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Math Help - Velocity as a function of time

  1. #1
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    Velocity as a function of time

    Please explain how to interpret this graph as well as the rest of the problem. Thank you!



    Two horizontal forces 1 and 2 act on a 3.0 kg disk that slides over frictionless ice, on which an xy coordinate system is laid out. Force 1 is in the positive direction of the x axis and has a magnitude of 6.7 N. Force 2 has a magnitude of 9.0 N. Figure 5-34 gives the x component vx of the velocity of the disk as a function of time t during the sliding. What is the angle between the constant directions of forces 1 and 2?
    Fig. 5-34
    Problem 12.
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  2. #2
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    This problem asks to to relate kinematics (motion) and dynamics (forces). This should instantly make you think Fnet=m*a. Mainily we are woried about the x component, though, so we'll say Fnet_x = m*a_x.

    Now, you should know, that acceleration is a derivative of velocity, and that on a graph, the derivative is the slope. so a = dv/dx = rise/run = 6/2 = 3 m/s^2.

    now, we have a mass of 3.0 kg, and an acceleration of 3m/s^2, so Fnet_x = 3*3 = 9N.

    now, its a matter of adding the forces:
    Fnet_x = F1_x + F2_x

    F1 is along the X axis:
    F1_x = F1 = 6.7N
    F2 is not so we multiply its magnitude by cos(theta):
    F2_x = F2*cos(th) = 9N*cos(th)
    and we already know:
    Fnet_x = 9N

    we plug these back into the above equation:
    9N = 6.7N + 9N*cos(theta)

    now its an algebra problem:
    9N*cos(th) = 9N - 6.7N = 2.3N
    cos(theta) = 2.3N/9N = .255555555555
    theta = arccos(.255555555555) = 75.19 degrees
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