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According to knowledgable sources, the coefficient of static friction between typical human clothing and steel ranges from 0.210 to 0.390. In the figure, the center of mass of a 54.6kg rider resides 3.6m from the axis of rotation. As a safety expert inspecting the safety of riades at a county fair, you want to reduce the chances of injury. What minimum rotational speed (expressed in rev/s) is needed to keep the occupants from sliding down the wall during the ride?

According to knowledgable sources, the coefficient of static friction between typical human clothing and steel ranges from 0.210 to 0.390. In the figure, the center of mass of a 54.6kg rider resides 3.6m from the axis of rotation. As a safety expert inspecting the safety of riades at a county fair, you want to reduce the chances of injury. What minimum rotational speed (expressed in rev/s) is needed to keep the occupants from sliding down the wall during the ride?

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**Gravitron Ride Physics Explanation** **Description:** The Gravitron is an amusement park ride where riders stand against the inner wall of a large rotating steel cylinder. At a certain point, the floor of the Gravitron drops out, creating the impression that riders might fall from a great height. However, the spinning motion keeps them safely inside. **Design Details:** - Most Gravitron rides have vertical walls, but the example illustrated here features sloped walls, inclined at an angle \( \theta = 25.2^\circ \) to the vertical. **Diagram Explanation:** - The diagram shows a side view of the Gravitron with a rider standing at an angle. - \( r \) is the distance from the axis of rotation to the rider. - \( \mu \) represents the coefficient of static friction. - \( \omega \) symbolizes the rotational speed. - \( \theta \) is the angle of the wall with respect to the vertical. **Friction Details:** - The coefficient of static friction between typical human clothing and steel ranges from 0.210 to 0.390. - In this scenario, the center of mass of a 54.6 kg rider is positioned 3.6 m from the rotation axis. **Safety Calculation Task:** As a safety expert assessing rides at a county fair, the task is to calculate the *minimum* rotational speed (expressed in revolutions per second) required to prevent riders from sliding down the wall.
Transcribed Image Text:**Gravitron Ride Physics Explanation** **Description:** The Gravitron is an amusement park ride where riders stand against the inner wall of a large rotating steel cylinder. At a certain point, the floor of the Gravitron drops out, creating the impression that riders might fall from a great height. However, the spinning motion keeps them safely inside. **Design Details:** - Most Gravitron rides have vertical walls, but the example illustrated here features sloped walls, inclined at an angle \( \theta = 25.2^\circ \) to the vertical. **Diagram Explanation:** - The diagram shows a side view of the Gravitron with a rider standing at an angle. - \( r \) is the distance from the axis of rotation to the rider. - \( \mu \) represents the coefficient of static friction. - \( \omega \) symbolizes the rotational speed. - \( \theta \) is the angle of the wall with respect to the vertical. **Friction Details:** - The coefficient of static friction between typical human clothing and steel ranges from 0.210 to 0.390. - In this scenario, the center of mass of a 54.6 kg rider is positioned 3.6 m from the rotation axis. **Safety Calculation Task:** As a safety expert assessing rides at a county fair, the task is to calculate the *minimum* rotational speed (expressed in revolutions per second) required to prevent riders from sliding down the wall.
**Title: Understanding Ride Safety at a County Fair** As a safety expert inspecting the rides at a county fair, ensuring the prevention of injuries is paramount. One critical aspect is determining the appropriate rotational speed to keep riders safely against the wall during a thrill ride. **Key Question:** What *maximum rotational speed* (expressed in revolutions per second, rev/s) is necessary to prevent occupants from sliding down the wall during the ride? --- To address this, consider factors such as friction, the ride’s radius, and gravitational forces. Calculating the ideal speed ensures both safety and an enjoyable experience for fairgoers. Understanding the physics involved can make a difference in ride safety inspections.
Transcribed Image Text:**Title: Understanding Ride Safety at a County Fair** As a safety expert inspecting the rides at a county fair, ensuring the prevention of injuries is paramount. One critical aspect is determining the appropriate rotational speed to keep riders safely against the wall during a thrill ride. **Key Question:** What *maximum rotational speed* (expressed in revolutions per second, rev/s) is necessary to prevent occupants from sliding down the wall during the ride? --- To address this, consider factors such as friction, the ride’s radius, and gravitational forces. Calculating the ideal speed ensures both safety and an enjoyable experience for fairgoers. Understanding the physics involved can make a difference in ride safety inspections.
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