What is the velocity of m when it reaches point P?

[ahello888a]

1. Homework Statement - In this problem, "m" slides down "M" (that is inclined at angle alpha) to the point "P" at the bottom-right of the triangle. "m" starts with zero velocity and "M" starts with zero velocity. There is zero friction between "m" and "M". There is also zero friction between "M" and the surface that it rests on (not shown in picture). So the questio is what is the velocity of "m" when it reaches the "P"? I don't even know how to approach this problem, so I don't have any work done, but my teacher told me that I would have to use the conservation of linear momentum and mechanical energy. Thanks for all the help.



2. Homework Equations - Emech = delta k + delta u; p = m1v1f + m2v2f = 0



3. The Attempt at a Solution - my teacher mentioned the relavent equations. but i really don't know how to even start this problem. i only know that for the free body diagram of "m" that there's sumFy = n-mgcosalpha; mgsinalpha to the right and for "M" umFy = n-mg; i know for sure that the free body for "M" is missing forces from the "m" but I am not sure how to account for that

 

[Bill Foster]

$$m$$ is a block and $$M$$ is a wedge?

 

[ahello888a]

yes that is correct

 

[Bill Foster]

Is the point "P" on the wedge or on the flat surface?

 

[ahello888a]

it is on the wedge

 

[Bill Foster]

Never mind. I can see your attached image now.

 

[ahello888a]

haha. I am so sorry i didnt mention that.

 

[rl.bhat]

What is the direction of the velocity of M?

 

[ahello888a]

The direction will be to the left, but it has no initial velocity. Nothing in this system has an initial velocity. "m" is released from rest and will slide down by gravity and since the surfaces are frictionless, "M" will begin to move as a result of gravity pushing down on "m" pushing down on "M"