Two shuffleboard disks of equal mass, one orange and the other yellow, are invol

Question

Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in an elastic, glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving with a speed of 4.20 m/s. After the collision, the orange disk moves along a direction that makes an angle of 36.0° with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine the final speed of each disk.

note: the answers aren't 3.95 and 5.436

Explanation / Answer

Separately, the x- and y-components of the total momentum are conserved.

Pxi = m vorg,o + m vyel,o
Pxi = m vo + 0 = m (4.2 m/s) + 0

Pxi = m vo

Pyi = . . . = 0

We can substitute 4.2 m/s = vo at the end.

Pfx = m vorg,x + m vyel,x
Pfx = m vorg cos 36o + m vyel cos 54o

Pfx = m vorg (0.8) + m vyel (0.6)

Pfx = m [ vorg (0.8) + vyel (0.6) ]

Pfx = m [ vorg (0.8) + vyel (0.6) ] = m vo = Pix

vorg (0.8) + vyel (0.6) = vo

Of course, this is one equation with two unknowns so we need some additional information. We will get that from looking at the y-equation for the conservation of momentum.

Now, for the y-component,

Pfy = m vorg,y + m vyel,y
Pfy = m vorg sin 36o - m vyel sin 54o

Pfy = m vorg (0.6) - m vyel (0.8)

Pfy = m [ vorg (0.6) - vyel (0.6) ]

Pfy = m [ vorg (0.6) - vyel (0.8) ] = 0 = Piy

[ vorg (0.6) - vyel (0.8) ] = 0

Now we have two equations and two unknowns, vorg and vyel.

0.6 vorg = 0.8 vyel
vorg = 1.333 vyel

vorg (0.8) + vyel (0.6) = vo

(0.8)(1.33 vyel ) + 0.6 vyel = vo

1.667 vyel = vo

vyel = 0.6 vo

vyel = 0.6 (4.2 m/s) = 2.52 m/s

vorg = (1.333) (2.52 m/s)

vyel = 3.35m/s

1.667 vyel = vo
vo= 5.58m/s

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