A carnival ride consists of a rotating disk on which the riders sit. It slowly s

Question

A carnival ride consists of a rotating disk on which the riders sit. It slowly starts speeding up until people start sliding off. Suppose the coefficient of friction between your pants and the floor is 0.35 and the radius of the circular path you’re taking is 2.0m. What’s the tangential velocity at which you’ll slide off?

I have a really hard time understanding these coefficient of friction problems, if there is anyway you could break it down to like a 1st grade level that would be great. I keep missing these types of porblems on my test. Thank you.

Explanation / Answer

As you can see this is a circular motion problem, so

Always Remember this equation to solve any type of circular motion problem

Fc = mv^2/r

here v = tangential velocity

r = radius of mpath = 2.0 m

m = mass

this force is necessary to move in circular motion.

Now you can see from this question that there will be friction force to slide you off from ride

friction force = Ff = uk*N

N = normal force = m*g

g = gravitational acceleration = 9.81 m/sec^2

uk = coefficient of friction = 0.35

Now you will slide off from ride if the frictional force will becomes equal to circular force

Fc = Ff

m*v^2/r = uk*m*g

m will cancel out.

v = sqrt (uk*g*r)

v = sqrt (0.35*9.81*2)

v = 2.62 m/sec

Comment below if you have any doubt.

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