Traffic light problem

1. Dec 5, 2003

cowgiljl

A traffic light weigh 235 Nt. It is supported by 2 wires cal the tension of each of the wires

T1 has an angle of 21 degrees
T2 has an angle of 38 degrees

There is no sag in the light

I have 2 equations

equ 1) Fx = T2 cos 38 - T1 cos 21 = 0
equ 2) Fy = T1 sin 21 + T2 sin 38 = 0

I set T2 = to T1

T2 = T1 (cos 21 / cos 38) = 1.2 T1

then subsitutedthat into equatin 2

T1 sin 21 + (1.2 T1)(sin 38) - 235 Nt = 0

T1 = 214 N

T2 = 1.2T1= 1.2(214)

T2 = 257 N

thanks

2. Dec 5, 2003

Staff: Mentor

I didn't check your arithmetic, but it looks good to me (assuming angles are with respect to the x-axis). A few comments:

- I don't know what you mean by no sag: of course the wires "sag", that's why they are at an angle.
- Your equation #2 has a typo (you left out the weight), but you correct it later on.

3. Dec 5, 2003

HallsofIvy

Staff Emeritus
It doesn't look so good to me.

What reason do you have for setting T1= T2?? It doesn't look to me like the tension in the two wires will be the same (the situation is not symmetric because the angles are different).

Oh, wait! You didn't set T1= T2! You solved equation 1 for T1. That's a whole different matter.

Also, as DocAl said, you second equation (for the vertical component of force) should be
equ 2) Fy = T1 sin 21 + T2 sin 38 - 235 = 0
so that the total vertical force is 0
or equ 2)
T1 sin 21 + T2 sin 38 = 235 so that the upward force of the wires balances the downward force of the light.

You did manage to get the right answer!