Question

A particle A and B are traveling counter-clockwise around a circular track at a constant speed of 8 m/s. What is the speed of particle A and B?

1) 4 m/s
2) 8 m/s
3) 16 m/s
4) 32 m/s

Answer 1

Using conservation of momentum for the elastic collision where Mass A and Mass B have equal masses, we find that after the collision, Mass A moves with a speed of 4 m/s in the -x-direction, and Mass B's final velocity is 0 m/s.

Step-by-step explanation:

The question pertains to the principles of conservation of momentum and kinetic energy in the context of an elastic collision between two particles of equal mass. In the scenario provided, Mass A and Mass B collide, with Mass A's velocity changing as a result of the collision. To find the final velocity of Mass B after the collision, we apply the conservation of momentum, which states that in the absence of external forces, the total momentum before collision is equal to the total momentum after collision.

The initial momentum of Mass A is (2 m/s) multiplied by its mass (m), and the initial momentum of Mass B is (6 m/s) multiplied by its mass, but in the opposite direction (-m). After the collision, the momentum of Mass A is (4 m/s in the -x direction) multiplied by its mass (m). Using the conservation of momentum:

• 
  
• Initial total momentum = Final total momentum
• 
  
• 2m - 6m = -4m + m * Vb

Solving for the velocity of Mass B (Vb), we find:

• 
  
• -4m = -4m + m * Vb
• 
  
• 0 = m * Vb
• 
  
• Vb = 0 m/s

Therefore, the final velocity of Mass B after the collision is 0 m/s.