A compact disc spins at 2.8 revolutions per second. An ant is walking on the CD and finds that it just begins to slide off the CD when it reaches a point 3.1 cm from the CD's center.

(a) What is the coefficient of friction between the ant and the CD?

I don't understand how to solve

To solve this problem, we need to consider the forces acting on the ant as it moves on the spinning CD.

The ant experiences two forces: the force of gravity pulling it downward, and the force of friction acting in the opposite direction, preventing it from sliding off the CD.

Let's first calculate the force of gravity acting on the ant. We can use the formula:

F_gravity = m * g

where m is the mass of the ant and g is the acceleration due to gravity (9.8 m/s²).

Next, we need to calculate the force of friction. The force of friction can be found using the equation:

F_friction = μ * F_normal

where μ is the coefficient of friction and F_normal is the normal force, which is equal to the force of gravity acting on the ant.

Since the ant just begins to slide when it reaches a point 3.1 cm from the center, we can assume that the friction force is equal to the centripetal force acting on the ant. The centripetal force can be calculated using the formula:

F_centripetal = m * (v^2 / r)

where m is the mass of the ant, v is the velocity of the ant (tangential to the circular path), and r is the radius of the CD.

In this case, the velocity of the ant is equal to the tangential velocity of a point on the CD's surface, which is given by the formula:

v = ω * r

where ω is the angular velocity, given by 2π * f, where f is the frequency of revolution (2.8 revolutions per second).

Now, we can equate the centripetal force to the force of friction:

F_centripetal = F_friction

m * (v^2 / r) = μ * m * g

We can cancel out the mass of the ant on both sides, giving us:

(v^2 / r) = μ * g

Finally, we can solve for the coefficient of friction (μ):

μ = (v^2 / (r * g))

Now we can substitute the given values into the equation to find the coefficient of friction.