AP Physics C Mechanics: Linear Momentum for Colliding Billiard Balls

[Daniel Guh]

Homework Statement

A billiard ball moving at 5 m/s strikes a stationary ball of the same mass. after the collision, the original ball moves at a velocity of 4.35 m/s at an angle of 30° below its original motion. find the velocity and angle of the second ball after the collision.

Relevant Equations

Pi = Pf
P = mv

I'm guessing this question can be solved using the law of conservation of momentum
Vi = 5 m/s

(5 m/s) M = (4.33 m/s) cos30 M + V sinθ M

I don't know what to do after this... I'm also not sure if I use the sin and cos correctly.

 

[erobz]

Assuming planar motion, you want to look at conservation of momentum in each direction. I believe that will give you two equations two unknowns i.e. the velocity of the initially stationary ball after collision, and the mass of the billiard balls.

Edit: I guess you aren’t after the mass (couldn’t solve for it anyway). Either way two equations two unknowns to find the angle.

 

[Daniel Guh]

So momentum in the y direction should cancel out?
4.33 M sin30 = MV sin θ
And the momentum in the x direction will equal the original momentum so
5M = 4.33 M cos30 + MV cosθ

 

[erobz]

Yeah, but remember you are going to find the component of the second balls velocity in each direction.

Edit: I guess you can have the unknown angle in those equations, but I wouldn’t bother in this step. I would just find $v_x$ and $v_y$. Then get the angle from their ratio. Up to you though.

Also, the question says $4.35~ \rm {m/s}$ not $4.33$. Which is it?

 

[kuruman]

So momentum in the y direction should cancel out?
4.33 M sin30 = MV sin θ
And the momentum in the x direction will equal the original momentum so
5M = 4.33 M cos30 + MV cosθ

That looks OK. You have two equations and two unknowns, V and θ. How are you going to extract them from the equations?

I would use V₀ for the initial speed of the first ball, V₁ for the final speed of the first ball and V₂ for the final speed of the target ball. I would then find V₂ and θ algebraically and substitute numbers at the very end. The algebra is easier to troubleshoot that way, for you and for us.