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You are planning to build a log cabin in northern Minnesota. You will pull the logs up a long, smooth hill to the building site by means of a rope attached to a winch. You need to buy a rope for this purpose, so you need to know how strong the rope must be. Stronger ropes cost more. You know that the logs weigh a maximum of 188 kg. You measure that the hill is at an angle of 30o with respect to the horizontal, and the coefficient of kinetic friction between a log and the hill is 0.90. When pulling a log up the hill, you will make sure that the rope stays parallel to the surface of the hill and the acceleration of the log is never more than 0.74 m/s2. How strong a rope should you buy?

  • physics -

    Wl = mg = 188kg * 9.8N/kg = 1842 N. =
    Wt. of Log.

    Fl = 1842N @ 30o =Force of Log.
    Fp = 1842*sin30 = 921 N.=Force parallel to hill.
    Fv = 1842*cos30 = 1595 N. = Force perpendicular to the hill.

    Fk = u*Fv = 0.9*1595 = 1436 N = Force of kinetic friction.

    Fn = Fap-Fp-Fk = m*a.
    Fap-921-1436 = 188*0.74
    Fap-2357 = 139
    Fap = 139+2357 = 2496 N.=Force applied.
    = Strength of rope.

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