Question

The spin cycles of a washing machine have two angular speeds, 439 rev/min and 602 rev/min . The internal diameter of the drum is 0.500 m . Part A What is the ratio of the maximum radial force on the laundry for the higher angular speed to that for the lower speed

Answer 1

The ratio of the forces is F2/F1 = 1.86

Step-by-step explanation:

From Newton's second law applied to circular motion, the total force F acting on a body in circular motion is given by

F = mv²/r

Where

m = mass of the body undergoing circular motion

v = linear velocity = ω×r

ω = angular velocity

r = radius of the circular path through which the force acts

So

F = m(ω×r)²/r = mω²×r

Given 2 angular speeds ω1 = 439re/min = 439×2π/60 rad/s = 46 rad/s and

ω2 = 602rev/min = 602×2π/60 rad/s = 63 rad/s

Required to calculate the ratio F2/F1

The mass m and radius r is the same for both forces, so F is dependent on the angular speed

So F2/F1 = ω2²/ω1² = (ω2/ω1)²

F2/F1 = (63/46)² = 1.86