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A pulley is a simple machine in which the rope passes over the grooved wheels. The load to be moved is attached to one end of the rope and effort is applied at the other end of the rope. A pulley can change the direction of the force acting upon the body. Also, it can lift weights against gravity.
Measure the weight of the nut using the spring balance. Pass a string over a pulley. Tie one end of the string to the nut and other to the hook of the spring balance. Fix the pulley at suitable place. Steadily pull the spring balance and lift the nut. Note the reading. This is the force required to lift the nut using a pulley. Is this force less than the weight of the nut.
When you use a pulley, you have to apply force to lift the bucket as well as overcome the friction. So more force is required to pull the bucket with a pulley. Pulley only changes the direction of force to make it convenient to pull.
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