Question(s) Regarding Magnitude of Force (Window Washer Problem)

AI Thread Summary
The discussion revolves around calculating the magnitude of force in a window washer problem, specifically addressing the weight of 12.0N, an angle of 53.1 degrees, and a coefficient of kinetic friction of 0.100. The user initially applied the equations for normal force and kinetic friction but encountered errors in their calculations. It is emphasized that the equation for normal force, Fn=mg*cos(theta), is not applicable in this scenario as it pertains to an inclined plane setup. Participants suggest creating a free body diagram to better analyze the forces involved and construct accurate equations. Understanding the context and forces at play is crucial for correct calculations in this problem.
mazia
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Homework Statement
A window washer pushes his scrub brush up a vertical window at constant speed as shown in the figure (Figure 1). The head of the brush (when wet) weighs 12.0 N and the coefficient of kinetic friction between the bristles and the window surface is 0.100.

a) Calculate the magnitude of the force exerted on the head of the brush by the handle of the brush; the direction of the force is as shown in the figure.

b) Calculate the magnitude of the normal force exerted on the brush by the window.
Relevant Equations
f_k=mu_k*Fn
Fn=mg*cos(theta)
So, ignore the -0.72, I was just trying to see if I had a sign error (I then remembered magnitude is absolute value) but basically:

Since the weight is 12.0N, theta is 53.1, and the coefficient of kinetic friction is 0.100, I just plugged those values into the equations above:
Fn=(12.0N)*cos(53.1) = 7.21N (which was wrong as well, per question B), and f_k=(0.100)*(7.21).

Both were incorrect but I'm wondering how. It seems pretty cut-and-dry; use the given values, plug them into the equations, and boom. I'm not sure what I'm missing or doing wrong. My calculator is in degrees too. Any help is appreciated, thanks!
 

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You should start by producing a free body diagram of the broom head. "I just plugged in some values to some formulas" is never a good strategy for understanding.
 
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Likes Tomy World and Steve4Physics
A magnitude is always positive.
 
And in addition to what @erobz said...

mazia said:
Relevant Equations: f_k=mu_k*Fn
Fn=mg*cos(theta)
The equation 'Fn=mg*cos(theta)' applies to a mass resting on an inclined plane. That's not the setup here. Use your free body diagram to analyse the horizontal and vertical forces and then construct your own equations.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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