Calculating Centripetal Force on a Rotating Sphere
Question:
A sphere with a mass of 20g rotates in a horizontal plane at a constant tangential speed of 0.5 m/s. It is known that the distance between two opposite points on the circumference passing through the center is 50 cm. What is the value of the centripetal force acting on the sphere?
Answer:
The magnitude of the centripetal force is expressed as:
F = mv² / r
Given:
m = 20g = 20/1000 kg = 0.02 kg
v = 0.5 m/s
r = diameter / 2
Since the distance between two opposite points on the circumference passing through the center is 50 cm, the diameter will be 50 cm. So, the radius, r = 25 cm = 0.25 m
Calculate the magnitude of the force:
F = 0.02 * 0.5² / 0.25
F = 0.02 * 0.25 / 0.25
F = 20N
Therefore, the magnitude of the centripetal force acting on the sphere is 20N.
Explanation:
In this scenario, we are dealing with the concept of centripetal force in circular motion. The centripetal force is the force that acts on an object moving in a circular path, keeping it in that path instead of moving in a straight line.
Centripetal Force Formula:
The centripetal force F is calculated by the formula F = mv² / r, where m is the mass of the object, v is the speed of the object, and r is the radius of the circular path.
In the given data:
Mass, m = 20g = 0.02 kg (converted to kilograms)
Tangential speed, v = 0.5 m/s
Radius, r = 25 cm = 0.25 m
Substitute the values into the formula F = mv² / r and calculate to find the centripetal force, which in this case is 20N.
This calculation demonstrates how the centripetal force is influenced by the mass, speed, and radius of the object in circular motion. By understanding and applying the concept of centripetal force, we can analyze and predict the behavior of rotating objects in various scenarios.