Chapter 8.5, Problem 30E

To determine

To Find:Which method will result in the greatest force applied to the stump?

Answer to Problem 30E

Method (b)

Explanation of Solution

Given:

(a)Tie the rope to the stump and pull.

(b)Tie one end to the stump and other end on the nearby pole. Then pull on the rope perpendicular to it at a point about half way between the two.

Let $F$ be the force exerted by the tractor and $T$ be the tension in two half.

Let $x$ be the angle between the original line of the rope and the half of the rope after pulled.

Therefore

At equilibrium

  $\begin{array}{l}2T\sin x-F=0\\ T=\frac{F}{2\sin x}\\ thus\\ if{0}^{°}<x<{30}^{°}\end{array}$

Thus the force applied using the method (b) is greater than the force exerted by the tractor.

Hence, method (b).