Question

two forces act on an object. a 36 n force acts at 225° , A 48-N force acts at 315°. what would be tge magnitude and directionof their equilibrant?

Answer 1

Let's first find $x$- and $y$-components of resultant force:

$$F_x=36\ N\cdot cos225^{\circ}+48\ N\cdot cos315^{\circ}=8.48\ N,$$ $$F_y=36\ N\cdot sin225^{\circ}+48\ N\cdot sin315^{\circ}=-59.4\ N.$$

We can find the magnitude of the resultant force acting on an object from the Pythagorean theorem:

$$F=\sqrt{F_x^2+F_y^2}=\sqrt{(8.48\ N)^2+(-59.4\ N)^2}=60\ N.$$

We can find the direction of the resultant force acting on an object from the geometry:

$$\theta=sin^{-1}(\dfrac{F_y}{F})=sin^{-1}(\dfrac{-59.4\ N}{60\ N})=278^{\circ}.$$

The resultant force directed at $278^{\circ}$ counterclockwise from the positive $x$-axis.