Minimal coefficient of friction

[Karol]

Homework Statement

The rectangle in the drawing is held by the horizontal rope and the friction on the wall.
What's the minimal coefficient of friction

Homework Equations

Friction force: f=μN

The Attempt at a Solution

Moments round the point of contact with the wall. the side of the rectangle is a, half the diagonal to the center is $\sqrt {a}$. the distance of the CoM to the wall: $\sqrt {a}\cdot\sin 55^0=1.16a$
$$1.16a\cdot mg=T\cdot \sin 10^0\rightarrow T=6.68mg$$
$$6.68mg\cdot\mu=mg\rightarrow\mu=0.15$$
It should be 0.3

 

[BvU]

So from the wall to the center of mass is 1.16 times the length of a side ? That's in mid-air ! ;)

 

[CWatters]

Is it a square or rectangle? If it's a square check your calculation for "half the diagonal".

 

[Karol]

So from the wall to the center of mass is 1.16 times the length of a side ? That's in mid-air !

I thank you very much BvU for i didn't laugh so much for some time

 

[Brian T]

I believe what you used for the normal force is incorrect.

 

[BvU]

@Brian T: Could you elaborate ?

 

[Karol]

The distance of CoM from the wall: $\frac{a}{\sqrt{2}}\cdot\sin 55^0=0.58a$
$$0.58a\cdot mg=T\cdot \sin 10^0\rightarrow T=3.41mg$$
$$3.41mg\cdot\mu=mg\rightarrow\mu=0.3$$