A mass of 2 kg traveling at 3 m/s undergoes a one-dimensional elastic collision with a group of four 1-kg masses that are at rest in contact with each other and lined up in the same direction as the velocity of the 2-kg mass. As a result of the collision
A) the 2-kg mass comes to a stop and one of the 1-kg masses takes off at 6 m/s.
B) the 2-kg mass comes to a stop and two of the 1-kg masses take off at 3 m/s.
C) the 2-kg mass comes to a stop and three of the 1-kg masses take off at 2 m/s.
D) the 2-kg mass comes to a stop and all four of the 1-kg masses take off at 2 m/s.
E) the 2-kg mass and the five other masses travel at 1 m/s.

Question

Quizplus · Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved. Initially, the momentum of the system is 2 kg x 3 m/s = 6 kg m/s, and after the collision, the momentum is still conserved. Let us assume that two of the 1-kg masses take off in one direction at a speed of v and the other two masses take off in the opposite direction at the same speed v. Then, the final momentum of the system would be (2 kg)(0 m/s) + (1 kg)(v m/s) + (1 kg)(v m/s) + (1 kg)(-v m/s) + (1 kg)(-v m/s) = 0 kg m/s. Solving for v, we get v = 3 m/s. Thus, two of the 1-kg masses take off in one direction at 3 m/s, while the other two take off in the opposite direction at 3 m/s, leaving the 2-kg mass at rest. Therefore, the correct answer is B.

A Mass of 2 Kg Traveling at 3 M/s Undergoes