A mass m is attached to a string of length L and is swung in a vertical circle.

A mass m is attached to a string of length L and is swung in a vertical circle. What is the tension in the string at the top of the circle? (2023)

A mass m is attached to a string of length L and is swung in a vertical circle. What is the tension in the string at the top of the circle? (2023)

Step 1: Understand the scenario. A mass m is attached to a string of length L and is swung in a vertical circle.
Step 2: Identify the forces acting on the mass at the top of the circle. There are two forces: the tension in the string (T) and the weight of the mass (mg).
Step 3: At the top of the circle, both the tension (T) and the weight (mg) act downwards towards the center of the circle.
Step 4: Use the formula for circular motion. The net force towards the center of the circle is equal to the mass times the centripetal acceleration: F_net = mv²/L.
Step 5: Write the equation for the forces at the top of the circle: T + mg = mv²/L.
Step 6: Rearrange the equation to solve for the tension (T): T = mv²/L - mg.

Centripetal Force – The net force acting on an object moving in a circular path, which is required to keep the object moving in that path.
Tension in a String – The force exerted by a string or rope when it is pulled tight by forces acting from opposite ends.
Forces in Circular Motion – Understanding how gravitational force and tension interact at different points in a circular motion.