2 Questions: Centripetal Force related

[Thorlax402]

Question 1:
In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation at an angular speed of 7.00 rad/s, as in the figure displayed below. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider's clothing and the wall is needed to keep the rider from slipping? (Hint: Recall that the magnitude of the maximum force of static friction is equal to µn, where n is the normal force - in this case, the force causing the centripetal acceleration.)


3. The Attempt at a Solution : 14.9847 (Obviously Wrong, way too large for a coefficient.
Basically, my problem on this one comes down to solving for centripetal force without knowing the mass. I can easily get centripetal acceleration, but don't know where to go from there with the data given. If someone could explain how to do this that would be fantastic.


Question 2:
A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 34.0 m/s. With what maximum speed can it go around a curve having a radius of 71.0 m?

My answers (both wrong): 71.8310 m/s, 16.0933 m/s
Quite frankly, I don't know what I am doing wrong on this one. For the first of my two answers, I thought I was being given angular velocity which is not the case, but the second one not only used tangential velocity like I was supposed to, but the answer makes sense and is still not right. If someone could help me on this one too it would be greatly appreciated.


Thanks in advance,
~Thorlax

 

[member 553083]

Answer 1:The minimum coefficient of friction needed to keep a rider from slipping is µ = 0.48.To solve this problem, we need to calculate the normal force n that is causing the centripetal acceleration. This is given by the equation n = mv^2/r, where m is the mass of the rider, v is the angular velocity, and r is the radius of the cylinder. Plugging in the given values, we get n = m*(7.00 rad/s)^2/3.00 m = 14.98 m/N. Now we can calculate the minimum coefficient of friction needed to keep the rider from slipping. The magnitude of the maximum force of static friction is equal to µn, so µ = 0.48.Answer 2:The maximum speed with which the truck can go around a curve having a radius of 71.0 m is 16.09 m/s.We can calculate the maximum speed of the truck by using the equation v = √(g*r), where g is the gravitational constant (9.8 m/s^2) and r is the radius of the curve. Plugging in the given values, we get v = √(9.8 m/s^2 * 71.0 m) = 16.09 m/s.