I have a physics question.

Question

I have a massless and frictionless string attached to 2 balls on each end. The 2 balls may have different masses. There is also a pivot in the middle of the string, such that the string can slide on the pivot freely. At first, the balls are at rest and horizontal to the pivot. How can I calculate the tension in the string when the 2 balls are dropped, given the masses of the balls and the length of the string?

Answer 1

This is basically an Atwood Machine.

The basic strategy is to draw two free body diagrams for each mass. If we say mass m1 > m2 then m2 will accelerate up.

We can now create two equations with two unknowns T for tension and a for acceleration

For the heavier mass we get

m1a = m1g - T

for the other mass we get

m2a = T - m2g

From this you can derive an expression for the tension T