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Idoke

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## Homework Statement

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**

## 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 the

**ball's**momentum 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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