Calculating Mass of Light Fixture from Cable Tensions

[tony873004]

Homework Statement

The figure shows a light fixture suspended from the ceiling. If the tension in cable 1 is 34N and the tension in cable 2 is 24N, what is the mass of the light fixture?

Homework Equations

Image
http://orbitsimulator.com/misc/IMG00034-20101024-1557.jpg

The Attempt at a Solution

I know to add the y-components of the tension of each cable, and to use m=F/a to get the mass. But how do I get the y-component of the triangle on the right if I don't know the angle? The place where cable 2 attaches to the horizontal bar can be slid back and forth, changing the angles of the triangle therefore changing the y-component of the 24N force.

 

[thrill3rnit3]

If you're stuck in the y-component, work in the x-component, see what you can figure out from there.

 

[tony873004]

If you're stuck in the y-component, work in the x-component, see what you can figure out from there.

I run into the same problem. Without knowing an angle or another side I can't compute either component.

 

[thrill3rnit3]

I run into the same problem. Without knowing an angle or another side I can't compute either component.

Then we have to solve for the missing angle.

What's your equation for the x-component?

 

[tony873004]

Then we have to solve for the missing angle.

What's your equation for the x-component?

24 N * cos(unknown angle #1)
or
24 N * sin(unknown angle #2)

 

[thrill3rnit3]

24 N * cos(unknown angle #1)
or
24 N * sin(unknown angle #2)

When you're doing a component, you need to consider both ends.

In the x component, take the sum of forces that act on the mass.

ΣF_x = ma_x = ?

 

[tony873004]

When you're doing a component, you need to consider both ends.

In the x component, take the sum of forces that act on the mass.

ΣF_x = ma_x = ?

ok, got it! It's not accelerating in x, so 34 sin(40) = 24 sin theta. Now I've got an angle I can work with to get the other y-component. Thanks!

 

[PMC_l0ver]

uhm hi

i have an idea about ur problem
but i may not able to explain this well since I am really sleepy
so uhm ill just put the equation u have to use


mg*sin50 = 34

m is ur mass, g is 9.8m/s2, angle = 90-40=50
do the rest of calculation

if u want to make sure u have a correct answer
calculate the angles for both sides and apply all possible forces acting on it
and in the end should have the same force of tension and force of gravity

Fg(force of gravity)=Ft(force of tension)
Fg=mg

 

[thrill3rnit3]

ok, got it! It's not accelerating in x, so 34 sin(40) = 24 sin theta. Now I've got an angle I can work with to get the other y-component. Thanks!

I'm glad you were able to figure it out

 

[tony873004]

Thanks again Thrill...

uhm hi

...angle = 90-40=50
do the rest of calculation...

Hi PMC_l0ver. I see this is your 1st post at Physicsforums.com. I'm honored you used it to answer my question. That's the way I first did the problem. But we both fell into the same trap. We can not just assume that since the angle between the 2 strings looks like a right angle that the triangle on the right has an angle of 50 degrees. There was no guarantee that the diagram was drawn to scale. The fact that there is no horizontal acceleration gives me what I need to know to find the missing angle. Thanks for your effort!