## 6.5 - Pulleys

If a 50 Kg mass is suspended from the ceiling by a vertical rope, the tension on the rope must be 490 N up (calculating the weight using the more precise

**g = 9.8 m/s/s**). If it is suspended by two vertical ropes, each rope has a tension of 245 N up. If one rope were to be attached to the ceiling and both its ends attached to the mass, the tension would still be 245 N. This is the advantage of pulley systems. The pulley is used to provide a relatively frictionless turning point for the rope. As the rope is threaded through the pulleys, each section only has to support a small fraction of the object’s total weight.Look at the figures below. On the left, if a person were to lift the weight in this orientation, he would have to pull with the same force as the object’s weight, 600 N. It is still a simple machine because the direction of the force has been changed. On the right, the rope is pulling up more than once. Therefore the tension is less than before. Since there are now three parts of the rope that pull up, the tension is 600 N / 3 = 200 N. The force applied is 3 times smaller than the actual weight, so the person pulling must pull three times more rope through his/her hands to lift it. If the mass is to be lifted 0.50 m, then 1.50 m (3 X 0.50 m) of rope has to go through the lifter’s hands. The mechanical advantage of this system of pulleys is 3.