posted by Josh on .
Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in a glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving with a speed vi. After the collision, the orange disk moves along a direction that
makes an angle theta with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine:
1) the final speed of each disk;
2) whether the collision was elastic or not.
I've seen this question many times on the internet and am bothered with the erroneous answers that were provided. I know that you are most likely done with this class (and hopefully you have passed it) but for the sake of anyone else who is looking for an answer here is the solution:
Common versions of this question have given theta values of 37 degrees for the orange shuffleboard and 53 degrees for the green shuffleboard.
v(initial) = 0
V(initial) = 5 m/s (along the horizontal)
V(final) = ?
This is an elastic collision, use the equation for this collision type (MV1 + MV2)i = (MV1-MV2)f (the M's cancel out since both masses are equal)
This is a 2-D collision so split them accordingly:
X: 5 = V1(cos53degrees) + V2(cos37degrees)
Y: 0 = V1(sin37degrees) - V2(sin53degrees)
solve for V1 or V2,
V1 = V2(sin53degrees)/(sin37degrees)
plug this value into the first equation
X: 5 = [1.33 V2](cos53degrees) + V2(cos37degrees)
Solve for V2 to get 3.127
plug this into V1=1.33V2 to get the value for V1 and there you go!