Student Exploration: Roller Coaster Physics (ANSWER KEY)

Student Exploration: Roller Coaster Physics
Vocabulary: friction, gravitational potential energy, kinetic energy, momentum, velocity
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.
What happens at the beginning of every roller coaster ride?
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).
Press Play () to roll the 35-gram toy car down the track. Does the car break the egg?   
Click Reset (). Set Hill 1 to 80 cm, and click Play. Does the car break the egg?              
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? _
What factors seem to determine whether the car will break the egg

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?
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?                                         
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.
What happens to potential energy as the car goes down the hill?                             
What happens to potential energy as the car goes up the hill?                                              
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.
What happens to kinetic energy as the car goes down the hill?                                
What happens to kinetic energy as the car goes up the hill?                          
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. Describe what happens on 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?
(Activity B continued on next page)
Activity B (continued from previous page)
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/s2 on 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.)
What is the mass of the 50-gram car, in kilograms?                 
Set Hill 1 to 75 cm and the other hills to 0 cm. What is the height in meters?             
What is the potential energy of the car, in joules?
Calculate: Kinetic energy (K) depends on the mass and velocity of the object. (Velocity is the speed and direction of an object.) The equation for kinetic energy is:
With Hill 1 set to 75 cm, click Play and allow the car to reach the bottom.
What is the final velocity (speed) of the car, in meters per second?  
What is the kinetic energy of the car, in joules? (Use the mass in kg.)           
How does the car’s kinetic energy at the bottom of the hill compare to its potential energy at the top?
Challenge: With no friction, you can use the relationship between potential and kinetic energy to predict the velocity 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:
Use algebra to solve for the velocity.    v   =
With no friction, does the final velocity depend on the mass of the car?                    
With no friction, does the final velocity depend on the steepness of the hill?             
What is the final velocity of the car if the height of the hill is 55 cm (0.55 m)?                       
Use the Gizmo to check your answer.

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