Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem Problem_78

Moving heavy logs. Here is a way to move a heavy log through a tropical forest. Find a young tree in the general direction of travel; find a vine that hangs from the top of the tree down to the ground level; pull the vine over to the log and wrap it around a limb on the log; pull hard enough on the vine to bend the tree over; and then tie off the vine on the limb. Repeat this procedure with several trees. Eventually the net force of the vines on the log moves the log forward. Although tedious, this technique allowed workers to move heavy logs long before modern machinery (such as helicopters) was available. Figure 12.67 shows the essentials of the technique. There a single vine is shown attached to a branch at one end of a uniform log of mass \( M \). The coefficient of static friction between the log and the ground is 0.80. If the log is on the verge of sliding, with the left end raised slightly by the vine, what are (a) the angle \( \theta \) and (b) the magnitude \( T \) of the force on the log from the vine?