Case Study:

At an amusement park, a roller coaster is pulled up to its highest point using a motor. After reaching this peak, the motor stops, yet the coaster continues to move along the track, climbing smaller hills and descending valleys without any additional engine support. Observations show that the initial height of the first peak is 40 m, while subsequent peaks reach only 30 m and 25 m respectively.

motor pulled up to its highest point using a motor. The motor provides the necessary power to save us time and effort in reaching that peak.

Students notice that the speed of the coaster increases as it moves downward and decreases as it climbs upward. At the lowest point, the coaster reaches its maximum speed. However, it never climbs higher than the initial 40 m height.

This behavior raises an important question: how does the roller coaster keep moving without an engine, and why does it fail to reach a higher height than the starting point?

This phenomenon can be explained using the Law of Conservation of Energy, If you're curious about how this applies to more than just rides, check out these real-life examples of energy conservation that we see every day. where the Potential Energy at the highest point converts into Kinetic Energy as the coaster descends. If the math behind these two forces feels a bit confusing, here is a simple breakdown of the differences between kinetic and potential energy to help you keep them straight. Due to friction and air resistance, some energy is lost as heat, preventing the coaster from reaching its original height again.

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CASE-BASED QUESTIONS

MCQ

Q1. At which point does the roller coaster have maximum kinetic energy?
A. Highest point (40 m)
B. Midway up a hill
C. Lowest point
D. At rest

Q2. Why does the roller coaster not reach the same height again?
A. Loss of mass
B. Increase in gravity
C. Loss of energy due to friction
D. Change in track design

Assertion - Reason

Q3.  Assertion (A): The total mechanical energy of the roller coaster decreases over time.
Reason (R): Some energy is lost due to friction and air resistance.

A. Both A and R are true, and R is the correct explanation of A
B. Both A and R are true, but R is not the correct explanation
C. A is true, R is false
D. A is false, R is true

Application-Based Question

Q4. If the roller coaster starts from a height of 50 m instead of 40 m, predict what will happen to the heights of subsequent peaks.

Q5. Explain why the speed of the coaster increases as it moves downward.

Data-Based Question

Q6. Given: Initial height = 40 m, second peak = 30 m, third peak = 25 m
What does this data suggest about energy transformation in the system?

ANSWER KEY WITH EXPLANATION

A1. C- Lowest point
Explanation: At the lowest point, gravitational potential energy is minimum and kinetic energy is maximum as per energy conversion principles.

A2. C- Loss of energy due to friction
Explanation: Some mechanical energy is converted into heat due to friction and air resistance, reducing total usable energy.

A3. A. Both A and R are true, and R is the correct explanation
Explanation: Mechanical energy decreases because non-conservative forces (friction) convert it into heat.

A4. Explanation: Higher initial height means more initial potential energy, so subsequent peaks will also be higher, though still less than the starting point due to energy loss.

A5. Explanation: As the coaster descends, potential energy converts into kinetic energy, .increasing its speed.
This is a classic example of how gravity does work on the coaster; you can learn more about how positive and negative work affects motion right here.

A6. Explanation: The decreasing heights indicate loss of mechanical energy due to friction, supporting the Law of Conservation of Energy with energy transformation and dissipation.

HOTS EXTENSION QUESTIONS

1. If friction could be completely eliminated, predict how the roller coaster would behave after the first drop.

2. How would increasing the mass of the roller coaster affect its motion and energy transformations?