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    Homework 5-1
    Due date: Mon 22 Mar 2004 09:00:00 AM MST
    18 point(s)
    Pulling Out Tree Stump
    You are in a truck trying to pull out a tree stump. The mass
    of the tree stump m is 170.0 kg. You have attached the winch
    at the front of the truck to the tree as shown in the diagram
    As you try to pull out the stump with the truck, the winch ex-
    erts a time dependant force with magnitude: Fws(t) = F0ebt
    where F0 and b are constants, and t is the time since the
    winch began pulling. If the force necessary to remove the
    trunk is Fout, how long will it take to pull out the stump?
    Use the following values in your calculation: F0 = 20.0 N
    b = 4.1 s��1
    Fout = 17000.0 N
     = 51.0 degrees
    tout =
    You are correct. Your receipt is 480-1079
    Find the work done on the stump from the time that you
    start pulling the stump with the truck until the time that the
    stump comes out from the ground.
    Wout =
    Tries 16/99
    Also, nd the power delivered to the stump at half the time
    from when the truck starts to pull to when the stump breaks
    free (tout=2).
    Pout =
    Tries 0/99
    Once the stump breaks free, all horizontal forces on the stump
    except the force from the cable are negligible for a time, and
    the force from the wire as a function of position becomes:
    Fws(x) = Fout
    8 [1+7e��cx] where Fout is the same as above, c is
    a constant, and x is the distance that the stump has traveled.
    After you pull out the stump, you drag it a horizontal distance
    x1 with the truck. Find the work done on the stump by the
    winch from when it started moving until it reaches a distance
    x1. The stump does not come o the ground during this
    time, and the angle doesn't change. Use the following values
    in your calculation: c = 7.0 m��1
    x1 = 3.9 m
     = 51.0 degrees W1 =
    Tries 0/99
    Find the speed of the stump when it is at position x1. Re-
    member, all horizontal forces on the stump are negligible ex-
    cept the force from the cable until after the stump has traveled
    past x1.
    v1 =
    Tries 0/99

    Homework 5-1
    What is the power being delivered to the stump by the cable
    when it is at the position x1?
    P1 =
    Tries 0/99

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    Solution Preview

    1. Force on the block F = F(t)Cos(90-51) = 0.777 F(t)

    The block will come out when the force F(t) reaches Fout = 17000 N

    We will write, 17000 N = 0.777 * Fo Exp(bt)

    Or, Exp(bt) = 17000/(0.777*20) where b = 4.1/sec

    exp(4.1 t) = 1093.95

    or, 4.1 t = ln(1093.95)

    ===> t = 6.997/4.1 = 1.7 Sec ---Answer

    2. Workdone = force x displacement

    Also work done = change in Kinetic enegy of the stump

    If we know the force as a function of time, then we can get the velocity of the mass after a time t from Newton's law.

    m dv/dt = F(t)

    dv = (1/m) F(t)dt

    V = integral from time t=o to t=1.7 of this value

    = (1/m) int(0 to 1.7) 0.777 ...

    Solution Summary

    Solution gives all mathematical steps.


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