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Consider a vertical loop in the roller coaster ride shown in the figure. Suppose you are designing such a loop and you want the normal force that the track exerts on the cars to be at least ¼ their weight at the instant the car is at the top of the loop. Let point A be a point on the roller-coaster track just before the track begins to rise into the loop, and suppose the vertical coordinate of a car’s center of mass as it passes the top of the loop is 15 meters above the vertical coordinate of the car’s center of mass as it passes point A. What minimum speed should the roller-coaster car have as it passes point A?  Assume the loop is a circle.  Answer: Greater than 19.6 m/s

Consider a vertical loop in the roller coaster ride shown in the figure. Suppose you are designing such a loop and you want the normal force that the track exerts on the cars to be at least ¼ their weight at the instant the car is at the top of the loop. Let point A be a point on the roller-coaster track just before the track begins to rise into the loop, and suppose the vertical coordinate of a car’s center of mass as it passes the top of the loop is 15 meters above the vertical coordinate of the car’s center of mass as it passes point A. What minimum speed should the roller-coaster car have as it passes point A?  Assume the loop is a circle.  Answer: Greater than 19.6 m/s

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Consider a vertical loop in the roller coaster ride shown in the figure. Suppose you are designing such a loop and you want the normal force that the track exerts on the cars to be at least ¼ their weight at the instant the car is at the top of the loop. Let point A be a point on the roller-coaster track just before the track begins to rise into the loop, and suppose the vertical coordinate of a car’s center of mass as it passes the top of the loop is 15 meters above the vertical coordinate of the car’s center of mass as it passes point A. What minimum speed should the roller-coaster car have as it passes point A?  Assume the loop is a circle.  Answer: Greater than 19.6 m/s

The image shows a roller coaster performing a vertical loop. This loop is a signature feature in many roller coaster designs, where the track makes a 360-degree turn. In this particular loop, the track begins at the ground level, ascends into a vertical circle, and then descends back down. Riders experience significant forces due to gravity and acceleration, especially at the top of the loop, where they may feel weightless. The structure is typically supported by a frame of beams, ensuring stability and safety. The roller coaster cars are shown with passengers enjoying the ride as they are securely fastened within the loop. Design elements like this are used to create thrilling experiences, combining speed, height, and gravity to entertain and challenge riders. Understanding the physics behind such loops, including concepts of centripetal force and acceleration, is crucial in roller coaster engineering.
Transcribed Image Text:The image shows a roller coaster performing a vertical loop. This loop is a signature feature in many roller coaster designs, where the track makes a 360-degree turn. In this particular loop, the track begins at the ground level, ascends into a vertical circle, and then descends back down. Riders experience significant forces due to gravity and acceleration, especially at the top of the loop, where they may feel weightless. The structure is typically supported by a frame of beams, ensuring stability and safety. The roller coaster cars are shown with passengers enjoying the ride as they are securely fastened within the loop. Design elements like this are used to create thrilling experiences, combining speed, height, and gravity to entertain and challenge riders. Understanding the physics behind such loops, including concepts of centripetal force and acceleration, is crucial in roller coaster engineering.
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