Final answer:
Centripetal force is necessary to maintain circular motion, and the tension in the string attached to a moving mass provides this force as a reaction to the mass pulling on the string due to Newton's third law. The tension changes around the circular path and can be calculated using the centripetal force equation.
Step-by-step explanation:
When a mass is moving in a circular path, such as a ball attached to a string being swung around, there must be a force directed towards the center of the circle to sustain the motion. This is known as the centripetal force. The physical origin of the tension in the string, which is the force that stretches the string, is the reaction force due to Newton's third law. According to this law, for every action there is an equal and opposite reaction. Thus, as the ball pulls on the string to maintain its circular path (action force), the string pulls back on the ball with equal strength (reaction force), which creates tension in the string.
An example of this would be a metal ball tied to a light string and used as a pendulum, swinging freely after being released. The tension in the string is directly related to the force needed to keep the ball moving in a circular path. This tension changes depending on the position of the ball in its swing due to the combined forces of gravity and centripetal acceleration.
At the top and bottom of the circular path, the tension in the string is influenced by the gravitational force. The equation for centripetal force Fc = mv2/r, where m is the mass, v is the velocity, and r is the radius, helps in calculating the tension at different points along the circular path. For instance, at the bottom of the circle, the tension has to support the weight of the mass as well as provide the necessary centripetal force to maintain circular motion.