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 v with arrowoi = 3.50 m/s as in Figure (a) shown below. After the collision, the orange disk moves in a direction that makes an angle of = 35.0° with the horizontal axis while the green disk makes an angle of phi = 55.0° with this axis as in figure (b). Determine the speed of each disk after the collision.

Explanation / Answer

The sum of their vertical momenta is zero:
1) Vo*sin35 = Vg*sin55

The sum of their horizontal momenta must equal the initial momentum of orange:
2) Vo*cos35 + Vg*cos55 = 3.50

In each case, since the masses are equal, they cancel out.

Vo= Vg*sin55 /sin35

Vg*sin55*cos35 / sin35 + Vg*cos55 = 3.50

Vg( sin55*cos35 / sin35 + cos55) = 3.50

Vg(1.16987 + 0.573576) = 3.50

Vg*1.743446 = 3.50

Vg = 2.007518 m/sec

Vo= Vg*sin55 /sin35 = 2.007518*sin55 /sin35 = 2.8670

Solving (1) & (2) simultaneously,
Vo = 2.867 m/s
Vg = 2.007 m/s

n the case of elastic collision, they will both move perpendicular to each is the property of this collision. To check the above answer, we can verify by checking if the law of conservation of KE is satisfied.
Initial KE = (1/2) m * (3.5)^2 = 6.125 m joule (m = mass of the disc)
Final KE = (1/2) m * (2.867)^2 + (1/2) m (2.007)^2 = 6.123 m joule
confirms very well.

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