Acceleration on inclined plane

[bongobl]

Hi guys I am trying too find a formula to figure out how I would find the acceleration of a block on an incline plane IF that plane itself were accelerating in the +Y direction.
I am not even sure which frame of reference to use since the acceleration is in 2 dimensions. This hinders me from being able to draw a free body diagram

Does anybody know how to go about finding the acceleration of the block (in cartesian vector form)?
Thanks
-Alex

 

[Dale]

Is the acceleration of the plane given, or is it to be determined by the force from the block?

If it is given then just remember that acceleration is a vector. So you can just add the known acceleration of the plane to the unknown acceleration of the block relative to the plane to get the total acceleration and you can still write Newton's 2nd law. The movement of the plane shouldn't change the free body diagram at all.

If it is not given then I would use a Lagrangian approach.

 

[Delta2]

I think it can be done in Newtonian mechanics since the problem states that the acceleration of the plane (and i hope it doesn't mean the acceleration of the c.o.m only) is only in the +y direction. Of course this means there is some sort of constraint that prevents the rotation of the plane around its c.o.m (like that the plane is moving between two vertical walls).

 

[Doc Al]

Hi guys I am trying too find a formula to figure out how I would find the acceleration of a block on an incline plane IF that plane itself were accelerating in the +Y direction.

Such as if the incline were fixed to the floor of an accelerating elevator? (The simplest case.)

If so, I would use the accelerating frame of the incline, being sure to add the appropriate inertial pseudo force due to the acceleration. (Of course, you have several options.)

 

[rcgldr]

If the inclined plane is accelerating upwards at a rate of "u" m/s^2, then let g' = g (gravitational acceleration) + u (inclined plane upwards acceleration). Solve as if the plane was not accelerating, using g' instead of g, then when completed, add the block's acceleration vector with respect to the incline plane and the upwards acceleration of the inclined plane with respect to the groung to get the total acceleration vector with respect to the ground.