Physics Help Momentum

Question

Two marbles collide. One is traveling at 10 cm/sec and has a mass of 60 grams. The other marble has a mass of 50 grams and travels at -12 cm/sec. If the first marble rebounds backwards with a velocity of -8.0 cm/sec, what is the rebound velocity of the second marble after the collision?

Answer 1

The momentum before the collision equals the momentum after the collision.

P (momentum) = mv (mass times velocity) so

P_before = 60(10) + 50(-12) = 600 - 600 = 0

P_after = (60)(-8) + 50(x) = -480 + 50x where "x" is the velocity of the second marble after the collision

P_before = P_after therefore 0 = -480 + 50x

Solve for x

Answer 2

In this problem we are dealing with the collision, and the law of conservation of linear momentum could be applied. The problem asks us about the velocity. Velocity is a vector, hence has magnitude and direction; so, we have to find both of them! We know that m₁ = 60 g, v₁ = 10 cm/s, m₂ = 50 g, v₂ = - 12 cm/s, u₁ = - 8 cm/s. It is interesting that for this problem we do not convert units to SI, because final answer could be given in cm/s.

Let select the x-axis in the direction of motion of the first body to the right.

Then the law of conservation of linear momentum in scalar form could be written as following:

m₁v₁ - m₂v₂ = - m₁u₁ + m₂u_2x ,

here u₁ and u_2x projections of the velocities of the marbles after collision respectfully.

Because we don't know the direction of the velocity of the second body after collision, I wrote u_2x. The sign of the projection of velocity u₂ will tell us its direction after collision.

Solving against u_2x, gives us

u_2x = (m₁(v₁ + u₁) - m₂v₂) / m₂

If you plug in all numbers into this equation, you should get an answer + 9.6 cm/s. The plus sign tells us that after collision the body will change the direction of its motion to opposite, it means in the direction of x-axis.

Answer: 9.6 cm/c in the opposite direction of its initial motion