Mechanical Energy Examples: Roller Coasters and Energy Conversion

📚 Quick Study Guide

• 🎢 Mechanical Energy: The sum of potential and kinetic energy in a system.
• ⬆️ Potential Energy (PE): Energy due to an object's position or condition. Formula: $PE = mgh$, where $m$ is mass, $g$ is the acceleration due to gravity, and $h$ is height.
• 🏃 Kinetic Energy (KE): Energy due to an object's motion. Formula: $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.
• 🔄 Energy Conversion: The process of changing energy from one form to another (e.g., potential to kinetic).
• 🔒 Conservation of Energy: In a closed system, the total mechanical energy (PE + KE) remains constant, assuming no energy loss due to friction or air resistance.
• 💡 Roller Coasters: Illustrate energy conversion; at the highest point, PE is maximum, and at the lowest point, KE is maximum.
• ✍️ Work-Energy Theorem: The work done on an object equals the change in its kinetic energy. $W = \Delta KE$

🧪 Practice Quiz

1. What type of energy is associated with the height of a roller coaster at the top of a hill?
   1. Kinetic energy
   2. Potential energy
   3. Thermal energy
   4. Chemical energy
2. Which formula correctly represents kinetic energy?
   1. $KE = mgh$
   2. $KE = \frac{1}{2}mv^2$
   3. $KE = mc^2$
   4. $KE = \frac{gh}{2}$
3. As a roller coaster descends a hill, what energy conversion occurs?
   1. Kinetic energy to potential energy
   2. Potential energy to kinetic energy
   3. Thermal energy to potential energy
   4. Chemical energy to kinetic energy
4. In an ideal roller coaster (no friction), what happens to the total mechanical energy?
   1. Increases
   2. Decreases
   3. Remains constant
   4. Becomes zero
5. If a roller coaster car has a mass of 500 kg and is at a height of 30 meters, what is its potential energy (assuming g = 9.8 m/s²)?
   1. 14,700 J
   2. 147,000 J
   3. 1,470 J
   4. 147 J
6. What does the Work-Energy Theorem state?
   1. Work is equal to potential energy.
   2. Work is equal to the change in kinetic energy.
   3. Work is always zero.
   4. Work is equal to mass times height.
7. Which of the following factors does NOT affect kinetic energy?
   1. Mass
   2. Velocity
   3. Height
   4. Speed