How Do You Calculate Tension in Strings Supporting a Meter Stick in Equilibrium?

[dance0486]

Homework Statement

A uniform meter stick with a mass of 180 g is supported horizontally by two vertical strings, one at the 0 cm mark and the other at the 90 cm mark. What is the tension in the string at 0 cm and at 90 cm?



2. The attempt at a solution I changed 180 g to .18 kg. Using F=mg, I found mg=1.764 N. From there, I have made numerous attempts, but none make sense! I am making this problem way harder than it should be. Please help!

 

[dance0486]

Sorry, I also know that the sum of the forces needs to be 0; and there is only forces in the y direction.

 

[nlightner]

I would suggest approaching this problem by drawing a free body diagram for the meter stick. This will help visualize the forces acting on the stick and make it easier to solve for the tension in the strings.

First, we know that the weight of the meter stick is acting downward at the center of mass, which is at the 45 cm mark. This weight can be calculated using the mass and gravity as you have already done (F=mg).

Next, we need to consider the forces acting at each end of the stick. At the 0 cm mark, there is only one string supporting the stick, so the tension in that string must be equal to the weight of the stick at that point. At the 90 cm mark, there are two strings supporting the stick, so the tension in each string must be half of the weight of the stick at that point.

Using these principles, we can set up equations for the forces at each end of the stick and solve for the tension in each string. This approach will ensure that the stick is in equilibrium, meaning that the net force and net torque on the stick are both equal to zero.

I hope this helps and good luck with your homework! Remember to always approach problems with a clear and logical thought process.