Student Exploration: Roller Coaster Physics, Exercises of Mathematical Physics

Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes.

Typology: Exercises

2025/2026

Available from 01/28/2026

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At the beginning of a roller coaster ride, the coaster
car is pulled to the top of the first hill, and released
afterwards. The car accelerates downwards, and the
velocity of the car increases from 0 to maximum
while rolling down on the track due to gravity.
The roller coaster does not get higher than the first hill
if it is not powered by any other source. The highest
position of the car would have the maximum potential
energy.
At the top of the first hill, potential energy is maximum,
and the total mechanical energy would be the same as
potential energy. When there is friction, the total
mechanical energy will be decreased, and the
maximum height reached by the roller coaster would
be less than the height of the first hill. But if there
wasn't any friction, the total mechanical energy would
be conserved. Therefore, the maximum height that the
roller coaster car would go would be the same as the
Name
:
Student Exploration: Roller Coaster Physics
Directions: Follow the instructions to go through the simulation. Respond to the questions and
prompts in the orange boxes.
Vocabulary: friction, gravitational potential energy, kinetic energy, momentum
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Sally gets onto the roller coaster car, a bit nervous already. Her heart beats
faster as the car slowly goes up the first long, steep hill.
1. What happens at the beginning of every roller coaster ride?
2. Does the roller coaster ever get higher than the first hill? Explain.
Gizmo Warm-up
The Roller Coaster Physics Gizmo models a roller coaster with a toy
car on a track that leads to an egg. You can change the track or
the car. For the first experiment, use the default settings (Hill 1 =
70 cm,
Hill 2 = 0 cm, Hill 3 = 0 cm, 35-g car).
No, just
Date:
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At the beginning of a roller coaster ride, the coaster car is pulled to the top of the first hill, and released afterwards. The car accelerates downwards, and the velocity of the car increases from 0 to maximum while rolling down on the track due to gravity. The roller coaster does not get higher than the first hill if it is not powered by any other source. The highest position of the car would have the maximum potential energy. At the top of the first hill, potential energy is maximum, and the total mechanical energy would be the same as potential energy. When there is friction, the total mechanical energy will be decreased, and the maximum height reached by the roller coaster would be less than the height of the first hill. But if there wasn't any friction, the total mechanical energy would be conserved. Therefore, the maximum height that the roller coaster car would go would be the same as the Name :

Student Exploration: Roller Coaster Physics

Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: friction, gravitational potential energy, kinetic energy, momentum Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Sally gets onto the roller coaster car, a bit nervous already. Her heart beats faster as the car slowly goes up the first long, steep hill.

  1. What happens at the beginning of every roller coaster ride?
  2. Does the roller coaster ever get higher than the first hill? Explain. Gizmo Warm-up The Roller Coaster Physics Gizmo models a roller coaster with a toy car on a track that leads to an egg. You can change the track or the car. For the first experiment, use the default settings ( Hill 1 = 70 cm, Hill 2 = 0 cm, Hill 3 = 0 cm, 35-g car). No, just Date:
  1. Press Play ( ) to roll the 35-gram toy car down the track. Does the car break the egg?

Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All

  1. Analyze: Look at the data carefully. Notice that it is organized into two sets of three trials.

The only factor that affects the final speed is the total height lost, and the final speed is not affected by the mass of the car, or the height of the middle hill. The energy does not change. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All A. What did each set of trials have in common? The final speed was the same B. Did hill 2 have any effect on the final speed? No C. Label the last column of the table Total height lost. Fill in this column by subtracting the height of hill 3 from the height of hill 1. D. What do you notice about the Total height lost in each set of trials? In each set, the height lost was the same.

  1. Draw conclusions: When there is no friction, what is the only factor that affects the final speed of a roller coaster? What factors do not affect the final speed of a roller coaster? Activity B: Energy on a roller coaster Get the Gizmo ready: ● Click Reset. Select the 50-g car. ● Check that the Coefficient of friction is 0.00. ● Set Hill 1 to 100 cm, and Hill 2 and 3 to 0 cm. Question: How does energy change on a moving roller coaster?
  2. Observe: Turn on Show graph and select E vs t to see a graph of energy ( E ) versus time. Click Play and observe the graph as the car goes down the track. Does the total energy of the car change as it goes down the hill?
  3. Experiment: The gravitational potential energy ( U ) of a car describes its energy of position. Click Reset. Set Hill 3 to 99 cm. Select the U vs t graph, and click Play. A. What happens to potential energy as the car goes down the hill? It decreases B. What happens to potential energy as the car goes up the hill? It increases

3. Experiment: The kinetic energy ( K ) of a car describes its energy of motion. Click Reset. Select

the K vs t (kinetic energy vs. time) graph, and click Play. A. What happens to kinetic energy as the car goes down the hill? It increases

They are related because they both have a potential to store energy Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All

  1. Compare: Click Reset. Set Hill 1 to 80 cm, Hill 2 to 60 cm, and Hill 3 to 79 cm. Be sure the 50- g toy car is selected, and press Play. ✏Sketch the U vs t , K vs t , and E vs t graphs below.
  2. Draw conclusions: How are potential energy, kinetic energy, and total energy related?
  3. Calculate: Gravitational potential energy ( U ) depends on three things: the object’s mass ( m ), its height ( h ), and gravitational acceleration ( g ), which is 9.81 m/s^2 on Earth’s surface: U = mgh Energy is measured in joules (J). One joule is equal to one 1 kg•m^2 /s^2. When calculating the energy of an object, it is helpful to convert the mass and height to kilograms and meters. (Recall there are 1,000 grams in a kilogram and 100 centimeters in a meter.) A. What is the mass of the 50-gram car, in kilograms? 0.050 Kg B. Set Hill 1 to 75 cm and the other hills to 0 cm. What is the height in meters? 0.75 m C. What is the potential energy of the car, in joules? 0.367 J
  4. Calculate: Kinetic energy ( K ) depends on the mass and speed ( v ) of the object. The equation for kinetic energy is: K = mv^2 With Hill 1 set to 75 cm, click Play and allow the car to reach the bottom. A. What is the final speed of the car, in meters per second? 3.836 m/s B. What is the kinetic energy of the car, in joules? (Use the mass in kg.)

K = ½ (0.05)(3.836)^

0.367 J

Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All C. How does the car’s kinetic energy at the bottom of the hill compare to its potential energy at the top? Both values are the same.

  1. Challenge: With no friction, you can use the relationship between potential and kinetic energy to predict the speed of the car at the bottom of this hill from its starting height. To do this, start by setting the kinetic and potential energy equations equal to one another: K = U mv^2 = mgh A. Use algebra to solve for the speed. v = sqrt.2gh B. With no friction, does the final speed depend on the mass of the car? No, the final speed does not depend on the mass of the car. C. With no friction, does the final speed depend on the steepness of the hill? No D. What is the final speed of the car if the height of the hill is 55 cm (0. m)? Use the Gizmo to check your answer. 3.285 m/s Gizmo shows a speed of 328.5 cm/s

Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All they required that minimum amount of energy to break the egg.

0.25 J is the minimum energy to break the egg. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All

  1. Draw conclusions: What is the minimum energy required to break the egg?