Question

A scattering experiment is done with a 32 kg disc and two 8 kg discs on a frictionless surface. In the initial state of the experiment, the heavier disc moves in the x direction with velocity v = 25 m/s toward the lighter discs, which are at rest. The discs collide elastically. In the final state, the heavy disc is at rest and the two smaller discs scatter outward with the same speed. What is the x -component of the velocity of each of the 8 kg discs in the final state?

• A. 12.5 m/s
• B. 16 m/s
• C. 25 m/s
• D. 50 m/s
• E. 100 m/s

Answer 1

Answer: (D)

50 m/s

The law of conservation of linear momentum tells us that the x-component of the system’s momentum must be equal before and after the collision.

Let the x-component of the final velocity be $v$. The large disc comes to rest after collision.

From conservation of momentum :

$32\times 25+0=0+8v+8v$

$⟹v=50m/s$.