I posted this question this morning but I'm not sure of the response Damon provided.
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
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
Damon's response is correct. To find the minimum speed you would need to stick to the wall of the ride, you can use the formula he provided: v^2 = 2 r g. Here's how to derive that formula:
In this scenario, the riders are moving in a circular path, so they experience an inward force called centripetal force that keeps them moving in a circular motion. This centripetal force is provided by the friction between their clothes and the wall of the ride.
The force of friction acts towards the center of the circular path and is equal to the coefficient of friction (mu) multiplied by the normal force (which is equal to the rider's weight, m g, where m is the mass and g is the acceleration due to gravity).
The maximum force of friction that can be exerted is given by the equation Force down = friction force up:
m g = mu m v^2/r
Simplifying this equation gives:
g = mu v^2/r
Since we want the minimum speed needed to stick to the wall, we want the maximum force of friction. Therefore, we can substitute the maximum value of mu, which is 0.5, into the equation.
So, we have:
g = 0.5 v^2/r
We can rearrange this equation to solve for v^2:
v^2 = 2 r g
So, the minimum speed you would need to stick to the wall of the ride is given by v^2 = 2 r g, as Damon explained.