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When the bob of a conical pendulam is mo...

When the bob of a conical pendulam is moving in a horizontal circle at constant speed, which quantity is fixed?

A

velocity

B

Acceleration

C

Centripetal force

D

Kinetic energy

Text Solution

AI Generated Solution

The correct Answer is:
To determine which quantity is fixed when the bob of a conical pendulum is moving in a horizontal circle at constant speed, we can analyze the situation step by step. ### Step-by-Step Solution: 1. **Understanding the Conical Pendulum**: - A conical pendulum consists of a mass (bob) attached to a string that traces out a horizontal circle while the string makes a constant angle with the vertical. 2. **Analyzing Velocity**: - The bob moves with a constant speed in a circular path. While the speed (magnitude of velocity) is constant, the direction of the velocity vector changes continuously as the bob moves around the circle. Therefore, the velocity as a vector quantity is not fixed. 3. **Analyzing Acceleration**: - The bob experiences centripetal acceleration directed towards the center of the circular path. Although the magnitude of this acceleration can remain constant if the speed is constant, its direction changes continuously as the bob moves around the circle. Thus, acceleration is not fixed. 4. **Analyzing Centripetal Force**: - The centripetal force acts towards the center of the circular path and is responsible for keeping the bob in circular motion. Similar to acceleration, while the magnitude of the centripetal force can remain constant, its direction changes as the bob moves. Therefore, centripetal force is not fixed. 5. **Analyzing Kinetic Energy**: - Kinetic energy (KE) is given by the formula \( KE = \frac{1}{2}mv^2 \). Here, \( m \) (mass of the bob) is constant and \( v \) (speed) is also constant. Since both the mass and the speed are constant, the kinetic energy remains constant. Therefore, kinetic energy is the quantity that is fixed. ### Conclusion: The quantity that remains fixed when the bob of a conical pendulum is moving in a horizontal circle at constant speed is **kinetic energy**. ---
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