I have a problem I'm working on where the general premise is that there is a box being pushed along the ceiling at a constant speed. The force F is at some angle with respect to the vertical. There is a coefficient of kinetic friction between the box and the ceiling and the persons hands and the box. The latter of which keeps the persons hands from slipping.(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to be deliberately vague because I want help on the concept not the problem itself.

A = angle

[tex]F_a[/tex] = Force along the angle A

[tex]\mu_k[/tex] = coefficient of friction along the ceiling

[tex]\mu_{k2}[/tex] = coefficient of kinetic friction with persons hands

My thinking is that

[tex]\sum f_x = f_a*sinA - ff = 0 \Rightarrow f_a*cosA = \mu_k*N + \mu_{k2} *N[/tex]

and

[tex]\sum f_y = f_a*cosA - mg - n = 0[/tex]

Is there a flaw in my logic? Because when I put in all the information my result is unrealistic. I have attached the free body that goes along with my thinking.

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# The sums of forces along x and y

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