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 = 6.10 m/s as in Figure a, shown below. After the collision, the orange disk moves in a direction that makes an angle of = 38.0° with the horizontal axis while the green disk makes an angle of = 52.0° with this axis as in Figure b. Determine the speed of each disk after the collision.

Explanation / Answer

mo =mg, voi=6.1 m/s,vyi =0

= 38.0°

vox = vocos(38) = 0.79 m/s

voy = vosin(38) = 0.62 m/s

= 52.0°

vgx = vycos(52) = 0.62 m/s

vgy = vysin(52) = 0.79 m/s

According conservation of momentum along x-direction:

movoxi +mgvgxi =movox +mgvgx

voxi = vox +vgx

6.1 = 0.79 vo +0.62 vg ---- (1)

According conservation of momentum along y-direction:

movoyi +mgvgyi =movoy -mgvgy

voyi = voy -vgy

0 = 0.62 vo -0.79 vg ---- (2)

By solving (1) and (2) equations we get

Velocity of orange disk after collision vo = 4.803 m/s

Velocity of green disk after collision vg = 3.77 m/s

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