Inclined Plane Inside an Elevator

[rwx1606]

Homework Statement

An inclined plane, fixed to the inside of an elevator, makes a 25 angle with the floor. A mass m slides on the plane without friction. What is the acceleration relative to the block if the elevator is a)accelerating upwards .35g b)accelerating downwards .35g? c)constant speed

Homework Equations

F=Ma

The Attempt at a Solution

I know there's two accelerations I have to take into the account. The acceleration as the block slides down the incline, and the acceleration of the elevator. Combining these two, I can find the relative acceleration. I chose the reference frame to be titled so that the x-axis is along the incline. The thing I can't figure out is how the motion of the elevator affects the motion of the block. For example, when the elevator is accelerating upwards. Does the block accelerate upwards with it? From the block's force diagram I only have the normal force and mg down. the weight provides the acceleration down the incline but I have no clue what the elevator's acceleration does to the system. Any help would be appreciated.

 

[Rake-MC]

Okay so the first thing you want to do is find the net force on the object in the y direction. There is obviously mg pointing down, however the elevator is accelerating up at 0.35g.

therefore net force y = 0.35mg - mg.
Now you can treat the question as a normal inclined plane question where the only y force acting on it is -0.65mg.

You can figure out the rest with this.

 

[Doc Al]

View the problem from the accelerating reference frame of the elevator. In that frame there will be an additional inertial force acting on the block equal to -ma (where "a" is the acceleration of the elevator).

 

[rwx1606]

why does this inertial force act downwards on the block?

 

[Doc Al]

why does this inertial force act downwards on the block?

It acts opposite to the direction of the acceleration. When the elevator accelerates upwards, the inertial force acts downwards.

 

[Rake-MC]

You can look at it simply like this, the elevator is accelerating upwards, therefore, relative to the elevator, the block is accelerating downards.