Sliding egg I think the books wrong, could someone please verify?

[Beamsbox]

***EDIT***Sorry for a second there, I tried to convince myself that F_N was not equal to _Fg, but it must.

Given the coefficient of static friction (.4) between an egg and a pan, what is the smallest angle from the horizontal taht will cause the egg to slide?

Here's my drawing:

(http://i51.photobucket.com/albums/f362/BeamsBox/PhysicsEgg.jpg)

Here's my work:
x, implying that it's along the x-axis
F_s is static friction force
F_g is the force of gravity
m = mass
a = acceleration
(mue) = .4, the coefficient of friction


F_s(max) = (mue)F_N Equation 1
F_N = mg
Substitute to get:
F_s(max) = (mue)(mg) Equation 2


F_(net)x = ma_x
F_s - F_gx = ma_x

Since it is stationary, a = 0

F_s - F_gx = m(0)
F_s = F_gx Equation 3

Now substitute (mue)(mg) for F_s,
(mue)(mg) = F_gx, and substitute the F_gx from the diagram,
(mue)(mg) = F_gsin(theta), and substitute mg for F_g
(mue)(mg) = (mg)sin(theta), mg cancels out
(mue) = sin(theta), and substitute the known .4 for (mue),
.4 = sin(theta)
theta = sin^-1(.4)
theta = about 23.6 degrees

The book says 2... any ideas on where I may have gone wrong?

 

[D H]

The magnitude of the normal force is not equal to mg.

 

[kuruman]

To elaborate on DH's remark. If the egg is just about to slide, it is still at rest and the sum of all the forces on it must be zero. Look at your drawing. For the sum of the three vectors to be zero, the magnitudes of the vectors must form a closed triangle. F_g is the hypotenuse and F_n one of the right sides. Can they be equal? What is it that must be equal instead?

 

[Beamsbox]

F_N = F_gcos(theta)... that seems to make more sense.

 

[kuruman]

Can you finish the problem now?

 

[Beamsbox]

Ya, I figured it out... finally thanks again.