Confusing problem....?

Question

Each ball has a set mass of 0.46 kg. A green ball is traveling at 11.7 m/s and strikes a blue ball which is at rest. Assume that the balls slide frictionless on the surface and all collisions are head on. Find the final speed of the BLUE ball in each of the following situations (in units of m/s):

1. The green ball stops moving after it strikes the blue ball.

2. The green ball continues moving after the collision at 2.9 m/s in the same direction.

3. The green ball continues moving after the collision at 0.2 n/s in the same direction.

Answer 1

This is solved using conservation of momentum. The momentum of the two balls originally must equal the momentum of the two balls after the collision. Momentum is mass x velocity, and since the blue ball has no velocity at first, the momentum before the collision is the momentum of the green ball

Momentum = mass x velocity
Momentum = 0.46 kg x 11.7 m/s = 5.382 kg m/s

Now the momentum of the two balls must equal this before and after collision

1. If the green ball stops, that means it lost all momentum, and it was transferred to the blue ball, and since the blue ball has the same mass, it will also be going the same velocity 11.7 m/s

2. Initial momentum = final momentum
(momentum of green) + (momentum of blue) = 5.382 kg m/s
(0.46 x 2.9) + (0.46 x velocity of blue) = 5.382
velocity of blue = 8.8 m/s

3. Same as number 2, just different speed
(0.46 x 0.2) + (0.46 x velocity of blue) = 5.382
velocity of blue = 11.5 m/s

Answer 2

You are looking for complete or partial transfer of kinetic energy from the green ball to the blue ball. KE = 1/2 mv^2. So the initial kinetic energy of the green ball is 1/2 (0.46 kg)(11.7 m/s)^2 = 31.485 Joules. So in the first example, a totally elastic collision occurs in which all the kinetic energy is transferred to the blue ball, so the blue ball possessed a final kinetic energy of 31.485 Joules, and since it has the same mass as the green ball, it must have a final velocity equal to the initial velocity of the green ball, 11.7 m/s.

In problem 2 and 3, just subtract the kinetic energy of the green ball from its initial KE to find out how much energy was transferred to the blue ball, then solve for v.

Answer 3

This is not confusing, since if the collisions are all head-on, and if the surface is frictionless, option 1 is the ONLY possible outcome. Both energy AND momentum must be conserved simultaneously. To satisfy both, the green ball MUST stop moving, and the blue ball MUST continue at the same speed as the green ball was travelling before the collision (11.7m/s). Case 2 and case 3 both violate the conservation of energy AND conservation of momentum.

Answer 4

You need to use conservation of momentum. Momentum is equal to mv, or (m_1)(v_1) + (m_2)(v_2) in this case, where m_1 would be the mass of the first ball, m_2 that of the second, and v_1 and v_2 are the velocities of the respective balls. The original ball has a momentum of (0.46 kg)(11.7 m/s) = 5.4 kg-m/s. Given the velocity of the first ball, and the mass of both balls, you have m_1, v_1, and m_2 for all three cases (where only v_1 is changing), and just need to solve for v_2 so that the full momentum expression is equal to 5.4 kg-m/s.

Answer 5

You should really do your own homework. ;)