Normal force when slope accelerates horizontally

[mystmyst]

We have a slope, with mass M, at x degrees. Mass m is on the slope. The slope moves right at constant acceleration $$a_0$$. There is no friction between M and m, and no friction between M and ground.

Determine the Normal Force between M and m.

[PLAIN]http://img638.imageshack.us/img638/620/imaginaryforces2.png

The Attempt at a Solution

I'm a bit confused with this because the slope is moving.
I would just think the answer would be N = mgcosx.
But since the slope is moving, I have to take into consideration $$a_0$$ but I don't know how to.

Can someone please help?
Thanks!

 

[cupid.callin]

Hint: Use Pseudo force

Edit: For using Pseudo(fictitious) force, you have acc. of incline

These forces come into action when you need to apply Newton's laws in non inertial frame(i.e. a is not 0 of frame)

In this case it will be -ma_o, where - sign indiate that its direction is opposite to a_o

 

[tiny-tim]

hi mystmyst!

I'm a bit confused with this because the slope is moving.
I would just think the answer would be N = mgcosx.
But since the slope is moving, I have to take into consideration $$a_0$$ but I don't know how to.

well, you know from the question that a fictitious force is involved …

what is that fictitious force in this case?

draw it on the free body diagram, and proceed as normal …

fictitious forces go on the fbd just like ordinary forces … that's the point! ​

 

[mystmyst]

hi mystmyst!


well, you know from the question that a fictitious force is involved …

what is that fictitious force in this case?

draw it on the free body diagram, and proceed as normal …

fictitious forces go on the fbd just like ordinary forces … that's the point! ​

The fictitious force is $$a_0$$ but I don't know how to draw it on a fbd. Am I supposed to split it into x and y coordinates (I'm using the slope as the x-axis...)

 

[cupid.callin]

as the acceleration of incline is along +X ... so this fictitious force will be along -X

as i told you ...

In this case it will be -ma_o, where - sign indiate that its direction is opposite to a_o

 

[cupid.callin]

write all other forces like gravity, normal rxn.. and also include this force in your FBD

 

[tiny-tim]

The fictitious force is $$a_0$$ but I don't know how to draw it on a fbd. Am I supposed to split it into x and y coordinates (I'm using the slope as the x-axis...)

a₀ is horizontal, so you draw it horizontal

if you're using coordinates (you could use trig instead), then yes you'll have to split it into components along the axes you've chosen

 

[cupid.callin]

Taking X along incline will be easier!

 

[tiny-tim]

Taking X along incline will be easier!

cupid.callin, he is taking X along the incline …

Am I supposed to split it into x and y coordinates (I'm using the slope as the x-axis...)

 

[cupid.callin]

OH! sorry