The Basics: Work and Energy on a Roller Coaster

Work

Work is done when a force causes an object to move in the direction of the force. On a roller coaster, work is primarily done by the motors that lift the coaster to the top of the first hill. This work is transformed into gravitational potential energy and becomes the starting point for the ride.

Do I have enough energy to reach this height again?

Energy

• Potential Energy (PE): At the top of the first hill, the coaster has its maximum potential energy, calculated as: PE=mgh

• where:

  • m: Mass of the coaster

  • g: Acceleration due to gravity (9.8 m/s2)

  • h: Height of the hill

• Key Facts:

  • The coaster will never have more energy during the ride than it does at the top of the first hill.

  • It cannot go higher than the first hill unless an external force (like a motor) is applied.

• Kinetic Energy (KE): As the coaster descends, potential energy is converted into kinetic energy, increasing its speed. Kinetic energy is calculated as: KE=½ mv2

Forces Acting on the Roller Coaster

1. Gravity: This force pulls the coaster downward, converting potential energy into kinetic energy. Gravity is what gives the coaster its acceleration on the way down.

2. Normal Force: This force acts perpendicular to the track and creates the thrilling sensations you feel:

   • The normal force decreases at the top of a curve, creating a sense of weightlessness.

   • The normal force increases at the bottom of a curve, making you feel heavier.You can calculate the normal force by analyzing the forces in a circle at the top and bottom of the loop.

3. Friction and Air Resistance: These two forces gradually reduce the total mechanical energy of the coaster. The coaster can’t reach the same height as the first hill without external work.

Keep It Simple: Energy Conservation

When friction is ignored, the total energy of the roller coaster remains constant throughout the ride. This means the energy at the start of the ride equals the energy at the end. Mathematically, you can express this as:

ΔKE=−ΔPE

This equation tells us that the gain in kinetic energy equals the loss of potential energy. Using this principle, you can solve most roller coaster problems by focusing on energy transformations.

Need Help? I’m Here for You!

If you need extra help or have specific questions about solving roller coaster problems, using your calculator, or understanding the concepts of work and energy, I’m here to guide you.

Contact me at Kevin@doyletutor.com to schedule a tutoring session. Together, we’ll build your confidence and ensure your success in physics!