What Determines the Block's Motion on an Accelerating Wedge?

[zeena2009]

Homework Statement

A 2kg block rests on a frictionless wedge that haas 60 degree incline and an acceleraion a to the right such that the mass remains stationary relative to the wedge.
a) determine a?
b) what would happened if the wedge were given an acceleration larger than this value?
c) what would happened if the wedge were given an acceleration smaller than this value?



I got a, it's b and c i didnt get
i think that when you give larger accelertaion, the block would slides up
and smaller, the blick slides down the incline
that's my common sense

however, when i tried to do it mathmatically and algebrically, it didnt make sense.

so please help me ??

 

[LowlyPion]

Welcome to PF.

Draw a diagram. Consider the interface between the incline and the block.

The inertia of the block will have a force in reaction to the force of the accelerating incline. Viewed in the frame of reference of the incline then the block is subject to the two accelerations - 1 horizontal and the other vertical. You found the answer when they were in balance, but as you note then when the acceleration is greater than equilibrium condition, the component || along the plane will be greater than needed to resist the || component of the vertical gravity.

If you think about it, this is similar to a car on a banked curve. But rather than the incline accelerating, you have the centripetal acceleration from the circular motion.