Question

A penny is placed a distance r from the center of a record spinning at = 90 rad/min. The coefficient of static friction between the penny and the record is s = 0.14 on the horizontal plane. Select an expression for the maximum distance, r, the penny can be placed from the center and not move. What is the distance, r in meters?

Answer 1

Step-by-step explanation:

The maximum distance, r, that the penny can be placed from the center of the record without moving can be found by setting the maximum static friction force equal to the centripetal force required to keep the penny in circular motion:

μsN = mv^2/r

where μs is the coefficient of static friction, N is the normal force (equal to the weight of the penny), m is the mass of the penny, v is the tangential velocity of the penny (equal to the angular velocity of the record times the distance from the center, v = ωr), and r is the distance from the center.

Solving for r, we get:

r = sqrt(μsgv^2 / (4*pi^2))

where g is the acceleration due to gravity.

Substituting the given values, we get:

r = sqrt(0.149.81(902pi/60)^2 / (4*pi^2)) = 0.0574 meters

Therefore, the maximum distance, r, that the penny can be placed from the center without moving is approximately 0.0574 meters.