Calculating normal force for wedge

[PhySci83]

Homework Statement

Prove that normal force between a block and wedge is: N = m*sqrt(g^2-a^2)

Homework Equations

I used the pythagorean theorem to attempt this.

The Attempt at a Solution

See attached.

Am I doing this right, or am I making up math here to fit the answer?

 

[rock.freak667]

I think that is correct but that is only for the given case when a=gsinθ. (Which is correct as your free body diagram is showing)

 

[PhySci83]

Thanks for your help!

 

[iRaid]

$F_{N}=F_{g}sin\theta$

 

[ElijahRockers]

Looks right. I assume you are wondering about pulling the m from the square root. It may be the long way around, but try expanding.

$$N^2 = (mg)^2-(ma)^2$$

can be expanded into:

$$N^2 = mmgg-mmaa$$

factor out the m squared:

$$N^2 = mm(gg-aa)$$
$$N^2 = m^2(g^2-a^2)$$

Take the square root of both sides (raise both sides to the half power):

$$N = \sqrt{m^2(g^2-a^2)}$$
$$N = m\sqrt{g^2-a^2}$$

I know this is a long winded response to a relatively simple question, but I am new to helping on the forums and trying to figure out how to use LaTeX. Sorry I am just a beginner myself, but I hope it may give you some insight into the math involved.