Mass on frictionless wedge

[sheepcountme]

Homework Statement

A 2.0 kg mass rests on a frictionless wedge that has an acceleration of 15 m/s2 to the right. The mass remains stationary relative to the wedge, moving neither higher nor lower. (a) What is the angle of inclination, θ, of the wedge? (b) What is the magnitude of the normal force exerted on the mass by the incline? (c) What would happen if the wedge were given a greater acceleration?

Homework Equations

F=ma
trig identities

The Attempt at a Solution

I just can't get my mind around this one to get started. I am unsure how to interpret the acceleration of the box since it has no additional acceleration other than that of the wedge.

I believe the second part will be something akin to Fn=mgsintheta...

And if the wedge accelerated more the box would probably move up the wedge.

 

[rl.bhat]

The acceleration of the mass is parallel to the base of the wedge.
The mass will be at rest when the component of the acceleration along the inclined plane is equal to the component of the weight of the mass in the down ward direction along the inclined plane. Equate them to get the angle of inclination of the wedge.

 

[sheepcountme]

So, I set mgcostheta=15 and solved for theta getting 40.1 degrees.

Then for the normal force Fn=mgsintheta, so Fn=12.62N

Is this correct??

 

[rl.bhat]

mgsinθ is the component of the weight along the inclined plane in the downward direction.
Component of the acceleration along the inclined plane in the upward direction is a*cosθ. Equate them to find θ.

 

[sheepcountme]

Ah, okay so solving for theta I get 37.42 degrees...and then for the normal force..it's still mgcostheta, yes?

 

[rl.bhat]

Yes.