A 24.0 g marble sliding to the right at 61.2 cm/s overtakes and collides elastically with a 12.0 g marble moving in the same direction at 15.3 cm/s.

Question

After the collision, the 12.0 g marble moves to the right at 76.5 cm/s. Find the velocity of the 24.0 g marble after the collision.

Answer 1

This problem tests our understanding of the conservation of momentum. We know that the total momentum of the system must be the same before and after the collision. The equation for the momentum of a single object is M=mv, or momentum is mass times velocity. If we calculate the sum of the momentum for each marble before the collision, it should equal the sum of the momentum for each marble after the collision.

We can express this concept mathematically as m₁*v_{1 before}+m₂*v_{2 before}=m₁v_{1 after}=m₂v_{2 after}. We then substitute in our values and get (24)*(61.2)+(12)*(15.3)=(24)(v_{1 after})+(12)*(76.5) We then solve for v

(24)*(61.2)+(12)*(15.3)=(24)(v_{1 after})+(12)*(76.5)

((24)*(61.2)+(12)*(15.3)-(12)(76.5))/24=v_{1 after}=30.6 cm/s to the right