In a popular amusement park ride, a rotating cylinder of radius 2.90 meters is set into rotation with a period of 2.28 seconds. The floor then drops away, leaving the riders suspended against the wall in a vertical position.
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To understand how the riders are suspended against the wall in a vertical position on the amusement park ride, we need to analyze the rotational motion and the forces acting on the riders.
First, let's consider the rotational motion. The rotating cylinder has a radius of 2.90 meters and a period of 2.28 seconds. The period is the time taken for one complete revolution. We can calculate the angular velocity (ω) of the cylinder using the formula:
ω = 2π / T,
where ω is the angular velocity and T is the period. Plugging in the given values, we can calculate the angular velocity:
ω = 2π / 2.28 seconds.
Next, let's examine the forces acting on the riders as they are suspended against the wall. When the floor drops away, the vertical component of the riders' weight provides the necessary centripetal force to keep them against the wall. This force is provided by the friction between the riders and the wall.
The magnitude of the centripetal force can be calculated using the formula:
Fc = m * ω^2 * r,
where Fc is the centripetal force, m is the mass of the rider, ω is the angular velocity, and r is the radius of the cylinder. In this case, we assume the mass of each rider is constant.
Now, to understand why the riders are suspended against the wall in a vertical position, we can assume there is friction between the riders and the wall acting as the centripetal force. This friction force is directed towards the center of the cylinder and is what keeps the riders in place.
In this amusement park ride, the riders experience a combination of gravitational force and friction force. The net force acting on each rider is the difference between the gravitational force and the friction force. When the net force is zero, the rider is in equilibrium and is suspended against the wall.
To summarize, the rotational motion of the cylinder provides the angular velocity, which, when combined with the gravitational force, creates a net force that is balanced by the friction force between the riders and the wall. This allows the riders to be suspended in a vertical position on the amusement park ride.