2.8 * 2 pi radians/s = 17.6 rad/s
r = .032 meters
Ac = w^2 r = (17.6)^2(.032) = 9.9 m/s^2
m g (mu) = m Ac
mu g = 9.9
mu (9.8) = 9.9
mu is about 1
What is the coefficient of friction between the ant and the CD?
r = .032 meters
Ac = w^2 r = (17.6)^2(.032) = 9.9 m/s^2
m g (mu) = m Ac
mu g = 9.9
mu (9.8) = 9.9
mu is about 1
The formula for centripetal force is as follows:
F = (m * v²) / r
Where:
F = centripetal force
m = mass of the object
v = velocity of the object
r = radius of the object
In this case, the ant is just about to slide off the CD, which means the friction force acting on the ant is equal to the maximum static friction force. The maximum static friction force can be calculated using the equation:
Friction Force (maximum) = coefficient of friction * Normal force
Assuming the normal force acting on the ant is equal to its weight (mg), and the weight of the ant is neglected compared to the CD, we can say that the normal force is equal to the ant's weight.
Since the ant is sliding off the CD due to the centripetal force acting on it, we can equate the maximum friction force with the centripetal force:
coefficient of friction * Normal force = (m * v²) / r
Now, we can solve for the coefficient of friction:
coefficient of friction = ((m * v²) / r) / Normal force
To calculate the coefficient of friction, we need information about the ant's mass, velocity, radius, and the acceleration due to gravity.