Imagine a string passing over a pulley, with a monkey hanging on one end of the string, and an iron bob on the other end balancing the monkey. Monkey and bob are equal in weight, and both are initially at rest. The weight of the string and the friction in the pulley can be neglected.
What happens to the iron bob when the monkey begins to climb up the string? In other words, will the bob rise with the monkey, will it descend, or will it remain stationary?
To solve the problem we must apply Newton's Laws of Motion. When the monkey begins to climb, he is accelerated upward. Therefore, according to Newton's Second Law, the string must not only support the monkey's weight, but it must supply additional force for the acceleration. As a test of this conclusion, you might stand on bathroom scales sometime when you are going up in an elevator. You will find that as the elevator starts upward, the scales will register several pounds more than your weight. The added push upward on the bottom of your feet serves to accelerate your body. For a simpler experiment, one which can be done less conspicuously, hang a weight on a string, and jerk upward. You will feel a sudden added tension in the string as the mass is accelerated.
Even though the monkey moves upward by his own efforts, there must be an added tension in the string to provide force for the acceleration. By Newton's Third Law the tension in the string must pull equally on the iron bob. Therefore, the bob is accelerated upward just like the monkey. The solution to the problem, then, is this: the monkey and the bob rise together.
When the monkey stops climbing, and thus decelerates, the tension in the string is decreased, and the bob comes to rest at the same time as the monkey. Likewise, if the monkey turns and starts down the string, the bob descends with the monkey.
From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena
By OVERTON LUHR