Homework Help: Determine the final speed of each disk.

1. Nov 12, 2007

Th3Proj3ct

1. The problem statement, all variables and given/known data
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 4.40 m/s. After the collision, the orange disk moves along a direction that makes an angle of 38.0° with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine the final speed of each disk.

2. Relevant equations
p=mv

3. The attempt at a solution
Well i've tried conservation of momentum, and even have this link at my disposal; i just cannot get the correct answer (probably due to basic algebra errors.)

Granted that my angle is 1° off, and the speed is different; I end up with a final formula of sqrt(Uo^2-Vo^2)=Vo/tan(38)
=Uo^2-Vo^2 = (Vo/Tan38)^2
=Uo^2-Vo^2=Vo^2/tan(38)^2.
=Tan(38)^2*Uo^2-Tan(38)^2*Vo^2=Vo^2
=tan(38)^2*^Uo^2=0.6104Vo^2
=(tan(38)^2*(4.4^2))/(0.6104)=Vo^2
=19.3602=Vo^2
=4.4=Vo
Yet... that's not right, because it's the original speed and unless the yellow didn't move at all; it would be impossible. But I dont know what else to do.

Last edited by a moderator: May 3, 2017
2. Nov 13, 2007

catkin

In an elastic collision you have conservation of momentum in two perpendicular directions and conservation of energy. Easiest to pick the initial path of the orange disk as one of the directions.

That gives you 3 simultaneous equations ...

3. Nov 13, 2007

rl.bhat

In oblique elastic collision conserve momentum in x and y direction separately. And apply conservation of energy.
Orange disc is moving horizontally. So its y- componet of momentum must be zero. Hence y component of vo=vosin38, and y component of vy = vysin52. To make y component zero, they must be equal and opposite, So vosin38 = vysin52 (Since mass is same it gets cancelled out.) write vy in terms of vo, and put it in the equation Vy^2 = vy^2 + vo^2 and solve for vo.And hence find vy.

4. Nov 13, 2007

Th3Proj3ct

So Vosin38=Vysin52, Vy=(vosin38)/sin52)
Vy^2 = vy^2 + vo^2 <--- Plugging it into this
(vosin38)/sin52)^2 =(vosin38)/sin52)^2 + Vo^2
Vosin38^2 = Vosin38^2 + Vo^2sin52
Vosin38^2 -Vosin38^2 -Vosin52^2 = 0
Vo(sin38^2-sin38^2-Sin52^2)=0
Vo(Sin52^2)=0
Vo=0/(sin52^2) ??

5. Nov 13, 2007

rl.bhat

(vosin38)/sin52)^2 =(vosin38)/sin52)^2 + Vo^2
In the expression Vy indicates the initial velocity of the yellow disc.
So (4.4)^2 =(vosin38)/sin52)^2 + Vo^2 Now try.