1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: The sums of forces along x and y

  1. May 8, 2006 #1
    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.
    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]
    [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.

    Attached Files:

    Last edited: May 8, 2006
  2. jcsd
  3. May 9, 2006 #2
    If the person's hands aren't slipping then ignore the coeffecient of friction between the hands and the box for now.

    Now resolve your forces:

    In the y direction:
    [tex]F_a*cos(A) - mg - N = 0 [/tex] N is normal reaction between box and ceiling
    [tex]N = F_a*cos(A) - mg[/tex]

    In the x direction:
    [tex]F_a*sin(A) - \mu*N = 0 [/tex]
    [tex]F_a*sin(A) - \mu(F_a*cos(A) - mg) = 0[/tex]

    Now as far as the coeffecient of friction between the hands and the box, this should be a limiting condition.

    [tex]F_a*sin(A) < F_a*cos(A)*\mu[/tex]
    [tex]A < Tan^-1(\mu)[/tex], so the above equations only hold true if this condition is met.
  4. May 9, 2006 #3
    The force along the x direction in your problem is incorrect because the friction between the box and the hands is important to the problem overall.

    However in bug fixing your problem I was able to see where I went wrong so thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook