A ceiling fan operates at 1500 rpm at full speed and has a diameter of 120 cm (for the circle traced by the outer edges of its three blades). Consider a particle of mass 1 g that is stuck to the outer end of a blade. When the fan is running at full speed, what is the magnitude of the force experienced by the particle, and what is the magnitude of the force exerted by the particle on the blade along its surface?

Step-by-step solution

The angular velocity of the fan is given by: = 2 N 60 = 2 1500 60 = 50 rad/s The radius of the circular path is r = 120 2 = 60 cm = 0.6 m . The mass of the particle is m = 1 g = 10⁻³ kg . The force experienced by the particle is the centripetal force required to keep it in circular motion, which is provided by the blade: F = m ^2 r = 10⁻³ (50 )^2 0.6 F = 10⁻³ 2500 ^2 0.6 = 1.5 ^2 N Using ^2 9.87 , we get: F 1.5 9.87 = 14.8 N By Newton's third law of motion, the particle exerts an equal and opposite force on the bla