posted by nate on .
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?
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.