# Calculate Normal Force in Mass M & m Slope System with no Friction

• mystmyst

#### 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 [Broken]

## 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.

Thanks!

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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 -mao, where - sign indiate that its direction is opposite to ao

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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! 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...)

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 -mao, where - sign indiate that its direction is opposite to ao

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

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 Taking X along incline will be easier!

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...)

OH! sorry 