5) (6 points) An object is acted on by three forces. All three forces have exact

Question

5) (6 points) An object is acted on by three forces. All three forces have exactly the same magnitude. Two of the forces are perpendicular and the third acts at an angle as shown above. No other forces act on this object. Which of the following is true? For full credit, explain your answer 1) It is possible for this particle to remain at rest 2) It is not possible for this particle to remain at rest. 3) You cannot answer this question without knowing the value of the angle 0 4) You cannot answer this question without knowing both the value of the angle 0 and the magnitude of the forces F 0

Explanation / Answer

As we can see in the figure, for any wale of angle O

from force balance, net force in x direction = F(cos(O) - 1)

from force balance, net force in y direction = F(sin(O) - 1)

so net force on the particle = F' = F*sqroot((cos(O) - 1)^2 + (sin(O) - 1)^2)

F' = F*sqroot(cos^2(O) + 1 - 2cos(O) + sin^2(O) + 1 - 2sin(O))

F' = F*sqroot(3 - 2(cos(O) + sin(O))))

for the object to be at rest F' = 0

so, 3 = 2(cos(O) + sin(O))

1.5 = cos(O) + sin(O)

2.25 = 1 + sin(2O)

1.25 = sin(2O), but this cvant be true

hence for any value of O this particle cannot be at rest

2) It is not possible for the particle to stay at rest

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.