In the rollercoaster shown in the figure, the height of the first hill is 24.5 meters, and the height of the second hill is 12.8 meters. The track of the rollercoaster is frictionless. If the rollercoaster car’s velocity is 20.4 m/s, what was its velocity at the top of the first hill? v = m/s
In the rollercoaster shown in the figure, the height of the first hill is 24.5 meters, and the height of the second hill is 12.8 meters. The track of the rollercoaster is frictionless. If the rollercoaster car’s velocity is 20.4 m/s, what was its velocity at the top of the first hill? v = m/s
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)...
Related questions
Question
100%
In the rollercoaster shown in the figure, the height of the first hill is 24.5 meters, and the height of the second hill is 12.8 meters. The track of the rollercoaster is frictionless.
| If the rollercoaster car’s velocity is 20.4 m/s, what was its velocity at the top of the first hill? | |||||
|
![### Potential and Kinetic Energy on a Roller Coaster
This diagram illustrates a simple roller coaster scenario to demonstrate the conservation of energy.
**Diagram Explanation:**
- The diagram shows a roller coaster car on a track with varying heights.
- The car starts at the top of the first hill with a height \( h_1 \).
- As the car moves down and then up the next hill, it reaches a second height \( h_2 \).
- The objective is to determine the velocity (\( v \)) of the roller coaster at various points, assuming no friction or air resistance.
**Key Concepts:**
1. **Potential Energy (PE):**
- At the top of the first hill (\( h_1 \)), the car has maximum potential energy given by \( PE = m \cdot g \cdot h_1 \), where \( m \) is the mass of the car and \( g \) is the acceleration due to gravity.
2. **Kinetic Energy (KE):**
- As the car descends from the height \( h_1 \), potential energy is converted to kinetic energy. The kinetic energy at any point is given by \( KE = \frac{1}{2} m v^2 \).
3. **Conservation of Mechanical Energy:**
- The total mechanical energy (sum of potential and kinetic energy) remains constant if we neglect friction and air resistance:
\[
m \cdot g \cdot h_1 = \frac{1}{2} m v^2 + m \cdot g \cdot h_2
\]
- Solving for the velocity (\( v \)) provides insight into how energy conservation affects the speed of the roller coaster at different points on the track.
### Educational Goals:
- To understand how potential and kinetic energy interact in a closed system.
- To apply the conservation of energy to determine speeds at various points on a roller coaster.
This visualization can be used to reinforce concepts in physics related to energy conservation and motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcdf414d3-d29b-4191-96ca-d58cb5b5d0a5%2Fa97d0d2c-ef24-417e-b5f5-4fb788656a09%2Fpqiy9xh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Potential and Kinetic Energy on a Roller Coaster
This diagram illustrates a simple roller coaster scenario to demonstrate the conservation of energy.
**Diagram Explanation:**
- The diagram shows a roller coaster car on a track with varying heights.
- The car starts at the top of the first hill with a height \( h_1 \).
- As the car moves down and then up the next hill, it reaches a second height \( h_2 \).
- The objective is to determine the velocity (\( v \)) of the roller coaster at various points, assuming no friction or air resistance.
**Key Concepts:**
1. **Potential Energy (PE):**
- At the top of the first hill (\( h_1 \)), the car has maximum potential energy given by \( PE = m \cdot g \cdot h_1 \), where \( m \) is the mass of the car and \( g \) is the acceleration due to gravity.
2. **Kinetic Energy (KE):**
- As the car descends from the height \( h_1 \), potential energy is converted to kinetic energy. The kinetic energy at any point is given by \( KE = \frac{1}{2} m v^2 \).
3. **Conservation of Mechanical Energy:**
- The total mechanical energy (sum of potential and kinetic energy) remains constant if we neglect friction and air resistance:
\[
m \cdot g \cdot h_1 = \frac{1}{2} m v^2 + m \cdot g \cdot h_2
\]
- Solving for the velocity (\( v \)) provides insight into how energy conservation affects the speed of the roller coaster at different points on the track.
### Educational Goals:
- To understand how potential and kinetic energy interact in a closed system.
- To apply the conservation of energy to determine speeds at various points on a roller coaster.
This visualization can be used to reinforce concepts in physics related to energy conservation and motion.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON