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

[mazia]

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!

 

[erobz]

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.

 

[kuruman]

A magnitude is always positive.

 

[Steve4Physics]

And in addition to what @erobz 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.