The discussion centers on the concept of unequal tension in a pulley system, particularly when different masses are attached to either end of a rope. It is established that when a pulley has mass and is subject to acceleration, the tension in the rope must differ on both sides to create a net moment for rotational acceleration. Specifically, the tension on the side of the heavier mass is greater, allowing the pulley to rotate. This principle is crucial for understanding dynamics in mechanical systems involving pulleys.
PREREQUISITESStudents of physics, mechanical engineers, and anyone interested in understanding the mechanics of pulley systems and the principles of tension in ropes.
Maybe you can explain to us first about what you mean by "unequal tension." Are you referring to tension variations along the length of the rope? And where does the pulley come in?tchentroll said:I am having a bit of difficulty with the concept of unequal tension in a rope. What are the conditions for unequal tension? I read that the tension is the same when there is no acceleration. Why is this the case? Can someone explain this concept to me? Thanks :)
To accelerate the massive pulley, the rope must exert a tangential force on it, and the pulley will exert an equal but opposite tangential force on the rope. To balance that force on a piece of rope, the tensions at both ends of that piece must be different.tchentroll said:For example if two different masses are attached to the ends of a rope and the rope is part of a pulley system that has mass, why is the tension in the rope unequal on both sides?
To get the pulley to accelerate (rotationally), you need to apply a net moment to the pulley. So the part of the rope attached to one of the masses must have a higher tension in it than the part of the rope attached to the other mass. This will translate into a net moment about the axis of the pulley. If the tensions were the same, there would be no net moment, and the pulley would not rotate.tchentroll said:For example if two different masses are attached to the ends of a rope and the rope is part of a pulley system that has mass, why is the tension in the rope unequal on both sides?