How Do You Calculate Tension in a String Connecting Two Masses on an Incline?

[jordanilyily]

I had a quiz today and part two of a question asked for the tension on a string. The problem was something along the lines of -- mass 1 = 6kg and mass 2 = 5kg. Mass 1 is attached to mass 2 by a weightless rope on an incline of 33 degrees. For mass 1 the kinetic friction is mu = 0.50; find the acceleration of mass 1 (which I found) and the tension of the string.

I turned in the quiz at the end of class etcetc and asked the professor if the work I had done was correct for that portion of which he said no. So I was wondering if anyone could display the formula for me so I can try out a few problems using it? Thanks!

 

[PhanthomJay]

Is mass 1 on the incline and mass 2 hanging straight down from a pulley attached to the top of the incline? If you correctly calculated the acceleration, the tension (not tensor) in the string can be found by isolating one of the masses in a Free Body Diagram, looking at the forces acting on it, and using Newton 2 for that mass to solve for the tension. Then look at the other mass , identify the force, and use Newton 2 to see if you get the same tension value, as a check.

 

[jordanilyily]

yes, mass 1 is on the incline and mass 2 is hanging from a rope straight down via pulley. thank you! :3

 

[PhanthomJay]

And so the tension is____??

 

[rwisz]

Hello,

Thank you for sharing your experience with us. I am happy to assist you with understanding the formulae for tension/tensors.

Tension is a force that is transmitted through a string, rope, or cable when it is pulled tight by forces acting on opposite ends. It is a vector quantity, meaning it has both magnitude and direction. Tensors, on the other hand, are mathematical objects that describe the relationship between physical quantities in a specific coordinate system.

The formula for tension can be derived using Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In the case of your quiz question, the tension on the string can be calculated as follows:

Tension = (Mass 1 * Acceleration) - (Mass 1 * Gravitational acceleration * sin(angle)) - (Mass 1 * Kinetic friction coefficient * Gravitational acceleration * cos(angle))

In this formula, the first term represents the force due to the acceleration of mass 1, the second term represents the component of gravitational force acting on mass 1 in the direction of the incline, and the third term represents the force due to kinetic friction acting in the opposite direction of motion.

I hope this helps to clarify the formula for you. It is important to note that the formula may vary depending on the specific scenario and variables involved. I encourage you to discuss any further questions with your professor to ensure a better understanding of the concept.

Best of luck with your future problem-solving!