Exhibit 3-1

The three forces shown act on a particle. Use this exhibit to answer the following question(s)..
-Refer to Exhibit 3-1.What is the direction of the resultant of these three forces?
A)35$\degree$
B)45$\degree$
C)65$\degree$
D)55$\degree$
E)85$\degree$

Question

Exhibit 3-1

The three forces shown act on a particle.  Use this exhibit to answer the following question(s)..
-Refer to Exhibit 3-1.What is the direction of the resultant of these three forces?
A)35$\degree$ 
B)45$\degree$ 
C)65$\degree$ 
D)55$\degree$ 
E)85$\degree$

Quizplus · Accepted Answer

The resultant of the three forces is in the direction of the vector sum of the three forces. The vector sum of the three forces is:F1 + F2 + F3 = (F1 cos 30°) + (F1 cos 45°) + (F1 cos 60°) = F1 (cos 30° + cos 45° + cos 60°) = F1 (√3 + 1 + 1/2) = F1 (2√3 + 3/2)The direction of the resultant is therefore:θ = tan^-1 (F1 sin 30° / F1 (2√3 + 3/2)) = tan^-1 (1 / (2√3 + 3/2)) = 35°

Exhibit 3-1 the Three Forces Shown Act on a Particle

Exhibit 3-1

the Three Forces Shown Act on a Particle