You may be looking for the answers for Student Exploration: Roller Coaster Physics on Gizmo. If so, you are able to check the answers below according to the StuDocu. However, it is important for you to note that the answers below are for learning only, not for cheating.

**Prior Knowledge Questions**

- What happens at the beginning of every roller coaster ride?

Answer: the car is pulled up a long hill.

- Does the roller coaster ever get higher than the first hill? Explain.

Answer: the roller coaster cannot go higher because the total energy of the roller coaster can’t increase.

**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).

- Press Play to roll the 35-gram toy car down the track. Does the car break the egg?

Answer: No

- Click Reset. Set Hill 1 to 80 cm, and click Play. Does the car break the egg?

Answer: Yes

- Click Reset. Lower Hill 1 back to 70 cm and select the 50-gram toy car. Click Play. Does the 50-gram car break the egg?

Answer: Yes

- What factors seem to determine whether the car will break the egg?

Answer: the mass of the car and the speed of the car determine whether the car will break the egg.

**Questions: What factors determine the speed of a roller coaster?**

- Observe: Set Hill 1 to 100 cm, Hill 2 to 0 cm, and Hill 3 to 0 cm. Be sure the Coefficient of friction is set to 0.00. (This means that there is no friction, or resistance to motion.)

A. Click Play. What is the final speed of the toy car?

Answer: 442.9 cm/s

B. Try the other cars. Does the mass of the car affect its final speed?

Answer: No

- Collect data: Find the final speed of a toy car in each situation. Leave the last column blank.

Hill 1 | Hill 2 | Hill 3 | Final Speed | Total Height Lost |

40 cm | 0 cm | 0 cm | 280.1 cm/s | 40 cm |

40 cm | 30 cm | 0 cm | 280.1 cm/s | 40 cm |

60 cm | 50 cm | 20 cm | 280.1 cm/s | 40 cm |

60 cm | 0 cm | 0 cm | 343.1 cm/s | 60 cm |

60 cm | 45 cm | 0 cm | 343.1 cm/s | 60 cm |

90 cm | 75 cm | 30 cm | 343.1 cm/s | 60 cm |

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

A. What did each set of trials have in common?

Answer: The final speed was the same.

B. Did hill 2 have any effect on the final speed?

Answer: 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.

Answer: The answer is in the chart above.

D. What do you notice about the Total Height Lost in each set of trials?

Answer: In each set of trials, the total height lost was the same.

- 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?

Answer: the only factor that affects the final speed is the total height lost.

**Question: How does energy change on a moving roller coaster?**

- 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?

Answer: No

- 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?

Answer: Dec

B. What happens to potential energy as the car goes up the hill?

Answer: Inc

- 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?

Answer: Inc

B. What happens to kinetic energy as the car goes up the hill?

Answer: Dec

- 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.

- Draw conclusions: How are potential energy, kinetic energy, and total energy related?

Answer: The total energy of the car is equal to the sum of its gravitational potential energy and its kinetic energy.

- 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/s2on Earth’s surface:

U = mgh

Energy is measured in joules (J). One joule is equal to one 1 kg•m2/s2. 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?

Answer: 0.050 kg

B. Set Hill 1 to 75 cm and the other hills to 0 cm. What is the height in meters?

Answer: 0.75 m

C. What is the potential energy of the car, in joules

Answer: 0.368 J

- Calculate: Kinetic energy (K) depends on the mass and speed (v) of the object. The equation for kinetic energy is:

K = ½ mv2

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?

Answer: 3.836 m/s

B. What is the kinetic energy of the car, in joules? (Use the mass in kg.)

Answer: 0.368 J

C. How does the car’s kinetic energy at the bottom of the hill compare to its potential energy at the top?

Answer: the same

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