(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A ball, with mass [tex]m_{1}=6 kg[/tex] and speed [tex]v_{0}[/tex] (unknown) hits an inclined plane (as shown) of mass [tex]m_{2}=42 kg[/tex] at rest on a frictionless floor.

there is no friction between the ball and the plane.

the angle [tex]\beta[/tex] is 10 degrees.

Question: what is the value of [tex]\alpha[/tex]?

2. Diagram

3. The attempt at a solution

I used three things:

1. The conservation of momentum parallel to the X axis, because there are no forces on the system in that axis:

[tex]m_{1}v_{0}=m_{1}v_{1}cos\beta+m_{2}v_{2}[/tex]

where [tex]v_{1}[/tex] and [tex]v_{2}[/tex] are the velocities after the collision of the ball and plane, respectively.

EDITED: the equation was wrong, the inclined plane had no velocity before the collision.

2. The conservation of theball'smomentum on the axis parallel to the inclined plane (because no forces are acting on the ball in that axis) :

[tex]m_{1}v_{0}sin\alpha=m_{1}v_{1}sin\beta[/tex]

3. Conservation of kinetic energy:

[tex]1/2m_{1}v_{0}^{2}=1/2m_{1}v_{1}^{2}+1/2m_{2}v_{2}^{2}[/tex]

Now I have a problem, I have 3 equations but 4 unknowns (v1, v2, alpha and v0). could someone shed some light on this?

I thought about doing this in the center of mass reference frame but i always get stuck with the fact that the momentum is not conserved in the Y direction.

help would be appreciated.

Thanks.

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# Momentum and Energy problem (ball and incline collision)

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