Question

You are planning to built a log cabin and will need to pull the logs up a hill to the building site by means of a rope attached to a winch. In order to buy the rope, you need to know how strong the rope must be and decide to do a quick calculation for this. The log's weight is W = 2250 N at most, and the hill is at an angle of 30 degrees with respect to the horizontal. You estimate that 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 that a = 0.80 m/s^2. How much force must the rope be able to withstand?

Answer 1

Answer:3062.37 N

Explanation:

Given

log weight =2250 N

$\theta =30$

coefficient of kinetic friction $\mu =0.9$

$a_{max}=0.80 m/s^2$

During Pulling Forces on cable is log sin component and friction and tension (T)

$T-mg\sin \theta -f_r=ma$

$T=2250\sin (30)+\mu 2250 \cos (30)+\frac{2250}{g}\times 0.8$

T=1125+1753.70+183.67=3062.37 N

so Rope must be able to withstand a force of 3062.37 N