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Finding the applied force at an angle?

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    A 2000 kg car is driving up a 20° grade at a speed of 85 km/h. What force must be applied to the car to accelerate it up to 100 km/h in 10s?

    m= 2000 kg
    θ= 20°
    Vo= 85 km/hr = 23.6 m/s
    Vf = 100 km/hr = 27.8 m/s
    t = 10 s

    2. Relevant equations
    F = ma (Fx = max)
    Fx= Fcosθ
    Vox = Vo cosθ
    Voy = Vo sinθ
    Vx = Vox + axt
    Vx= Vox +axt

    3. The attempt at a solution
    I found these using the cos or sin equations above:
    Vox = 22.1 m/s
    Voy = 8.07 m/s
    Vx = 26.1 m/s
    Vy = 9.51 m/s

    Using the last equation, I found ax = 0.4 m/s2

    Fx= 800 N

    I then solved for F using the second equation by dividing Fx by cosθ, making F= 851 N. I think I did something wrong when I solved for a, and my guess is that I couldn't use 10s for that since it was the incline, when I used it for the x values. I'm stuck on how to fix it, or on how to solve the problem a different way. These are practice problems that I have the answers to, but no solutions, so I know that F=7.5 kN.

    I tried working backward and got that a=3.75 m/s2 and ax=3.52 m/s2. Using F=ma and the cos, I got Fx = 7040 N, which gets me the right answer however I do it. This makes me fairly certain that I'm doing something wrong with getting the acceleration.

    Thanks in advance!
     
  2. jcsd
  3. Oct 26, 2014 #2

    PhanthomJay

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    Science Advisor
    Homework Helper
    Gold Member

    you are making the problem complex by not choosing the x axis parallel to the incline and the y axis perpendicular to the incline. You are also not noting that it is the net force that produces the acceleration , not just the applied force, regardless of how you choose your axes. Draw a free body diagram.
     
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