How Do You Calculate Tension in a Two-Mass Pulley System?

[frosti]

Homework Statement

A 2.00 kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 8.00 kg object, as shown in the figure. Find the magnitude of the acceleration of the two objects and the tension in the string.


http://img260.imageshack.us/img260/79/tensionpg7.th.png http://g.imageshack.us/thpix.php

The Attempt at a Solution

Through calculation, I know both objects are accelerating at 7.84 m/s². Since the surface is frictionless, I assume the tension is contributed by the 8kg object accelerating downward and gravitational force. so T= 8 x (9.8+7.84) = 141.12N. Is my answer correct?

 

[frosti]

nvm, I got this. Thank you anyway.

 

[baba89]

I would like to commend your attempt at solving the problem. However, your answer for the tension in the string is incorrect.

The tension in the string is actually equal to the sum of the forces acting on the 2kg object, which is accelerating at 7.84 m/s2. This includes the force of gravity acting downwards on the 2kg object (2kg x 9.8m/s2 = 19.6N) and the tension in the string (T). Therefore, T = 19.6N + 2kg x 7.84m/s2 = 33.28N.

To check your answer, you can also use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force on the 2kg object is equal to the tension in the string (T), so T = 2kg x 7.84m/s2 = 15.68N. This is consistent with the value we calculated earlier.

Therefore, the correct answer for the tension in the string is 33.28N. Keep up the good work in your scientific studies!