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 = 4.50 m/s as in Figure (a) shown below. After the collision, the orange disk moves in a direction that makes an angle of theta = 36.0 with the horizontal axis while the green disk makes an angle of phi = 54.0 with this axis as in figure (b). Determine the speed of each disk after the collision.

Vof = ___

Vgf = ___

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 = 4.50 m/s as in Figure (a) shown below. After the collision, the orange disk moves in a direction that makes an angle of theta = 36.0 with the horizontal axis while the green disk makes an angle of phi = 54.0 with this axis as in figure (b). Determine the speed of each disk after the collision. Vof = ___ Vgf = ___

Explanation / Answer

ma = mass of orange ball...............vaf = vof.

mb = mass of green ball....Vbf = Vgf

ma = mb = m
along x axis (horizantal)

ma*Vaix + mb*vbix = ma*vafx + mb*vbfx

(m*4.5)+(m*0) = (m*Vaf*cos36) +(m*Vbf*cos55)

4.5 = 0.809*Vaf + 0.573*Vbf...........(1)

along y ( vertical)

ma*Vaiy + mb*vbiy = ma*vafy + mb*vbfy

(m*0)+(m*0) = (m*Vaf*sin36) - (m*Vbf*sin55)

0 = 0.587*Vaf - 0.82*Vbf

Vbf = 0.72 Vaf...............(2)

substitute 2 in 1

4.5 = 0.809*Vaf + (0.573*0.72)*Vaf

Vaf = Vof = 3.68 m/s

Vbf = Vgf = 2.65 m/s

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