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### Roller Coaster Problem: Physics Application **Problem Statement:** A roller coaster is at the top of a 14 m hill with a loop at the bottom. The loop has a radius of 5 meters, and the coaster starts from rest at the top of the 14 m hill. Ignore friction for this problem. **Questions:** 1. **How fast is the roller coaster moving at the bottom of the hill?** *(Before the loop)* 2. **How fast is the roller coaster moving at the top of the loop?** 3. **What is the normal force exerted by the seat of the roller coaster on a 45 kg child at the top of the loop?** **Diagram Explanation:** The provided diagram depicts the roller coaster's path as follows: - A descent from a 14-meter high hill. - A loop at the bottom with a radius of 5 meters. --- **Solution Approach:** 1. **Determining the Speed at the Bottom of the Hill:** - Utilizing energy conservation principles where potential energy at the top is converted into kinetic energy at the bottom. 2. **Calculating the Speed at the Top of the Loop:** - Accounting for the change in height and applying the conservation of mechanical energy. 3. **Finding the Normal Force on the Child:** - Using the centripetal force requirement and the gravitational force acting on the child to compute the normal force exerted by the seat. By working through these calculations, students can apply fundamental physics concepts such as gravitational potential energy, kinetic energy, and forces in circular motion to solve real-world problems.

### Roller Coaster Problem: Physics Application **Problem Statement:** A roller coaster is at the top of a 14 m hill with a loop at the bottom. The loop has a radius of 5 meters, and the coaster starts from rest at the top of the 14 m hill. Ignore friction for this problem. **Questions:** 1. **How fast is the roller coaster moving at the bottom of the hill?** *(Before the loop)* 2. **How fast is the roller coaster moving at the top of the loop?** 3. **What is the normal force exerted by the seat of the roller coaster on a 45 kg child at the top of the loop?** **Diagram Explanation:** The provided diagram depicts the roller coaster's path as follows: - A descent from a 14-meter high hill. - A loop at the bottom with a radius of 5 meters. --- **Solution Approach:** 1. **Determining the Speed at the Bottom of the Hill:** - Utilizing energy conservation principles where potential energy at the top is converted into kinetic energy at the bottom. 2. **Calculating the Speed at the Top of the Loop:** - Accounting for the change in height and applying the conservation of mechanical energy. 3. **Finding the Normal Force on the Child:** - Using the centripetal force requirement and the gravitational force acting on the child to compute the normal force exerted by the seat. By working through these calculations, students can apply fundamental physics concepts such as gravitational potential energy, kinetic energy, and forces in circular motion to solve real-world problems.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Roller Coaster Problem: Physics Application **Problem Statement:** A roller coaster is at the top of a 14 m hill with a loop at the bottom. The loop has a radius of 5 meters, and the coaster starts from rest at the top of the 14 m hill. Ignore friction for this problem. **Questions:** 1. **How fast is the roller coaster moving at the bottom of the hill?** *(Before the loop)* 2. **How fast is the roller coaster moving at the top of the loop?** 3. **What is the normal force exerted by the seat of the roller coaster on a 45 kg child at the top of the loop?** **Diagram Explanation:** The provided diagram depicts the roller coaster's path as follows: - A descent from a 14-meter high hill. - A loop at the bottom with a radius of 5 meters. --- **Solution Approach:** 1. **Determining the Speed at the Bottom of the Hill:** - Utilizing energy conservation principles where potential energy at the top is converted into kinetic energy at the bottom. 2. **Calculating the Speed at the Top of the Loop:** - Accounting for the change in height and applying the conservation of mechanical energy. 3. **Finding the Normal Force on the Child:** - Using the centripetal force requirement and the gravitational force acting on the child to compute the normal force exerted by the seat. By working through these calculations, students can apply fundamental physics concepts such as gravitational potential energy, kinetic energy, and forces in circular motion to solve real-world problems.
Transcribed Image Text:### Roller Coaster Problem: Physics Application **Problem Statement:** A roller coaster is at the top of a 14 m hill with a loop at the bottom. The loop has a radius of 5 meters, and the coaster starts from rest at the top of the 14 m hill. Ignore friction for this problem. **Questions:** 1. **How fast is the roller coaster moving at the bottom of the hill?** *(Before the loop)* 2. **How fast is the roller coaster moving at the top of the loop?** 3. **What is the normal force exerted by the seat of the roller coaster on a 45 kg child at the top of the loop?** **Diagram Explanation:** The provided diagram depicts the roller coaster's path as follows: - A descent from a 14-meter high hill. - A loop at the bottom with a radius of 5 meters. --- **Solution Approach:** 1. **Determining the Speed at the Bottom of the Hill:** - Utilizing energy conservation principles where potential energy at the top is converted into kinetic energy at the bottom. 2. **Calculating the Speed at the Top of the Loop:** - Accounting for the change in height and applying the conservation of mechanical energy. 3. **Finding the Normal Force on the Child:** - Using the centripetal force requirement and the gravitational force acting on the child to compute the normal force exerted by the seat. By working through these calculations, students can apply fundamental physics concepts such as gravitational potential energy, kinetic energy, and forces in circular motion to solve real-world problems.
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