On the Round Up at the amusement park, people stand in a cylindical "room" of radius 6.18 m and the room rotates until it reaches a rotational frequency of 0.89 revolutions per second. At this point, the floor drops out. What is the minimum coefficient of static friction needed so that people will not slide down the wall?

Question

On the Round Up at the amusement park, people stand in a cylindical "room" of radius 6.18 m and the room rotates until it reaches a rotational frequency of 0.89 revolutions per second. At this point, the floor drops out. What is the minimum coefficient of static friction needed so that people will not slide down the wall?

what is the equation i should use to find the coefficient

Answer 1

Normal:

Fn=mr(omega^2) You'll need to change rev/sec into rad/sec
Friction:
Ff= mg
Coefficient of friction
mu = Ff/Fn

Answer 2

To find the minimum coefficient of static friction needed so that people will not slide down the wall, we can use the equation for the net force acting on an object in circular motion:

Fnet = m * v^2 / r

where Fnet is the net force, m is the mass of the object, v is the tangential velocity, and r is the radius of the circular path.

In this case, the net force is equal to the frictional force between the people and the wall that prevents them from sliding down. Therefore, we can rewrite the equation as:

frictional force = m * v^2 / r

Now, we need to determine the tangential velocity (v) of the people inside the cylindrical room. To find this, we can use the formula:

v = 2πr * f

where v is the tangential velocity, r is the radius of the circular path, and f is the rotational frequency.

In this case, the radius (r) of the cylindrical room is given as 6.18 m, and the rotational frequency (f) is given as 0.89 revolutions per second. We need to convert the rotational frequency to radians per second before plugging it into the equation. Since 1 revolution is equal to 2π radians, we can multiply the given rotational frequency by 2π to convert it to radians per second:

f = 0.89 revolutions/second * 2π radians/revolution

Now we can substitute the values of r and f into the formula to find the tangential velocity (v).

Once we have the tangential velocity (v), we can substitute it into the equation for the frictional force:

frictional force = m * v^2 / r

Here, the mass (m) of the people is not provided, but it cancels out when comparing it with the gravitational force acting downward. Therefore, we don't need the exact mass value to find the minimum coefficient of static friction.