A coin is placed 33 cm from the center of a
horizontal turntable, initially at rest. The
turntable then begins to rotate. When the
speed of the coin is 100 cm/s (rotating at a
constant rate), the coin just begins to slip.
The acceleration of gravity is 980 cm/s2 .
What is the coefficient of static friction be-
tween the coin and the turntable?
To solve this problem, we can use the concept of centripetal force and static friction. The centripetal force required to keep an object in circular motion is given by:
Fc = mv^2 / r
Where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius.
In this case, the centripetal force is provided by the static friction between the coin and the turntable. When the coin just begins to slip, the force of static friction is at its maximum. The force of static friction can be expressed as:
Fs = μs * N
Where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
First, let's find the normal force. The normal force is equal to the gravitational force acting on the coin, which is given by:
N = m * g
Where g is the acceleration due to gravity.
Given:
Radius (r) = 33 cm
Velocity (v) = 100 cm/s
Acceleration due to gravity (g) = 980 cm/s^2
We need to use consistent units, so let's convert cm to m:
Radius (r) = 33 cm = 0.33 m
Velocity (v) = 100 cm/s = 1 m/s
Acceleration due to gravity (g) = 980 cm/s^2 = 9.8 m/s^2
Now we can calculate the normal force:
N = m * g
To solve for m, we need to know the mass of the coin. If the mass is not provided, we won't be able to calculate the coefficient of static friction.
Please provide the mass of the coin in order to proceed with the calculation.