Question

Consider a collision between two carts, one of mass mA= 5 kg and the otherof mass mB= 7 kg, on a frictionless track. (A). Find the final velocity of Cart A, if both objects are initially moving in opposite directions toward each other at 12 m/s, and Cart B completely stops due to the collision. (B). Is this an elastic or inelastic collision? Why?

Answer 1

a) mass of A=m_A = 5 kg

mass of cart B=m_B=7 kg

initial velocity of A=12 m/s

initial velocity of B=-12 m/s

initial momentum of system = (5*12)+(7*-12)=-24 kg-m/s

final velocity of cart B=0

Let final velocity of A=v_A

From momentum conservation,we get

-24 = 5*v_A

v_A = -24/5=-4.8 m/s

Therefore, cart A moves in opposite direction at 4.8 m/s

B)Since the cars do not stick to each other after collision, the collision is not inelastic

initial kinetic energy of system = 0.5*5*12²+0.5*7*12² = 864 J

finla kinetic energy of system = 0.5*5*4.8² = 57.6 J

Since the energy is not conserved , the collision is not elastic.

Therefore, the collision is neither elastic nor inelastic