A coin is placed 26 CM from the center of a horizontal turnable intially at rest. The turnable begin to ratate. When the speed of coin is 120 CMS rotating at constant rate the coin just begin to slip the acceleration of gravity is 980 CM/S2. What is the coefficient static friction between the coin and turnable?
normal force = m g
centripetal force = m v^2 / r
μ static = centripetal / normal = v^2 / (g r)
To find the coefficient of static friction between the coin and the turntable, we need to analyze the forces acting on the coin.
1. Centripetal Force: The coin moves in a circular path due to the rotation of the turntable. The centripetal force (Fc) acting on the coin is given by the equation: Fc = m * ω^2 * r, where m is the mass of the coin, ω is the angular velocity, and r is the radius (distance from the center of the turntable to the coin).
2. Friction Force: The friction force (Ff) between the coin and the turntable prevents the coin from slipping. The maximum static friction force (Fs) can be calculated using the equation: Fs = μs * N, where μs is the coefficient of static friction, and N is the normal force.
3. Normal Force: The normal force (N) is the force exerted perpendicularly by the turntable on the coin. In this case, it is equal to the weight of the coin since the coin is on a horizontal surface. The weight (W) is given by: W = m * g, where g is the acceleration due to gravity.
To solve for the coefficient of static friction (μs), we have to equate the centripetal force (Fc) to the maximum static friction force (Fs).
Fc = Fs
m * ω^2 * r = μs * N
m * ω^2 * r = μs * m * g
In the given problem, the angular velocity (ω) and radius (r) are known. We can calculate the value of ω by dividing the linear speed (V) of the coin by the radius (r). ω = V / r
Given:
- Angular velocity (ω) = (120 CMS) / (26 CM)
- Radius (r) = 26 CM
- Gravity (g) = 980 CM/S^2
Using these values, we can calculate the coefficient of static friction (μs):
μs = (m * ω^2 * r) / (m * g)
μs = (ρ * ω^2 * r) / g
Substituting the given values:
μs = [(120 CMS / 26 CM) ^ 2 * 26 CM] / 980 CM/S^2
Now, we can calculate this value:
μs = (60 ^ 2 * 26) / 980
μs = 1560 / 980
μs ≈ 1.59
Therefore, the coefficient of static friction between the coin and the turntable is approximately 1.59.