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 = 4.35 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.

vof = ?

vgf =?

Explanation / Answer

Let mass be m for both bodies

then by using the law Conservation of Momentum (horizontal direction)

m1u1 + 0 = mVo cos T + MVi cos phi

m*Vof = mV(of)cos + mV(gf)cos

simplifying we get

4.35 = V(of)(.788) + V(gf)(.616) -----------------------------------(1)

For vertical direction

V(gf)sin(52) = -V(of)sin(38)

0.788 V(gf) = -0.616 V(of)

Vgf = -0.78 Vof --------------------------------2

4.35 = Vof * 0.788 - 0.78 *Vof * 0.616

simplifying 1 and 2 we get

V(of) = 14.141 m/s

V(gf) = 11.24 m/s

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