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 v_i. After the collision, the orange disk moves along a direction that makes an angle ? with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine the final speed of each disk. (Use any variable or symbol stated above as necessary.)

V (yellow disk) =

V (orange disk) =

Answer 1

Let the final speed of the orange disk be vo, the final speed of the yellow disk be vy, and m be the mass of one disk. Calling the initial direction of the orange disk ˆi, and the direction perpendicular to that ˆj (such that the final direction of vo has positive components in both directions), we see

voˆi = vo cos?

voˆj = vo sin?

For the orange puck, and that since the motion of the yellow is perpendicular the the orange, the angle between the final motion of the

yellow and the ?ˆj direction is also ?, so

vyˆi = vy sin?

vyˆj = ?vy cos?

Conserving momentum in both directions we have

Piˆj = 0 = Pfˆj = mvyˆj +mvoˆj = mvo sin??mvy cos?

vy = vosin?/cos?

Piˆi = mvi = Pfˆi = mvyˆi +mvoˆi = mvo cos?+mvy sin?

vi cos? = vo cos² ?+(vosin?/cos?)sin?cos? = vo cos²?+vo sin²? = vo

Because

sin² ?+cos² ? = 1

So

vo = vi cos? (ans)

vy = vosin?/cos?

= visin? (ans)