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 vOi = 4.95 m/s as in Figure a, shown below. After the collision, the orange disk moves in a direction that makes an angle of = 36.0° with the horizontal axis while the green disk makes an angle of = 54.0° with this axis as in Figure b. Determine the speed of each disk after the collision.

vof = ____m/s

vgf = _____m/s

Explanation / Answer

Let us assume the initial direction of motion of orange disk be x axis

The mass of disks be m each

Momentum conservation in x direction

m*voi = m*vof cos theta + m*vgf cos phi

=> 4.95 = vof cos 36 + vgf cos 54 (eq 1)

Momentum conservation in y direction

m*voi = m*vof sin theta - m*vgf sin phi

0 = vof sin 36 - vgf sin 54

=> vof = 1.37638 vgf   (eq 2)

Replacing eq 2 in eq 1

=> 4.95 =1.37638 vgf * cos 36 + vgf cos 54

=> vgf = 2.9095 m/s

From eq 2

vof = 1.37638 vgf

=> vof= 1.37638 * 2.9095 = 4 m/s

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