A particle of mass 3 kg moving at 8 m/s makes an elastic collision with a particle of mass 5 kg moving at -4 m/s.The velocity of the center mass of the particles is
A)3 m/s.
B)1.8 m/s.
C)0.5 m/s.
D)0.35

Question

A particle of mass 3 kg moving at 8  m/s makes an elastic collision with a particle of mass 5 kg moving at -4  m/s.The velocity of the center mass of the particles is
A)3 m/s. 
B)1.8 m/s. 
C)0.5 m/s. 
D)0.35

Quizplus · Accepted Answer

We can use conservation of momentum to find the velocity of the center of mass. The total momentum before the collision is (3 kg)(8 m/s) + (5 kg)(-4 m/s) = 4 kg m/s. After the collision, the velocities of the particles will be reversed, so the total momentum will be (3 kg)(-8 m/s) + (5 kg)(4 m/s) = -4 kg m/s.

Since this is an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy before the collision is (1/2)(3 kg)(8 m/s)^2 + (1/2)(5 kg)(-4 m/s)^2 = 56 J, and after the collision it is (1/2)(3 kg)(-8 m/s)^2 + (1/2)(5 kg)(4 m/s)^2 = 56 J.

The velocity of the center of mass can be found using the formula:

vcm = (total momentum) / (total mass)

In this case, the total mass is 3 kg + 5 kg = 8 kg.

vcm = 4 kg m/s / 8 kg = 0.5 m/s

Therefore, the answer is choice C, 0.5 m/s.

A Particle of Mass 3 Kg Moving at 8