Mechanics - Uniform Circular Motion

[Fila Delphia]

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A popular ride at many amusement parks is the Rotor Ride. On this ride, participants walk into a large round room (radius = 4 m) with no ceiling and stand with their backs against the wall, facing into the center of the room. Once all riders are in the room, the ride operator starts the ride’s motor, which causes the room to spin around its center. When the tangential speed of the room is large enough, the floor of the room drops below the feet of the riders, and the riders are all stuck to the spinning wall. The static friction between each rider and the wall is sufficient enough to hold each rider in place without the floor. The average coefficient of static friction is approximately 0.4.

Typically, to ensure no injuries for the riders, the Rotor Ride is operated with a tangential speed that is greater than the minimum speed required before the floor is dropped. Once the tangential speed of the room has reached its operating speed, the motor operates at a constant power level to maintain a constant rotation speed for 1 minute. Then the floor is restored before the speed of the room slows and finally comes to a rest at the end of the ride. The average mass of the Rotor Ride and all riders is 10^6 kg.

NOW here's the question:
What is the minimum tangential speed at which the floor can be dropped on the Rotor Ride and the riders will not slide down the wall?

The issue with this question is in which direction must the normal force be assigned?

Apparently, to solve this problem, the normal force was assigned in the horizontal direction, equal to the centripetal force... as the explanation says "the only force acting on the rider is the normal force, so this must be providing the centripetal force and FN = Fc = mv2 / r."

Why is the Normal force set in the horizontal direction? Is it because the people are against the wall and the centripetal force is pulling the riders towards the center, so the normal force is also directed toward the center? Then why is it in most cases that the normal force is in the vertical direction and is equal to Fg. What's the distinction between these two cases?

Thanks for your help.

 

[ashtonjam]

The normal force is always perpendicular to a surface, and it usually (but not always) is due to weight. If you remember some other cases like when a box is sliding down an inclined plane or a roller coaster cart is going around a loop, the normal force will be pointed in some other direction rather than directly upwards.

The normal force isn't always due to weight, though, although it usually is. In this case, people are being smushed against a wall, so just being in contact with the wall provides a normal force pointing perpendicular to the surface. It happens to be pointing in the center of the circle.

 

[sps27]

A popular ride at many amusement parks is the Rotor Ride. On this ride, participants walk into a large round room (radius = 4 m) with no ceiling and stand with their backs against the wall, facing into the center of the room. Once all riders are in the room, the ride operator starts the ride's motor, which causes the room to spin around its center. When the tangential speed of the room is large enough, the floor of the room drops below the feet of the riders, and the riders are all stuck to the spinning wall. The static friction between each rider and the wall is sufficient enough to hold each rider in place without the floor. The average coefficient of static friction is approximately 0.4.

Typically, to ensure no injuries for the riders, the Rotor Ride is operated with a tangential speed that is greater than the minimum speed required before the floor is dropped. Once the tangential speed of the room has reached its operating speed, the motor operates at a constant power level to maintain a constant rotation speed for 1 minute. Then the floor is restored before the speed of the room slows and finally comes to a rest at the end of the ride. The average mass of the Rotor Ride and all riders is 10^6 kg.

NOW here's the question:
What is the minimum tangential speed at which the floor can be dropped on the Rotor Ride and the riders will not slide down the wall?

The issue with this question is in which direction must the normal force be assigned?

Apparently, to solve this problem, the normal force was assigned in the horizontal direction, equal to the centripetal force... as the explanation says "the only force acting on the rider is the normal force, so this must be providing the centripetal force and FN = Fc = mv2 / r."

Why is the Normal force set in the horizontal direction? Is it because the people are against the wall and the centripetal force is pulling the riders towards the center, so the normal force is also directed toward the center? Then why is it in most cases that the normal force is in the vertical direction and is equal to Fg. What's the distinction between these two cases?

Thanks for your help.

The way I understand this is - suppose if you have a merry go round and if you stand on it. As it goes round you are most likely to be thrown off, unless you catch hold of the bars and prevent yourself from sliding out. So the tendency to be thrown off is called 'centrifugal force' and your hold on the bars provides the necessary 'centripetal force' to remain in circular motion, directed towards the center and equal to centrifugal force.

Using the same analogy here, when I am in the Rotor Ride inside that room and it rotates, I am likely to be thrown off due to centrifugal force. But the wall prevents that from happening. Centrifugal force is exerted on the wall by the person and by newtons third law an equal and opposite reaction force is exerted by the wall on the individual directed towards the center. But there is another force acting on the person and that is gravitational force which also needs to be balanced. So to balance out both these forces, the force exerted by the wall on the person (Normal force) should have a vertical component to balance out the weight and a horizontal component to balance out the centrifugal force. The horizontal component is called the centripetal force and the vertical component is the frictional force. I hope that helps.....

 

[Fila Delphia]

Yes it does help, thank you both of you guys. It helped a lot

 

[mehc012]

A popular ride at many amusement parks is the Rotor Ride. On this ride, participants walk into a large round room (radius = 4 m) with no ceiling and stand with their backs against the wall, facing into the center of the room. Once all riders are in the room, the ride operator starts the ride’s motor, which causes the room to spin around its center. When the tangential speed of the room is large enough, the floor of the room drops below the feet of the riders, and the riders are all stuck to the spinning wall. The static friction between each rider and the wall is sufficient enough to hold each rider in place without the floor. The average coefficient of static friction is approximately 0.4.

Typically, to ensure no injuries for the riders, the Rotor Ride is operated with a tangential speed that is greater than the minimum speed required before the floor is dropped. Once the tangential speed of the room has reached its operating speed, the motor operates at a constant power level to maintain a constant rotation speed for 1 minute. Then the floor is restored before the speed of the room slows and finally comes to a rest at the end of the ride. The average mass of the Rotor Ride and all riders is 10^6 kg.

NOW here's the question:
What is the minimum tangential speed at which the floor can be dropped on the Rotor Ride and the riders will not slide down the wall?

The issue with this question is in which direction must the normal force be assigned?

Apparently, to solve this problem, the normal force was assigned in the horizontal direction, equal to the centripetal force... as the explanation says "the only force acting on the rider is the normal force, so this must be providing the centripetal force and FN = Fc = mv2 / r."

Why is the Normal force set in the horizontal direction? Is it because the people are against the wall and the centripetal force is pulling the riders towards the center, so the normal force is also directed toward the center? Then why is it in most cases that the normal force is in the vertical direction and is equal to Fg. What's the distinction between these two cases?

Thanks for your help.

Centripetal force is NOT a distinct force. It is pretty much just a label for whichever force happens to be pushing/pulling the object towards the center of the circle, whether that is friction, tension, gravity, or whatever.

The normal force is ALWAYS perpendicular to the contact surface. It is the result of Newton's third law (equal and opposite)...if you push on the wall with x amount of force, it pushes back in the opposite direction with x amount of force.

Now, in order for you to move in a circle, something must be accelerating you towards the center of that circle, as your natural inclination would be to continue in a straight line tangential to the RotorRide. That 'something' is the wall...as you push outwards (trying to move in a straight line), it pushes you back inwards. Your final motion is in a circle, so you can label that normal force as the 'centripetal force', which really just allows you to convert between it and the speed of rotation. All of this, however is purely horizontal.

The question is really asking about your vertical forces...you are never falling, so the downward force of gravity must be counteracted. Before you start spinning, it's just the normal force between you and the floor which counteracts the force of gravity. However, as you accelerate and the normal force between you and the wall increases, the friction force between you and the wall begins to counteract the gravitational force, and the normal force between you and the floor decreases. When it reaches zero, you are being held entirely by the friction force, and the floor can be dropped away.