A white billiard ball with mass m w = 1.33 kg is moving directly to the right wi

Question

A white billiard ball with mass mw = 1.33 kg is moving directly to the right with a speed of v = 2.97 m/s and collides elastically with a black billiard ball with the same mass mb = 1.33 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of ?w = 29

A white billiard ball with mass mw = 1.33 kg is moving directly to the right with a speed of v = 2.97 m/s and collides elastically with a black billiard ball with the same mass mb = 1.33 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of ?w = 29?degree and the black ball ends up moving at an angle below the horizontal of ?b = 61? degree . 1) What is the final speed of the white ball? 2) What is the final speed of the black ball? m/s 3) What is the magnitude of the final total momentum of the system? kg-m/s 4) What is the final total energy of the system? J

Explanation / Answer

Momentum is a vector (has direction), so it has horizontal and vertical components, each of which is conserved in a collision.

The total horizontal momentum of the system before the collision is:
(1.33 kg)*(2.98 m/s) + (1.33 kg)*(0 m/s) = 3.96 kg m/s
Or you might want to leave mass as "m," since it will cancel out.
horizontal momentum = m*2.98

After the collision, the total horizontal momentum of the system is:
m * (vw * cos(30)) + m*(vb * cos(-60)) = m(0.866 vw + 0.5 vb)

Because horizontal momentum is conserved, these two values must be equal.
m * 2.98 = m * (0.866 vw + 0.5 vb)
2.98 = 0.866 vw + 0.5 vb

Next calculate the vertical component of momentum before the collision, and an expression for the vertical component of momentum after the collision. Write an equation indicating that vertical momentum is conserved.

You now have a system of two equations in two variables. Solve using whichever algebraic method you like.

The problem actually gives too much information. The angles were sufficient to find the final speeds of the two balls. Check your answer by calculating the total kinetic energy of the system before and after the collision. The problem states that this collision is elastic, meaning kinetic energy was conserved.

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