A ball of mass 0.5kg moving at 10ms-1 collides with another ball of equal mass at rest. If the two balls move off together after the impact, calculate their...

Answer Details

The total momentum before the collision is equal to the total momentum after the collision (assuming no external forces act on the system). Before the collision, the first ball has a momentum of: p₁ = m₁v₁ = (0.5 kg)(10 m/s) = 5 kg m/s The second ball is at rest, so it has zero momentum: p₂ = m₂v₂ = (0.5 kg)(0 m/s) = 0 kg m/s The total momentum before the collision is: p₁ + p₂ = 5 kg m/s + 0 kg m/s = 5 kg m/s After the collision, the two balls move off together with a common velocity v. The total mass of the system is: m₁ + m₂ = 0.5 kg + 0.5 kg = 1 kg So the total momentum after the collision is: p_f = (m₁ + m₂)v_f = (1 kg)(v_f) Since the total momentum before the collision is equal to the total momentum after the collision, we have: p₁ + p₂ = p_f 5 kg m/s + 0 kg m/s = (1 kg)(v_f) v_f = 5 m/s Therefore, the common velocity of the two balls after the collision is 5 m/s. Answer: 5.0ms^-1