DD.2.3 1D Elastic Collision Velocities in CM Frame

TL;DR

In the center of mass reference frame, the velocities of objects remain constant during elastic collisions.

Transcript

Let's examine the velocities of objects in the center of mass reference frame. So we have object 1 and object 2. And we have CM. And we have r1 prime. And we have r2 prime. And recall that we found that the position vector, r1 prime, was equal to the reduced mass over mu m1 times the relative position to r1, 2. I'll draw that up here, r1, 2 from 2 ... Read More

Key Insights

• 💆 The positions of objects in the center of mass frame can be expressed using reduced mass and relative positions.
• 🤘 The velocities of objects in the center of mass frame are proportional to the relative velocities, with opposite signs.
• 🖼️ The magnitude of the relative velocity is constant in any reference frame, including the center of mass frame.
• 💥 The speeds of objects in an elastic collision in the center of mass reference frame do not change.
• 💥 The direction of the velocities of objects in an elastic collision in the center of mass reference frame changes.
• 🖼️ The relationship between velocities in the center of mass frame and relative velocities holds true in any reference frame.
• 💆 The initial and final velocities of objects in the center of mass frame are equal.

Questions & Answers

Q: What is the significance of the relationship between the velocities of objects in the center of mass frame and the relative velocities?

The significance is that the velocities of objects in the center of mass frame are directly proportional to the relative velocities, which means their speeds do not change during an elastic collision.

Q: Does the magnitude of the relative velocity change in different reference frames?

No, the magnitude of the relative velocity remains constant regardless of the reference frame.

Q: How can we express the positions of objects in the center of mass reference frame?

The positions of objects in the center of mass reference frame can be expressed as the reduced mass multiplied by the relative positions.

Q: What happens to the speeds of objects in an elastic collision in the center of mass reference frame?

The speeds of the objects remain constant in the center of mass reference frame, only the direction of their velocities change.

Summary & Key Takeaways

• In the center of mass reference frame, the positions of objects can be expressed as the reduced mass multiplied by the relative positions.

• The velocities of the objects in the center of mass frame are proportional to the relative velocities, but with opposite signs.

• The magnitude of the relative velocity remains constant in any reference frame, including the center of mass frame.