A coin is placed 14.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 31.0 rpm (revolutions per minute) is reached, at which point the coin slides off.

Question

A coin is placed 14.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 31.0 rpm (revolutions per minute) is reached, at which point the coin slides off.

Part A
What is the coefficient of static friction between the coin and the turntable?

Answer 1

To determine the coefficient of static friction between the coin and the turntable, we need to consider the forces acting on the coin when it is on the verge of sliding off. At the point of sliding, the frictional force between the coin and the turntable is at its maximum, equal to the product of the coefficient of static friction (μs) and the normal force (N).

First, let's find the normal force acting on the coin. The normal force is the force exerted by the turntable perpendicular to the surface of the coin.

We know that the coin remains fixed on the turntable until a rate of 31.0 rpm is reached, at which point the coin slides off. Since the speed of the turntable is given in revolutions per minute, we can convert it to radians per second (ω) using the relationship:

ω = 2πf

Where f is the frequency in revolutions per minute and ω is the angular frequency in radians per second. Plugging in the given value:

ω = 2π(31.0 rev/min) = 2π(31.0/60) rad/s

Next, we need to find the acceleration of the coin, which is directed radially outward. The acceleration (a) is related to the angular velocity (ω) and the distance from the axis (r) by the formula:

a = ω²r

Plugging in the given values:

a = (2π(31.0/60))²(0.14 m)

Now, we can calculate the normal force, assuming the coin is not in vertical motion:

N = m × a

The mass of the coin (m) is not given in the problem, so we need additional information to find the normal force. Once we have the normal force, we can find the frictional force by applying Newton's second law in the radial direction:

F_friction = μsN

Finally, the coefficient of static friction (μs) can be obtained by rearranging the equation:

μs = F_friction / N

Unfortunately, without the mass of the coin, we cannot calculate the coefficient of static friction. Additional information is needed to find the answer to this question.