I posted this question this morning but I'm not sure of the response Damon provided. I did it once but then I updated it later in this at the bottom- please check booth of my answers.

Question

I posted this question this morning but I'm not sure of the response Damon provided. I did it once but then I updated it later in this at the bottom- please check booth of my answers.

If you were in a rotor style ride and the riders accelerate until the speed of ride is reached- if the radius of the cylinder is 5.0m and the coefficient of friction between clothes and wall is 0.5, how do you find minimum speed you would need to stick to the wall of the ride? Is he saying that I take 2*5(r) *9.8(g)? If not, please explain.Thank you

Physics-Please help with formula - Damon, Tuesday, December 7, 2010 at 11:11am
you need a centripetal acceleration equal to 2g if the mu is 1/2
Force down = m g
friction force up = mu m v^2/r
g = mu v^2/r
v^2/r = g/mu = 2 g
v^2 = 2 r g

Physics-I think I have it-Please check - Joey, Tuesday, December 7, 2010 at 5:29pm
Is this correct? I published something else earlier-that has to be wrong but I think this is correct.

Force friction balances weight
Force friction comes from force normal to create centripetal force

mv^2/r = Force normal

Force friction = mu x Force normal = mg

mu x mv^2/r = mg

9.8/05 = 19.6 m/s^2
19.6/5=3.92
sqrt 3.92 = 1.98 rads/s

Answer 1

Please scroll down for the entire answer-I did it once in the first paragraph and than after Damon's response, I did it again-I think the 2nd one is correct, maybe-

Thanks you

Answer 2

To find the minimum speed you would need to stick to the wall of the ride, you can use the formula derived by Damon in his response. The formula is v^2 = 2rg, where v is the speed, r is the radius of the cylinder, and g is the acceleration due to gravity.

In your calculation, you used a different approach. You equated the friction force with the weight of the object to create centripetal force. So, your equation is mu x mv^2/r = mg.

To solve this equation, you can start by substituting mu x mv^2/r for mg:

mu x mv^2/r = mg

Next, you can cancel out the mass term m from both sides of the equation:

mu x v^2/r = g

Now, rearrange the equation to solve for v^2:

v^2 = rg/mu

Finally, substitute the given values into the equation to calculate the minimum speed:

v^2 = (5.0 m) x (9.8 m/s^2) / 0.5

v^2 = 98 m^2/s^2

v = √98 m/s

So, the minimum speed you would need to stick to the wall of the ride is approximately 9.90 m/s.