An object of mass 400 grams is whirled in a horizontal circle of radius 2 m. If it performs 60 rpm, calculate the centripetal force acting on it.
Answers
Given data :
• Mass of an object, m = 400 gram
• Radius of the horizontal circle, r = 2 m
• Frequency of an object, f = 60 rpm
Solution : Here, first we have to convert unit of mass and frequency of an object into kg and rev/sec or Hz respectively.
➜ m = 400 grams = (400/1000) kg = 0.4 kg
➜ f = 60 rpm = (60/60) rev/sec = 1 Hz
Here, we know that
➜ Angular velocity, ω = 2πf ----{1}
Now,
➜ Centripetal force, F = mω²r
[From {1}]
➜ Centripetal force, F = m * (2πf)² * r
➜ Centripetal force, F = m * 4 * π² * f² * r
➜ Centripetal force, F = 0.4 * 4 * (22/7)² * (1)² * 2
➜ Centripetal force, F = 1.6 * (484/49) * 1 * 2
➜ Centripetal force, F = 1.6 * (484/49) * 2
➜ Centripetal force, F = 3.2 * (484/49)
➜ Centripetal force, F = (3.2 * 484)/49
➜ Centripetal force, F = 1548.8/49
➜ Centripetal force, F = 31.6081 N
Answer : The centripetal force acting on the object is 31.6081 N.
More info :
Angular velocity : The time rate of angular displacement of a particle performing circular motion is called the angular velocity.
Centripetal force : centripetal force is the force required to provide centripetal acceleration to a particle to move it in a circular path.