What Is the Acceleration of the Inclined Plane with an Ice Cube Sliding Down?

[tamref]

Homework Statement

There is a cube of ice the top of inclined plane (for 20 degress) with height 4 meters. The inclined plane can move without friction along the surface. The mass of the ice is 1/4 of the mass of inclined plane. Calculate the acceleration of the inclined plane, when the ice will be at the middle of the inclined plane.

Homework Equations

The Attempt at a Solution

I tried to draw the forces acting on the cube. That are

x-axis along the inclined plane: M/4 g sin(20) - a_1 M/4 cos(20) = M/4 a_2... (where a_1 is the acceleration of the inclined plane)

y-axis perpendicular to the inclined plane: F_n + M/4 a_1 sin(20) = M/4 g cos(20)=0 ... (where F_n is the perpendicular force of the plane)

Forces acting on the inclined plane:

x-axis: F_n sin(20)= M*a_1

y_axis: F_n * cos(20) + M*g= F_s...(where F_s is the force of the surface to the incline)


The first three eqatuions give a_1 and a_2, since M is canceled out after substituting for F_n. I think, this would give correct answer. However, since this is probably a well known problem, I am interested in other possible approaches.

 

[tiny-tim]

Welcome to PF!

Hi tamref! Welcome to PF!

There is a cube of ice the top of inclined plane (for 20 degress) with height 4 meters. The inclined plane can move without friction along the surface. The mass of the ice is 1/4 of the mass of inclined plane. Calculate the acceleration of the inclined plane, when the ice will be at the middle of the inclined plane.
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I am interested in other possible approaches.

Try conservation of energy

 

[davieddy]

Hi tamref! Welcome to PF!


Try conservation of energy

I think momentum may also be relevant.

Neat problem, which I haven't come across before.

Try solving it two ways: conserve energy and horizontal momentum.

Also apply Newton's 2nd Law, remembering that the acceleration of the
ice cube (relative to the ground) is the vector sum of its acceleration
relative to the wedge, and the wedge's acceleration relative to the ground.

 

[tamref]

Hi tamref! Welcome to PF!

Thank you, tiny-tim.

Thank you also for help, tiny-tim and davieddy.