I measure the tension in a pulley system with two masses (one smaller, one larger) where I pull the small mass down and let it go so that the system accelerates in the direction of the larger mass. This is without friction. Then, I try to consider friction. Does the tension in the string change? How I tried to think about it was on either side of the pulley. So on the side with the smaller mass, which goes upward after letting go, if there is friction, then the friction force points downward and adds with the gravitational force. So therefore, I think that the tension force pointing upwards has to increase as well to balance the new friction force pointing downward. But if you look on the other side, with the large mass, you see that it is going down. So the gravitational force points down and the tension force points up. The new friction force also points up, but because the gravitational force can't change, I think that the tension force would have to decrease to match the increase in friction force upwards, so that the net force stays the same. But the tension can't increase on one side and decrease on the other, so I'm confused. Did I think about it in the wrong way?