When you’re done using an electric mixer, you can get most of the batter off of

Question

When you’re done using an electric mixer, you can get most of the batter off of the beaters by lifting them out of the batter with the motor running at a high enough speed. Let’s imagine, to make things easier to visualize, that we instead have a piece of tape stuck to one of the beaters.

(a) Explain why static friction has no effect on whether or not the tape flies off.
(b) Analyze the forces in which the tape participates.

(c) Suppose you find that the tape doesn’t fly off when the motor is on a low speed, but at a greater speed, the tape won’t stay on. Why would the greater speed change things? [Hint: If you don’t invoke any law of physics, you haven’t explained it.]

Explanation / Answer

a] The tape is not just in contact with one of the beaters but it is rather a part of the beater and hence static friction has no role here.

b] The tape experiences a radially outward centrifugal force (due to the finite mass of the tape) and a normal force which is perpendicular to the plane of rotation.

c] The centripetal acceleration due to the rotation of the blades is given by: a = v2/ r where r is the distance from the center of rotation to the place where the tape is stuck and v is the velocity of the blades. So, if the velocity of the blades are doubled, the acceleration will increase by a factor of 4 and it is this quadratic relation which will produce a significant centrifugal force for high velocities where the tape will come off.

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