Answer to Question #244550 in Physics for Asmar

Question

The helicopter view in Fig. 2 shows two people pulling on a stubborn mule. Find (a) the single force

that is equivalent to the two forces shown, and (b) the force that a third person would have to exert on the mule to make

the resultant force equal to zero. The forces are measured in units of newtons (abbreviated N).

Answer 1

(a) In the photo we see two farmers pulling the mull at 90° angle. The single force that is equivalent to the two forces is

$$F=\sqrt{F_1^2+F_2^2}$$

directed at

$$\theta=\arctan\frac{F_1}{F_2}$$

from F2 toward F1.

To make the resultant zero, the third farmer must pull with the third force F₃ directed in the opposite direction from F at the same magnitude, or apply force F found above at $\theta+180°$ from F2 thru F1.