A chandelier with mass m is attached to the ceiling of a large concert hall by t

Question

A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension t1 and makes an angle of theta1 with the ceiling. Cable 2 has tension t2 and makes an angle of theta2 with the ceiling.
http://session.masteringphysics.com/problemAsset/1010934/37/MFS_1l_3_v1_a.jpg
Find an expression for t1, the tension in cable 1, that does not depend on t2.
Express your answer in terms of some or all of the variables m, theta1, and theta2, as well as the magnitude of the acceleration due to gravity g.

Explanation / Answer

In the vertical direction, the forces are balanced:
Fnet = 0
T1sin1 + T2sin2 = mg

In the horizontal direction, the forces are also balanced:
Fnet = 0
T1cos1 = T2cos2
T2 = T1(cos1)/(cos2)

Using this result in the first equation:
T1sin1 + T2sin2 = mg
T1sin1 + T1(cos1)(sin2)/(cos2) = mg
T1sin1 + T1(cos1)(tan2) = mg
T1(sin1 + (cos2)(tan2)) = mg

T1 = mg / (sin1 + (cos2)(tan2))

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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