Does the tension in the rope or chain of a swing do any work on a child who is swinging?
No. Work is done when the force is applied in the direction of motion.
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In the case of a child swinging, the tension in the rope or chain primarily acts vertically to support the child's weight and keep them suspended in the air. However, the actual motion of swinging is happening horizontally. Since the force from the tension is acting perpendicular to the direction of the motion, it does not directly perform any work on the child. The work done on the child comes from the external forces applied, such as pushing them to start or maintain the swinging motion, or the gravitational force when the child is descending or ascending during the swing.
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