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Finding max acceleration with force at angle incl friction

  1. Apr 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Hey. I was doing some exam practice questions, but I hit a snag with this one and can't quite work out how to proceed.

    A 6kg block at rest is pulled along a horizontal surface by force F→ at angle θ. Given that the coefficient of kinetic friction is 0.15, find the optimal angle at which to apply the force to achieve maximum acceleration.

    2. Relevant equations
    F = ma
    fk = μkN
    F→2 = F2sin2θ + F2cos2θ


    3. The attempt at a solution
    N = mg - Fsinθ
    μk = 0.15/58.86
    fk = (2.55×10-3)(mg-Fsinθ)
    Fnetx = Fcosθ - fk
    ax = (Fcosθ - fk)/m

    From here I guess I need to form a differential equation and solve for maximum but this leads to θ being a ridiculous angle. Any advice? (P.S, sorry if this is in the wrong section, still trying to gauge the levels of physics being done in each)
     
  2. jcsd
  3. Apr 18, 2015 #2
    You just have to take the derivative of ##a_x## with respect to ##\theta## and set it to 0 and solve the equation involving ##\theta##, that is to solve ##\frac{da_x}{d\theta}=0##.
     
  4. Apr 19, 2015 #3
    Still getting a weird value for θ while solving for the maximum. Will work through and check my values, but can we confirm that the logic is sound?
     
  5. Apr 19, 2015 #4
    Do you get ##tan(\theta)=\mu_k## at the end? Why is this weird, since the friction coeeficient is small we expect theta to be small also (if friction coefficient was zero it would be theta=0 as can be understood easily).

    There is something i dont understand why you divide 0.15 / 58.86 for ##\mu_k##?
     
  6. Apr 19, 2015 #5
    My bad. Playing catch up at the moment and only started looking at this concept today. Another look at the derivative and I can see the manipulation. Thanks for the help
     
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