Find angle, given the tension of the rope.

[brikayyy]

Homework Statement

PROBLEM: Choose a pair of measurements of the forces from parts A5, A6, or A7, where the forces on the sensors were quite different. Imagine there was an angle between one cart and the string. Assuming that the larger force was the true tension in the string, what is the angle θ?

DIAGRAM (GIVEN):

INFORMATION:

M (of a cart with the sensor) = 457.3 g
F1 (Cart One) = 16.32 N
F2 (Cart Two) = 17.03 N

CONTEXT: This is for a lab conclusion I have to write. For the parts A5 - A7 mentioned in the problem below, those were all sections of the lab where we "played tug-of-war" with carts that had force sensors taped to them. The forces I chose are from when two people of equal mass lifted the carts and did tug-of-war, one for each cart.

Homework Equations

F = ma (?)
T = mgsinθ (?)

The Attempt at a Solution

At first, I thought I could do a simple trigonometry problem, but then I realized that I probably read the problem incorrectly.

I tried to work backwards with T = mgsinθ? So...

T/mg = sinθ
17.03 / ( 457.3 * 9.8 ) = 0.00380003302
0.00380003302 = sinθ
sin^-1(0.00380003302) = 0.217726378062

But that seems really off to me... Now I have no idea what to do. Thanks so much for your time!

4. Personal Information

I am a college freshman-sophomore (going into sophomore year and taking summer school classes) taking a basic level Physics class. I have never taken physics in my life prior to this; neither am I good at math. I am simultaneously taking Calculus II right now.

 

[tiny-tim]

hi brikayyy! welcome to pf!

what does g have to do with it?

(or m ?)​

 

[brikayyy]

hi brikayyy! welcome to pf!

what does g have to do with it?

(or m ?)​

Thanks!

I thought g was significant because you had the two sensors at an angle, basically one hanging off the other. But now I thought about it and this isn't the same as some other tension problems I've seen where one object is suspended in the air by a string. I'm assuming this censor is lying flat on a surface?

I admit I initially didn't think mass was significant, but I didn't know how to do a tension problem, so I tried to look up the formula for tension. I'm not sure if the same logic as I just explained above applies here, that it's not important because the sensor is not hanging off the other one?