Question

33. A 0.65 kg ball is attached to the end of a string. It is swung in a vertical circle of radius 0.50 m. At the top of the circle its velocity is 2.8 m/s. a. Draw a free body diagram for the ball when it is at the top of the circle. Next to that diagram indicate the direction of its acceleration

Answer 1

The free-body diagram for the ball at the top of the circle includes tension and gravitational force. Tension acts toward the center of the circle, and the gravitational force acts downward. The acceleration
`(\(a_c\))` required to keep the ball moving in a circular path is directed radially inward.

Certainly! When the ball is at the top of the vertical circle, two primary forces act on it: tension in the string and gravitational force. Additionally, the centripetal force, directed toward the center of the circle, provides the necessary acceleration to keep the ball moving in a circular path.

**Free Body Diagram (FBD):**

At the top of the circle, the forces acting on the ball are:

1. **Tension (T):** Directed radially inward (toward the center of the circle).

2. **Gravitational Force (Weight - mg):** Directed downward (toward the center of the Earth).

Now, let's consider the acceleration direction. At the top of the circle, the ball is moving in a circular path, and its acceleration is directed toward the center of the circle. Therefore, the centripetal acceleration (\(a_c\)) points radially inward.

In summary, at the top of the circle, the ball experiences tension and gravitational force, with centripetal acceleration directed toward the center of the circle.