. More information is required to determine the final velocities.

Key Concepts

Symmetry in Head-on Collisions

When two particles of equal mass and equal speed collide head-on, the symmetry of the situation often results in the particles exchanging velocities or simply reversing their directions after the collision. This symmetric property simplifies the analysis and is a key insight in understanding collision outcomes.

Elastic Collision

An elastic collision is one in which both momentum and kinetic energy are conserved during the interaction. This means that the total kinetic energy before and after the collision remains the same, allowing the use of both conservation laws to determine the final velocities of the colliding bodies.

Conservation of Momentum

Conservation of momentum is a fundamental principle stating that in a closed system with no external forces, the total momentum remains constant throughout the collision. For head-on collisions, this principle leads to equations that relate the velocities of the particles before and after impact.

Conservation of Kinetic Energy

In an elastic collision, the kinetic energy of the system is conserved. This conservation law provides an additional equation that, along with the conservation of momentum, can be used to uniquely determine the final speeds and directions of the particles involved in the collision.

Transcript

00:01 Hi, for this next question, we have two particles.

00:05 This one particle is another.

00:08 They have the same mass.

00:08 The mass of this is m, m, and the velocity, the same speed also.

00:13 So this, let's call this a u, initial velocity, called this u, meters per second.

00:19 And this one is actually going to be minus u because we're taking the right direction as positive.

00:24 So the left will be negative.

00:25 So this is minus u meters per second.

00:28 And what we want to do is figure out the velocities after collision.

00:32 And this is given as a completely elastic collision.

00:37 So that means that momentum is conserved and kinetic energy is conserved also.

00:42 So for conservation of momentum, let's do conservation of momentum.

00:47 Momentum, b, we go to mv, and the total initial momentum is equal to the total final momentum.

00:57 So what we do is multiply the mass and velocities for collision and add them together and then equate it to the sum of the products of the mass and velocities for each of the objects.

01:08 So for conservation of momentum, before momentum, before collision, we have m, u plus m minus u equal two.

01:20 So let's call the final velocities of this one, v1, it's called this v2.

01:26 Let's figure out what v1 and v2 are.

01:29 So this will be mv1.

01:34 And before we go any further, we can determine the directions of v1 and v2...

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