What is the Absolute Value of the Normal force on a block on this wedge?

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Discussion Overview

The discussion revolves around the calculation of the normal force acting on a block of mass M placed on a wedge, specifically exploring two different methods of deriving this force using Newton's Laws of motion. The focus includes the theoretical aspects of force balance in different coordinate systems.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents two methods for calculating the normal force, resulting in different values: N = mg/cos(theta) and N = mg.cos(theta).
  • The first method involves balancing forces in the vertical direction, which the participant later questions as potentially incorrect due to the block's acceleration down the incline.
  • The second method involves balancing forces perpendicular to the incline, which is suggested to be the correct approach.
  • Another participant challenges the first method's assumption about force balance, indicating that it leads to an incorrect conclusion.
  • The discussion includes a light-hearted acknowledgment of the question's perceived simplicity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the first method, with one participant asserting it is incorrect while another maintains that both methods should yield the same result if calculated correctly.

Contextual Notes

The discussion highlights potential misunderstandings in applying Newton's Laws and the importance of correctly identifying the forces acting on the block in different coordinate systems. There are unresolved assumptions regarding the block's motion and the conditions under which the normal force is calculated.

mdcreator
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So i have been solving problems of Newton's Laws of motion and this thing has been quite conflicting for me. I wont complicate my question. I just need one answer.

What is the absolute value of normal force on a block of mass M on a wedge?

I know it seems a pretty dull question but here me out!

I am getting 2 different values of normal using 2 different ways.

1st Method :-
images (1).png

Here, I balance out forces in vertical direction by taking a component of N in vertical direction. So here the value comes out to be,

N = mg/cos(theta)

2nd method :-
images.png


[Theta is still theta i just couldn't find appropriate image to put up]

Here, I balance out forces by taking a component of mg in direction on N.
(Basically rotating the coordinate axis in which i am balancing forces)
So here, N comes out to be,
N = mg.cos(theta)

So, In both of my methods, The block is same, wedge is same and the scenario in which i am calculating Normal is also same! So Why? Why do we have 2 different values of N?
Shouldn't it be same no matter how we calculate it?

This question may be silly but please!! If you can, Satisfy my curiosity!
 
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mdcreator said:
So, In both of my methods, The block is same, wedge is same and the scenario in which i am calculating Normal is also same! So Why? Why do we have 2 different values of N?
We don't, of course. In your first method, you assumed that forces balance in the vertical direction. Nope! (Assuming the usual setup, the block will accelerate down the incline.)

In your second method, you correctly assumed forces balance perpendicular to the incline. (Good thing, else the block would fly up or go through the wedge.)

mdcreator said:
Shouldn't it be same no matter how we calculate it?
Only if you calculate correctly. :wink:
 
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mdcreator said:
So i have been solving problems of Newton's Laws of motion and this thing has been quite conflicting for me.
...
What is the absolute value of normal force on a block of mass M on a wedge?
...
This question may be silly but please!! If you can, Satisfy my curiosity!
Sliding block on wedge 1.jpg


Sliding block on wedge 2.jpg


Sliding block on wedge 3.jpg


Sliding block on wedge 4.jpg
 

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So it really was a pretty dull question 😅
 
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