What mass could be lifted by the centrifugal force of an object having a mass of 98 g if it were revolving in a horizontal circle, 20cm in diameter, and making 240 revolutions per minute?
To determine the mass that could be lifted by the centrifugal force, we need to calculate the centrifugal force exerted by the object. Here's how:
1. Convert the mass of the object to kilograms:
Mass in kg = Mass in grams / 1000
Mass in kg = 98 g / 1000 = 0.098 kg
2. Convert the diameter of the circle to meters:
Diameter in meters = Diameter in centimeters / 100
Diameter in meters = 20 cm / 100 = 0.2 m
3. Calculate the radius of the circle:
Radius = Diameter / 2
Radius = 0.2 m / 2 = 0.1 m
4. Convert the revolutions per minute to radians per second:
Angular velocity (ω) = 2π × (Revolutions per minute) / 60
Angular velocity (ω) = 2π × 240 / 60 = 8π rad/s
5. Calculate the centrifugal force using the formula: Centrifugal force = Mass × Radial acceleration
Radial acceleration (a) = Radius × (Angular velocity)^2
Radial acceleration (a) = 0.1 m × (8π rad/s)^2 ≈ 8π^3 m/s^2
Centrifugal force = Mass × Radial acceleration
Centrifugal force = 0.098 kg × 8π^3 m/s^2 ≈ 77.8 N
Therefore, the centrifugal force exerted by the object is approximately 77.8 Newtons. This force could lift an object with a mass of 77.8 kg in the opposite direction.