Block and Wedge (all frictionless)

[RoKe]

I searched for this problem and could not find satisfactory information or information that applied to my specific concerns.

The wedge of mass M is resting on a horizontal surface. A block of mass m is placed on the wedge and the whole system is released from rest. There is no friction anywhere in the system.

I have the FBDs complete. I have the Newtonian equations of motion in both the x and y components (relative to the table, for an inertial frame) for the wedge and the block.

The question asks, use the concept of relative velocities to derive a statement of relative accelerations, then use that to apply the proper constraint.

Then, the acceleration of the wedge (relative to the table) and the block (relative to the table and the wedge) must be found. I think I can do this once I get the first part done.

Basically the wording of the first part of the question is confusing and I'm not sure where to progress after getting the motion equations.

Thanks in advance.

 

[Chi Meson]

The question asks, use the concept of relative velocities to derive a statement of relative accelerations, then use that to apply the proper constraint.

This is the exact wording of the question? I'm not sure what it means by "apply the proper constraint."

What did you get for your statement of relative accelerations?

 

[RoKe]

The statement of relative accelerations is a_(block/table) = a_(block/wedge) + a_(wedge/table). Was I supposed to derive this from a similar statement of relative velocity? I don't know what it wants me to do.

 

[Chi Meson]

I don't think that's what they want.

Go back to your FBD. THere should be one for the block and one for the wedge. The block has two forces on it, the wedge has three. The wedge has a net force that will be horizontal. The block has a net force that is angled down the incline (but not the same angle at incline),