Find force required to move pole with static friction

[bkw2694]

Homework Statement

The uniform 14-ft pole weighs 150 lbs and is supported as shown. Calculate the force P required to move the pole if the coefficient of static friction for each contact location is 0.40.

(Sorry for the sideways images!)
[/B]

Homework Equations

1.) F_max = μ_s*N
2.) ∑M = 0
3.) ∑F_x = 0
4.) ∑F_y = 0

The Attempt at a Solution

Step 1[/B]
I began by setting up a FBD (shown below). At points A and B I have a Normal force N and friction force F. I placed the weight vector (150 lbs) in the middle of the 14 ft beam (so 7 ft). I calculated the angle closest to point B in order to find the x-direction distance to the weight vector (which I found to be 5.6 ft).

Step 2
Next I took the moment at point B, which gave me (-8)(N_A) + (-5.6)(-150) - (6)(F_A) = 0.

Based on equation #1 I assumed F_A = (.40)(N_A), so I used that to find N_A = 80.769 lbs

Step 3
Using ∑Fy = 0, I found N_A + N_B - 150 = 0 to find N_B = 69.230 lbs

Step 4
∑Fx = 0: ⇒ F_A + F_B - P = 0, which I found P = 60.

My book says the answer is 118.5 lbs, so I know I'm way off, but I'm not sure where exactly. I'm thinking I'm off somewhere in my FBD, but could be elsewhere too.

 

[haruspex]

What is meant by a "normal" force? Which way is the normal force when a point contacts flat or curved surface?

 

[bkw2694]

What is meant by a "normal" force? Which way is the normal force when a point contacts flat or curved surface?

After thinking about it, I realize that it's force perpendicular to the surface, so I F_A direction would need to be perpendicular to the corner it's sitting on? And would the friction force then be perpendicular to the normal force? If that's the case, how would I go about solving for the magnitude of F_A and F_B without knowing the angle?

 

[haruspex]

After thinking about it, I realize that it's force perpendicular to the surface, so I F_A direction would need to be perpendicular to the corner it's sitting on? And would the friction force then be perpendicular to the normal force? If that's the case, how would I go about solving for the magnitude of F_A and F_B without knowing the angle?

Yes, except that it doesn't mean anything to say 'perpendicular to the corner'. You mean perpendicular to th surface, so friction is parallel to the pole.
You know the angle from the given lengths, but there's no point in calculating the angle as such. You will only need trig functions of the angle, and these can be derived directly from the lengths.
A tip: always work algebraically as far as possible, only plugging in numbers at the final step. It minimises rounding errors and maximises comprehensibility. It often reduces effort too, since some variables might cancel out.

 

[bkw2694]

Yes, except that it doesn't mean anything to say 'perpendicular to the corner'. You mean perpendicular to th surface, so friction is parallel to the pole.
You know the angle from the given lengths, but there's no point in calculating the angle as such. You will only need trig functions of the angle, and these can be derived directly from the lengths.
A tip: always work algebraically as far as possible, only plugging in numbers at the final step. It minimises rounding errors and maximises comprehensibility. It often reduces effort too, since some variables might cancel out.

That got it, thanks again! I see what you mean about working algebraically seeing as I ended up with 118.66 due to rounding errors, but that's definitely the right method.