Physics help, please?

Question

This mechanics problem is thoroughly kicking my ***. I would appreciate any help - preferably if you could take me step through step through how to solve it...

Two objects with masses of 2.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley.
Determine the tension in the string in Newtons.
Determine the acceleration of each object.
(c) Determine the distance each object will move in the first second of motion if both objects start from rest.

Thanks much!

Answer 1

So you understand it perfectly that the pulley can rotate and both masses (2.00kg and 5.00kg) may move up or down.
The problem is still not good---it should also state that the mass of the pulley may be ignored, otherwise the rotation of the pulley requires energy.
One way to solve this problem is to view both 2kg and 5kg as one UNIT, with the pulling force (5.00 - 2.00)g = 3g, and thus the acceleration is 3g/M = 3g/7. Remember that the string is pulling on the 2kg mass with the same acceleration after overcoming the gravity, so the tension in the string is 2g + (3g/7)*2 = 20g/7.
Another way to solve this problem is to view 2kg and 5kg separately. Assume also the tension in the string is T. The net pulling force on 5kg mass is 5g - T, while the net pulling force on 2kg mass is T - 2g. But their acceleration is the same, so we have: (5g - T)/5 = (T - 2g)/2. T = 20g/7 as in the first approach.
Do not mix the thinking / approaches!
Also, 0.5a = 3g/14 is the distance moved (2kg up and 5kg down).