Chapter 6, Problem 22P

You have seen dogs shake to shed water from their fur. The motion is complicated, but the fur on a dog’s torso rotates back and forth along a roughly circular arc. Water droplets are held to the fur by contact forces, and these forces provide the centripetal acceleration that keeps the droplets moving in a circle, still attached to the fur, if the dog shakes gently. But these contact forces—like static friction—have a maximum possible value. As the dog shakes more vigorously, the contact forces cannot provide sufficient centripetal acceleration and the droplets fly off. A big dog has a torso that is approximately circular, with a radius of 16 cm. At the midpoint of a shake, the dog’s fur is moving at a remarkable 2.5 m/s.

a. What force is required to keep a 10 mg water droplet moving in this circular arc?

b. What is the ratio of this force to the weight of a droplet?