ervation of Energy on a Coaster Worksheet.pdf ad Conservation of Energy on a Coaster Worksheet.pdf (260 KB) E=Ef if no work is done Use the coaster below to answer the questions. The coaster is released from rest at A and moves right. Assume no friction! E ?B F Mass of empty coaster is 500kg 20m 10m What location/s has: 1) Greatest speed? 2) Zero speed? 3) Greatest kinetic energy? 4) Least kinetic energy? 5) Greatest potential energy? 6) Kinetic energy equal to potential energy? 7) Potential energy of zero? 8) **(trick question) Where is the least total energy? 9) Will the coaster make it over the second hill? [yes/no] 10) Will the coaster stop at the top of the second hill? [yes / no] Explain your answers.
The Correct Answer and Explanation is:
Answers:
- Greatest speed? – Point F
- Zero speed? – Point A
- Greatest kinetic energy? – Point F
- Least kinetic energy? – Point A
- Greatest potential energy? – Point A
- Kinetic energy equal to potential energy? – Point B
- Potential energy of zero? – Point F
- Least total energy? – Trick question: all points have the same total energy
- Will the coaster make it over the second hill? – Yes
- Will the coaster stop at the top of the second hill? – No
Explanation
This roller coaster problem is a classic application of the Law of Conservation of Mechanical Energy, which states that in the absence of friction or external work, total mechanical energy (E = PE + KE) remains constant throughout the motion.
At Point A, the coaster starts from rest, meaning its kinetic energy (KE) is zero and its potential energy (PE) is at maximum, due to the 20 m height. Since it’s the highest point, it has the greatest potential energy and zero speed.
As the coaster descends to Point F, potential energy is converted entirely into kinetic energy. Since Point F is the lowest (0 m height), PE = 0 and KE is at its maximum, meaning the greatest speed occurs there.
Point B is halfway (10 m), where PE and KE are equal, so that’s where PE = KE.
Because there’s no friction, total energy is conserved: the sum of PE and KE is always constant. That’s why the “least total energy” question is a trick—total energy is the same at every point.
The second hill is 10 m high, so the coaster can easily make it over because it started from a higher point (20 m). It won’t stop at the top because it still retains kinetic energy—it’s just lower than at point F but still nonzero.
This illustrates how potential energy is converted into kinetic energy and vice versa, maintaining a constant total energy throughout the ride.
