1. Not finding help here? Sign up for a free 30min 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!

At what angle of force is Kinetic friction least?

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known data
    The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction Uk is least when the force is applied at an angle theta such that

    a.sin(theta) = Uk.

    b.cos(theta) = Uk.

    c.tan(theta) = Uk.

    d.cot(theta) = Uk.

    e.sec(theta) = Uk.

    2. Relevant equations
    F = ma
    Ff = Uk * Fn = m*g*Uk
    Fx = F *cos(theta)
    Fy = F*sin(theta)

    3. The attempt at a solution
    First the answer is d. cot(theta) = Uk
    I tried to solve it, but couldn't figure it out...
    This is my work
    Since it is dragged at constant speed, the acceleration is 0. So a = Ftotal/m = 0
    Ftotal = F*cos(theta) - (mg - F*sin(theta))Uk = 0
    F*cos(theta) / (mg - F*sin(theta)) = Uk... which is wrong...
    Can anyone help me?
     

    Attached Files:

  2. jcsd
  3. Mar 25, 2015 #2

    Doc Al

    User Avatar

    Staff: Mentor

    So far, so good.

    Realize that F is a function of theta. You'll need a bit of calculus to figure out the value of theta that minimizes F.

    Question: Did they give a diagram defining the angle theta?
     
  4. Mar 25, 2015 #3
    They did not give me any diagram defining the angle theta.. Can you help me out little bit more using calculus?? I still don't get it :(
     
  5. Mar 25, 2015 #4

    Doc Al

    User Avatar

    Staff: Mentor

    How would you use calculus to find the max or min of a function?
     
  6. Mar 25, 2015 #5
    You derive the function and make it as a 0 ??
     
  7. Mar 25, 2015 #6

    Doc Al

    User Avatar

    Staff: Mentor

    Yes! You'll set the derivative (##dF/d\theta##) equal to zero and solve for ##\theta##.

    Hint: What you have will require implicit differentiation.
     
  8. Mar 25, 2015 #7
    I need one more hint! What equation do I have to set the derivative??
    F*cos(theta) / (mg - F*sin(theta)) = Uk
    This one??
     
  9. Mar 25, 2015 #8
    Ftotal = F*cos(theta) - (mg - F*sin(theta))Uk = 0
    Oh nevermind it will be this one right?
     
  10. Mar 25, 2015 #9
    I don't think this requires calculus. Just some algebraic manipulation.
     
  11. Mar 25, 2015 #10
    Ok... I tried my best... and got tan(theta)..... Ughhhh why is this so hard to me
     

    Attached Files:

  12. Mar 25, 2015 #11
    Can you help me out???
     
  13. Mar 25, 2015 #12
    Were you assigned this problem in a calculus based physics class?
     
  14. Mar 25, 2015 #13
    Nope. I'm studying physics by myself so I can take AP physics on May! I don't have anyone to ask questions beside here and I got this questions from internet!
     
  15. Mar 25, 2015 #14
    Try solving for the coefficient of kinetic friction in terms of F and itself. You can then substitute this value ...somewhere...
     
  16. Mar 25, 2015 #15
    Also, I believe you made a sign error in your forces.
     
  17. Mar 25, 2015 #16

    Doc Al

    User Avatar

    Staff: Mentor

    Given how you defined theta, I would say that was correct. (That's why I asked if you had been given a diagram.)
     
  18. Mar 25, 2015 #17
    Ahh physics is killing me hahaha
     
  19. Mar 25, 2015 #18
    So when do I get cot(theta)?? where does the theta have to be to get an answer cot(theta)??
     
  20. Mar 25, 2015 #19

    Doc Al

    User Avatar

    Staff: Mentor

    Since cot(theta) = 1/tan(theta), you'd get cot(theta) if you let theta = angle with the vertical.

    Where did you find the problem?
     
  21. Mar 25, 2015 #20
    I found this question from internet! I think this question is based on the book "Physics for scientist and engineers" Serway and Jeweet, but I already read the book and couldn't find anything that explains this problem haha
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted