• Support PF! Buy your school textbooks, materials and every day products Here!

Tension chandelier problem

  • Thread starter ijd5000
  • Start date
  • #1
7
0
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 θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling.

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, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g.


i have for my Forces:

F(x) T2 cos ( θ2)-T1cos(θ1)=0
F(y) T2 sin(θ2)+T1 sin(θ1)-gm=0

not sure how to describe T1 without using T2
 

Answers and Replies

  • #2
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
131
These are two equations in two unknowns, T_1 and T_2.
If you write them as
T_1cos(v_1)=T_2cos(v_2)
T_1sin(v_1)-mg=-T_2sin(v_2)
then dividing the one equation with the other yields:
[tex]\frac{T_{1}\sin\theta_{1}-mg}{T_{1}\cos\theta_{1}}=-\tan\theta_{2}[/tex]

Hurray, T_2 has disappeared!! :smile:
Now, rearrange the last equation, so as to solve for T_1
 
  • #3
7
0
These are two equations in two unknowns, T_1 and T_2.
If you write them as
T_1cos(v_1)=T_2cos(v_2)
T_1sin(v_1)-mg=-T_2sin(v_2)
then dividing the one equation with the other yields:
[tex]\frac{T_{1}\sin\theta_{1}-mg}{T_{1}\cos\theta_{1}}=-\tan\theta_{2}[/tex]

Hurray, T_2 has disappeared!! :smile:
Now, rearrange the last equation, so as to solve for T_1
It's ok to combine equations from different directions? I thought you have to keep x and y seperate until you add the vectors.
 

Related Threads for: Tension chandelier problem

  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
2
Views
9K
  • Last Post
Replies
3
Views
8K
  • Last Post
Replies
3
Views
3K
Replies
2
Views
17K
Replies
5
Views
10K
  • Last Post
Replies
3
Views
1K
Replies
4
Views
11K
Top