Two shuffleboard disks of equal mass, one orange and the other green, are involv

Question

Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s as in Figure P6.38a. After the collision, the orange disk moves in a direction that makes an angle of 37.0degree with the horizontal axis while the green disk makes an angle of 53.0degree with this axis as in Figure P6.38b. Determine the speed of each disk after the collision.

Explanation / Answer

The horizontal axis is the x axis, so the other axis is the y axis.t the orange disk is moving on the x axis before the collision. So the initial momentum of the orange disk is in the positive x direction.

Since the green disc is at rest before the collision, initial moment and kinetic energy of the green disk is 0.
Initial momentum in x direction = m * 5.0 m/s
Initial momentum in y direction = 0
Initial KE = ½ * m * 5.0^2

Since the collision is perfectly elastic, momentum and kinetic energy are conserved. The collision is a glancing collision. So, if the orange disk is moving in the positive y direction after the collision, the green disk is moving in the negative y direction after the collision.
velocity in x direction = v * cos , velocity in the y direction = v * sin
Let vo = final velocity of the orange disk, let vg = final velocity of the green disk
For the x direction, final momentum = m * vo * cos 37 + m * vg * cos 53
This is equal to the initial momentum in x direction.

m * vo * cos 37 + m * vg * cos 53 = m * 5.0
Divide both sides by m
Eq#1: vo * cos 37 + vg * cos 53 = 5.0

For the y direction, final momentum = m * vo * sin 37 – m * vg * sin 53
This is equal to 0.
m * vo * sin37 – m * vg * sin 53 = 0
Divide both sides by m
vo * sin 37 – vg * sin 53 = 0
Eq#2: vo * sin 37 = vg * sin 50
Divide both sides by sin 37
vo = vg * sin 53/sin 37

Substitute (vg * sin 53/sin 37) for vo in Eq#1

(vg * sin 53/sin 37) * cos 37 + vg * cos 53 = 5.0
vg * [(sin 53/sin 37) * cos 37 + cos 53] = 5.0
vg = 5.0 ÷ [(sin 53/sin 37) * cos 37 + cos 53]
vg = 2.80 m/s
This is the velocity of the green disk after the collision.

vo = vg * sin 53/sin 37
vo = 5.0 ÷ [(sin 53/sin 37) * cos 37 + cos 53] * sin 53/sin 37
vo = 2.10 m/s
This is the velocity of the orange disk after the collision.

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