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Motion on an incline plane (detailed)

  1. Jul 10, 2011 #1
    Hey, folks! I've been working on this one problem for the past little bit. It has been giving me a lot of trouble and I think i just need a pointer or two on how to go about solving it.

    http://i.imgur.com/nTGVz.jpg"


    1. The problem statement, all variables and given/known data

    It's not the best image, but it gives the basic idea. I have two masses on an inclined plane connected with a cord over a pulley (kinetic friction included). It wants me to first solve for the acceleration in the system and then find the tension. The second part asks for me to find the final velocity after the masses have moved 1.00m (starting at rest)

    mass #1 - 27.2 kg
    mass #2 - 12.5 kg
    theta - 5.23 deg
    kinetic friction - 0.17


    2. Relevant equations

    [itex]\sum[/itex]Fx = max
    [itex]\sum[/itex]Fy= may

    ax = ay


    ramp (mass #1):
    [itex]\sum[/itex]Fx = -Ff - T + w1sin(theta) = max
    [itex]\sum[/itex]Fy= Fn - w1cos(theta) = max

    hanging weight (mass #2):
    [itex]\sum[/itex] T - w2=max


    3. The attempt at a solution

    T=m2a+w2
    T=12.5a + 122.625

    Fn= m1a+ w1
    Fn= 27.2a+ 265.721

    Sub values in:

    -Ff - T + w1sin(theta) = max

    Ff = (co-efficient x Fn)

    -(27.2a+265.721)0.17 -(12.5a + 122.625) + (27.2 x 9.81x sin of 5.23) = 27.2a

    combine values:

    44.324a= -143.48

    a= -3.24 m/s sq

    T= 12.5a + 122.625
    T=12.5(-3.24) + 122.625
    T= 82.1 N

    I solved the first part of this equation by resolving my Fx and Fy into their components and then solving for T and Fn (normal). I then substituted my T and Fn back into my Fx and solved for my acceleration. The answer I got was -3.24 m/s sq.

    Now with the second part of this problem i seem to be a little stuck. I am thinking i cannot use the traditional Vfsq= Visq + 2as (correct me if i am wrong). Since there is friction involved (kinetic =0.17) (static = ?) i somehow need to incorporate that as well as my components into my velocity equation but i am unsure on how to do this. If anyone has any tips on how to calculate the velocity it would be much appreciated. I am not looking for *the* answer, i just need some pointers

    Thank you!
     
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
  3. Jul 11, 2011 #2

    gneill

    User Avatar

    Staff: Mentor

    Hi thomsora, welcome to PF.

    Your value for the acceleration looks a bit high. Also, I'm not quite following your methodology; it looks to me like some of your force directions are mixed up. For example, on mass one (on the slope), shouldn't the frictional force OPPOSE the downslope force due to gravity of m1 AND the tension applied by the rope? Did you draw a Free Body Diagram for each mass?
     
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