Solving the Velocity of "m" at Point "P" with Momentum & Energy

[ahello888a]

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.

 

[member 553083]

The conservation of linear momentum states that the total momentum of a system before and after a collision must remain constant. The conservation of mechanical energy states that the total mechanical energy of a system before and after a collision must remain constant.In this problem, you can use the conservation of linear momentum to find the velocity of m. Since there is no friction and M has zero velocity, the initial momentum of the system is just that of m. So the momentum of the system before and after the collision is the same. Therefore, the velocity of m at point P is equal to the initial velocity of m (which is 0).You can also use the conservation of mechanical energy to solve this problem. The mechanical energy of the system before and after the collision must remain constant. Therefore, the kinetic energy of m at point P is equal to the potential energy of m at the starting point (where it was released). The potential energy of m at the starting point is equal to the weight of m multiplied by the height of the triangle. Therefore, the velocity of m at point P can be calculated using the formula:v = √(2gh)Where g is the acceleration due to gravity, h is the height of the triangle, and v is the velocity of m at point P.