Companion to the reading passage The Centripetal Dynamic of the Gravitron. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
In the Gravitron amusement-park ride, riders stand with their backs against the padded inside wall of a large vertical cylinder. The cylinder spins faster and faster until it turns at a constant rate. Then the floor drops away, yet the riders stay pinned to the wall without sliding down. A group of students used the ride’s published specifications, shown in Table 1, to analyze a rider moving in a horizontal circle at constant speed.
Table 1: Gravitron Operating Specifications
| Quantity | Value |
|---|---|
| Radius of cylinder | 4.50 m |
| Time for one full rotation at operating speed | 2.50 s |
| Mass of adolescent rider | 55.0 kg |
| Mass of adult rider | 90.0 kg |
Data are representative values for practice.
1. Substitute numerical values into a mathematical representation that can be used to determine the speed of a rider against the wall when the ride is at operating speed. Then calculate the speed.
Model 1 shows a top view of the cylinder with one rider against the wall on the left side of the drum; the center of the drum is to the rider’s right. After the floor drops, three forces act on the rider: the gravitational force of Earth, a normal force from the wall, and a static friction force from the wall. The rider does not move up or down.
Model 1: Top View of the Drum
2. Free-body diagram of the 55.0-kg adolescent rider in Model 1 after the floor drops, seen from the side (up is up; the center of the drum is to the right). The gravitational force Fg points down. Choose the direction of the static friction force Ff from the wall and determine its magnitude.
3. Same side view of the 55.0-kg rider. Choose the direction of the normal force FN from the wall and determine its magnitude at operating speed.
4. The 90.0-kg adult rider and the 55.0-kg adolescent rider ride the Gravitron at the same time, at the same operating speed. Which row correctly compares the adult rider with the adolescent rider?
(Normal force on the adult rider / Minimum coefficient of static friction the adult needs to avoid sliding)
Whether a rider stays pinned depends on the friction between the rider’s clothing and the vinyl wall padding. Engineers measured the coefficient of static friction for several fabrics on the ride’s wall material. Their results are shown in Table 2.
Table 2: Static Friction of Fabrics on Vinyl
| Fabric on vinyl | Coefficient of static friction |
|---|---|
| Dry denim | 0.45 |
| Damp cotton | 0.30 |
| Slick nylon | 0.20 |
Data are representative values for practice.
5. A ride engineer makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
6. Riders often arrive at the Gravitron wet from a nearby water ride. Which change to the ride’s operation would make it more likely that a rider in damp cotton stays pinned to the wall?
Many riders say they feel “thrown outward” against the wall. Imagine that, at one instant while the ride is at operating speed, the section of wall behind a rider suddenly vanished. At that instant, the rider is at the north side of the drum and is moving toward the east.
7. Describe the direction the rider would move immediately after the wall vanished, as seen from above, and explain why.