Problems with frictionless wedges

[zaurefirem]

Homework Statement

A 2.3kg block rests on a frictionless wedge that has an inclination of 30° and an acceleration to the left such that the block remains stationary relative to the wedge; i.e., the block does not slide up or down the wedge. The acceleration of gravity is 9.81 m/s^2.

Find the magnitude of the acceleration of the block-wedge system.

Homework Equations

ƩFx=ma=mgsinθ (?)

The Attempt at a Solution

[PLAIN]http://img36.imageshack.us/img36/456/physicsdiagram.png
(near-exact recreation of the diagram given, with force vectors added.)
ƩFx = 2.3kg * 9.81m/s^2 * sin30°
... = 11.2815 kg*m/s^2

If anyone is familiar with the UT Quest system, that's what we're using for this homework, and it's said that this answer is wrong. Enlightenment is encouraged, assistance is welcomed, etc. Your help would be greatly appreciated. Thank you! :)

 

[method_man]

Hello,

Try to draw your FBD a little bit precise. You've got three forces acting on your block: ma, G=mg and N.

 

[Doc Al]

There are only two forces acting on the block: The normal force and gravity. Those are shown correctly in your diagram. But if the block is not sliding down the wedge, what must be the direction of its acceleration?

Apply Newton's 2nd law to horizontal and vertical forces to solve for the acceleration.

 

[SammyS]

The "block remains stationary relative to the wedge". The acceleration of the wedge is to the left. (It's on a horizontal surface.)

 

[rwisz]

I would like to point out that there are a few problems with the concept of a frictionless wedge. Firstly, in reality, there is no such thing as a completely frictionless surface. Even surfaces that are considered to be very smooth still have some amount of microscopic roughness that can create friction. Therefore, the concept of a frictionless wedge is not entirely realistic.

Secondly, in this scenario, the block is not sliding up or down the wedge, which means that there is no net force acting on it in the vertical direction. This is not possible in a real-world scenario as gravity would always exert a force on the block, causing it to either slide down or be pushed up the wedge.

In the given solution, the equation ƩFx = mgsinθ is not applicable as it only considers the forces acting in the horizontal direction. In this case, the force of gravity is acting in the vertical direction and needs to be taken into account. Therefore, the correct equation to use would be ƩFy = 0, which would give us the correct answer of 0 for the magnitude of acceleration.

In conclusion, while the concept of a frictionless wedge may be useful for theoretical purposes, it is not a realistic scenario and should be approached with caution. It is important to consider all forces acting on a system, including gravity, in order to accurately solve for the acceleration of a block on a wedge.