problem 1.8 - express the 260 - n force in terms of components perpendicular and parallel to the inclined…

Explanation:

Step1: Calculate the hypotenuse of the right - triangle

The sides of the right - triangle are 5 and 12. By the Pythagorean theorem, the hypotenuse $r=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13$.

Step2: Find the component parallel to the inclined plane

The component of the force parallel to the inclined plane $F_{parallel}=F\times\frac{12}{13}$. Substituting $F = 260$ N, we get $F_{parallel}=260\times\frac{12}{13}=240$ N.

Step3: Find the component perpendicular to the inclined plane

The component of the force perpendicular to the inclined plane $F_{perpendicular}=F\times\frac{5}{13}$. Substituting $F = 260$ N, we get $F_{perpendicular}=260\times\frac{5}{13}=100$ N.

Answer:

The component parallel to the inclined plane is 240 N and the component perpendicular to the inclined plane is 100 N.