- #1
-Dragoon-
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Alright, so this question was giving me problems and I made one up to solve for practice, but I have no way to check if I did it correctly, so I would appreciate if you could I did it correctly.
A 150N chandelier is suspended from a ceiling at a single point by two chains that make angles of 25° and 30° with the ceiling. Calculate the tension on each chain.
[tex]T_{1}\cos{25} = T_{2}\cos{30}[/tex]
[tex]T_{1}\sin{25} + T_{2}\sin{30} = 150 N[/tex]
First, I'll label the chain that makes an angle of 25° with the ceiling be T_1 and the chain that makes an angle of 30° with the ceiling be T_2
First I decide to solve for T_2 by using the first equation:
[tex]T_{1}\cos{25} = T_{2}\cos{30}[/tex]
[tex]T_{2} = \frac{T_{1}\cos{25}}{\cos{30}}[/tex]
[tex]T_{2} = 1.05T_{1}[/tex]
Now I substitute this into the second equation:
[tex]T_{1}\sin{25} + 1.05T_{1}\sin{30} = 150 N[/tex]
[tex]0.423T_{1} + 0.525T_{1} = 150[/tex]
After doing simple algebra, I yield:
[tex] T_{1} \approx 158.23 N[/tex]
Now to substitute this to find the tension of the other chain:
[tex]T_{2} = 1.05(158.23N) => T_{2} \approx 166.14 N[/tex]
Therefore, the tensions in the two chains are approximately 166.14 N and 158.23 N. Did I do this correctly? Thanks in advance. Also, what would be an efficient way of checking my solution is correct?
Homework Statement
A 150N chandelier is suspended from a ceiling at a single point by two chains that make angles of 25° and 30° with the ceiling. Calculate the tension on each chain.
Homework Equations
[tex]T_{1}\cos{25} = T_{2}\cos{30}[/tex]
[tex]T_{1}\sin{25} + T_{2}\sin{30} = 150 N[/tex]
The Attempt at a Solution
First, I'll label the chain that makes an angle of 25° with the ceiling be T_1 and the chain that makes an angle of 30° with the ceiling be T_2
First I decide to solve for T_2 by using the first equation:
[tex]T_{1}\cos{25} = T_{2}\cos{30}[/tex]
[tex]T_{2} = \frac{T_{1}\cos{25}}{\cos{30}}[/tex]
[tex]T_{2} = 1.05T_{1}[/tex]
Now I substitute this into the second equation:
[tex]T_{1}\sin{25} + 1.05T_{1}\sin{30} = 150 N[/tex]
[tex]0.423T_{1} + 0.525T_{1} = 150[/tex]
After doing simple algebra, I yield:
[tex] T_{1} \approx 158.23 N[/tex]
Now to substitute this to find the tension of the other chain:
[tex]T_{2} = 1.05(158.23N) => T_{2} \approx 166.14 N[/tex]
Therefore, the tensions in the two chains are approximately 166.14 N and 158.23 N. Did I do this correctly? Thanks in advance. Also, what would be an efficient way of checking my solution is correct?