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

[mdcreator]

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 :-

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 :-

[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!

 

[Doc Al]

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.)

Shouldn't it be same no matter how we calculate it?

Only if you calculate correctly.

 

[Lnewqban]

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!

 

[mdcreator]

So it really was a pretty dull question