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

In summary: Yeah, so you should resolve it into two components. Now, remember, you have to draw all the forces acting on the body on the FBD. So, in this case, the horizontal component of pseudo force and gravity will be in opposite direction. Draw the horizontal component of gravity in the same direction as the horizontal component of pseudo force. Now, the vertical component of pseudo force will be in the same direction as normal reaction. And that's all you have to do. Just proceed as usual and you will get your answer. In summary, to determine the Normal Force between M and m on a slope with mass M at x degrees, where mass m is also on the slope and the slope is moving right with constant acceleration a_
  • #1
mystmyst
57
0
We have a slope, with mass M, at x degrees. Mass m is on the slope. The slope moves right at constant acceleration [tex]a_0[/tex]. 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 [tex]a_0[/tex] but I don't know how to.

Can someone please help?
Thanks!
 
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  • #2
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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  • #3
hi mystmyst! :smile:
mystmyst said:
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 [tex]a_0[/tex] 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! :biggrin:
 
  • #4
tiny-tim said:
hi mystmyst! :smile:


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! :biggrin:

The fictitious force is [tex]a_0[/tex] 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...)
 
  • #5
as the acceleration of incline is along +X ... so this fictitious force will be along -X

as i told you ...


cupid.callin said:
In this case it will be -mao, where - sign indiate that its direction is opposite to ao
 
  • #6
write all other forces like gravity, normal rxn.. and also include this force in your FBD
 
  • #7
mystmyst said:
The fictitious force is [tex]a_0[/tex] 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 :smile:
 
  • #8
Taking X along incline will be easier!
 
  • #9
cupid.callin said:
Taking X along incline will be easier!

cupid.callin, he is taking X along the incline :frown:
mystmyst said:
Am I supposed to split it into x and y coordinates (I'm using the slope as the x-axis...)
 
  • #10
OH! sorry :bugeye:
 

1. How do I calculate the normal force in a slope system with no friction?

To calculate the normal force in a slope system with no friction, you can use the equation FN = mgcosθ, where FN is the normal force, m is the mass, g is the acceleration due to gravity, and θ is the angle of the slope.

2. What is the purpose of calculating the normal force in a slope system?

The normal force is the force exerted by a surface on an object that is in contact with it. In a slope system, the normal force is important because it is the force that prevents an object from sliding down the slope due to gravity. It also helps to determine the amount of friction needed to keep an object in place on the slope.

3. Can the normal force ever be negative?

No, the normal force can never be negative. It is always a positive value because it is a force that acts perpendicular to the surface and prevents the object from sinking into the surface.

4. How does the mass of an object affect the normal force?

The mass of an object has a direct relationship with the normal force. As the mass of an object increases, the normal force also increases. This is because the weight of the object (mg) also increases, resulting in a higher normal force needed to balance it on the slope.

5. Can the angle of the slope affect the normal force?

Yes, the angle of the slope does affect the normal force. As the angle of the slope increases, the normal force needed to balance the object also increases. This is because a steeper slope exerts a greater gravitational force on the object, requiring a higher normal force to balance it.

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