if there is a cylindrical ride (radius r) and when it rotates the person feels pinned tot he wall and then the floor drops away. how would i start to find the equation of the angular speed needed to keep the person against the wall????
You need to know the coefficient of static friction, Us, between the person's clothing and the wall of the cylinder. Friction there is what keeps the person from sliding down.
Require that M*R*w^2*Us = M g
w^2 = g/(R*Us)
w is the required angular velocity in radians/s
You should have been given a Us value to assume. You could also look up some values with Google.
People wearing slippery clothing (low value of Us), like satin, will require a higher w.
Thanks so much :)
To find the equation for the angular speed needed to keep a person against the wall in a rotating cylindrical ride, we need to consider the concept of centripetal force.
When the ride rotates, the person experiences a centripetal force that pushes them towards the center of the cylinder. This force is provided by the friction between the person and the wall. To determine the equation for the required angular speed, we need to analyze the forces acting on the person.
Let's start by considering the forces involved. The two main forces acting on the person are the normal force (N) exerted by the wall, directed toward the center of the cylinder, and the person's weight (mg), directed downward. The frictional force (f) between the person and the wall opposes the centrifugal force and provides the centripetal force required to keep the person against the wall.
The centripetal force is given by:
f = m * (v^2 / r)
where:
- m is the mass of the person,
- v is the linear speed of the person, and
- r is the radius of the cylindrical ride.
The linear speed (v) can be expressed in terms of the angular speed (ω) and the radius (r) of the ride as:
v = ω * r
Substituting this into the previous equation, we have:
f = m * (ω^2 * r / r)
Simplifying:
f = m * ω^2 * r
To keep the person against the wall, the frictional force (f) must be equal to or greater than the maximum static frictional force (fs). Therefore, the maximum static frictional force can be expressed as:
fs = μs * N
where:
- μs is the coefficient of static friction between the person and the wall, and
- N is the normal force exerted by the wall.
Since the normal force (N) is equal to the person's weight (mg), we can rewrite this equation as:
fs = μs * mg
Setting fs equal to the centripetal force (f), we obtain:
μs * mg = m * ω^2 * r
Canceling out the mass (m) on both sides, we get:
μs * g = ω^2 * r
Finally, solving for the angular speed (ω):
ω = √(μs * g / r)
This equation gives you the required angular speed to keep the person against the wall of the rotating cylindrical ride, given the radius of the ride (r) and the coefficient of static friction (μs) between the person and the wall.