A solid sphere of radius R and mass M is held against a wall by a string being p

Question

A solid sphere of radius R and mass M is

held against a wall by a string being pulled at

an angle . f is the magnitude of the frictional

force and W = M g .

a)To what does the torque equation

about point O (the center of the sphere) lead?

1. F+W= f

2. W= f

3. Fsin(theta)= f

4. F=f

5. Fsin(theta)cos(theta)= f

b)To what does the vertical component of the

force equation lead?

1. Fcos(theta)+W=f

2. Fsin(theta)=f

3. Fsin(theta)+f=W

c)Find the smallest coefficient of friction ?

needed for the wall to keep the sphere from

slipping.

1. u=tan(theta)

2. u=cos(theta)

3. u=1/tan(theta)

4. u=sin(theta)

5. u=1/cos(theta)

6. u=1/sin(theta)

I know this is long, but I've worked on every part and I keep getting the answer wrong. I know it's a lot to ask, but I really need this problem explained.

Explanation / Answer

a)F is trying to rotate it clockwise, so the friction force will try to rotate it anticlockwise and will act upward.

Balancing moments,

F.r=f.r

F=f

4) is correct.

b)This is pretty obvious.

3. Fsin(theta)+f=W

c)The normal force on the wall be N.

Balancing horizontal forces,

N=FCos

f=N=FCos

From a)

f=F

FCos=F

=1/Cos

5) is correct.

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