Static Friction / Need Help Solving for Theta

[DarPodo]

Homework Statement

In the figure a fastidious worker pushes directly along the handle of a mop with a force F. (Note: For picture, imagine a worker standing in the second quadrant pushing the mop head into the origin) The handle is at an angle θ = 23.58° with the vertical, and 0.30 and 0.22 are the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop's mass m = 0.40 kg is in its head. If the mop head moves along the floor with a constant velocity, then what is F?

Given:
θ = 23.58°
u(static) = 0.30
u(kinetic) = 0.22
m = .4kgI have solved for the first part of the question. My answer (which is verified correct) is 4.35 N.

I have having trouble solving part 2:

Show that if θ is less than a certain value θ0, then F (still directed along the handle) is unable to move the mop head. Find θ0.

Homework Equations

Finding the angle for the second part I used:

u_s*(Fcosθ+(m*g)) - Fsinθ = 0

The Attempt at a Solution

After using the above equation with my TI-83 solver function my answer was 31.7 deg. My homework answer program (CAPA) said that it was wrong. I then used the quadratic formula and ended up with the same answer. FINALLY, I consulted with my brother, a Physics Professor, and he agreed that all of my work was correct and my answer was good.

So... Can someone spot an error? I used two different methods, received the same answer, and even consulted a Professor (my own Professor does not offer much help).

 

[fizzynoob]

static friction is not like kinetic friction

for kinetic you can say: f_{k} = \muk * N

for static it is : f_{s} <= \mus * N

 

[DarPodo]

static friction is not like kinetic friction

for kinetic you can say: f_{k} = \muk * N

for static it is : f_{s} <= \mus * N

I know equations.

For part two the question is referring to static friction because the mop is at rest.

 

[fizzynoob]

Yes, you can't simply say Fs = (uk) * N. Which i see you did

 

[PhanthomJay]

What is part 2 of the question? I don't see it in the original post.

 

[DarPodo]

What is part 2 of the question? I don't see it in the original post.

I am embarrassed... I just updated my original post with the trouble I am having.

 

[DarPodo]

Yes, you can't simply say Fs = (uk) * N. Which i see you did

To solve for part 1 I used F_friction = u_s*N

I don't see anywhere in my work where I had static friction = coeff. of kinetic * N

Sorry if I was misleading with my post - I updated it after someone pointed out I had forgot the actual problem I was having.

 

[PhanthomJay]

To solve for part 1 I used F_friction = u_s*N

You did? If it's moving at constant velocity, you should have used u_k*N. I think you may have, but recheck your math. Then when you solve for the correct value of F, your method of solving part 2 appears correct. That TI-83 sure came in handy!

 

[DarPodo]

You did? If it's moving at constant velocity, you should have used u_k*N. I think you may have, but recheck your math. Then when you solve for the correct value of F, your method of solving part 2 appears correct. That TI-83 sure came in
handy!

Ugh! Yes you're right, and I used kinetic, not static, for part 1... But I still am curious as to why my result of 31.7 deg is wrong. I was hoping someone could spot something wrong with my equation to part 2.

 

[PhanthomJay]

The 31.7 degree angle with the vertical looks corect to me. That appears to be the angle, at or below which, the 4.35 N force cannot move the mop forward, until it is set in motion by a greater force ( or larger angle), in which case kinetic friction takes over, and the angle can be reduced to 23.58 degrees to keep it moving at constant velocity.