What Is the Least Static Friction Coefficient for a Cat on a Merry-Go-Round?

[Vaness330]

Hi can someone help me on this problem.

a cat dozes around merry go round at radius 5.4 meters. the ride turns on and brought up to turning rate of 7.2 seconds in one complete rotation. how do i find the least static friction coefficient between the cat and the merry go round that will allow the cat to stay in place, without sliding out.

 

[rcgldr]

Compare the centripital force to gravitational force (the ratio).

 

[m2003]

Sure, I can help you with this problem. To find the least static friction coefficient between the cat and the merry go round, we need to use the formula for centripetal force, which is F = m*v^2/r, where m is the mass of the cat, v is the tangential velocity, and r is the radius of the merry go round.

First, we need to find the tangential velocity of the cat, which is equal to the circumference of the circle divided by the time it takes for one complete rotation. In this case, the circumference is 2*pi*r, so the tangential velocity is (2*pi*5.4)/7.2 = 4.24 m/s.

Next, we can plug in the values into the formula for centripetal force. Let's assume the mass of the cat is 5 kg. F = (5 kg)*(4.24 m/s)^2/5.4 m = 16.8 N.

Now, we can use the formula for static friction, which is Ff = uN, where u is the static friction coefficient and N is the normal force. In this case, the normal force is equal to the weight of the cat, which is mg = (5 kg)*9.8 m/s^2 = 49 N.

Finally, we can rearrange the formula to solve for u: u = Ff/N = 16.8 N/49 N = 0.34. This means that the least static friction coefficient between the cat and the merry go round that will allow the cat to stay in place without sliding out is 0.34.

I hope this helps you with your problem. If you have any further questions, please don't hesitate to ask. Good luck!