Roller Coasters—What Makes Them Go

Teacher Training Workshop II- April 23, 2005

Purpose--

The Purpose of this Activity is to become familiar with the use of the K’Nex Roller Coaster in teaching physics and mathematics concepts. This is accomplished by using three different approaches and combining these three to investigate the physical properties of the model roller coaster.

Introduction to the Activity

During the December workshop, you investigated several different types of roller coasters and model amusement park rides and their usefulness in teaching science, mathematics and engineering. Today, we will take this a step further and introduce quantitative means to interact with the models to provide a laboratory experience using the re-creation (i.e. modeling and simulation) of real-world objects.

We will start by looking at a simulation of a roller coaster. This simulation is an excellent tool to show how the various physical parameters come together to determine the behavior (or the excitement or “scare factor”) of a roller coaster. Take a few minutes to play around with this simulation, adjusting each parameter (mass, speed, gravity, and friction) in turn and seeing how these affect performance. You will also notice that the roller coaster does not quite make it to the end of the track. What did you have to do to change the simulation to enable the roller coaster to finish the course?

The simulation is located at http://www.funderstanding.com/k12/coaster/ (We will have it loaded on the large Smart Board screen at the end of the room)

The roller coaster is a treasure-trove of physics, from forces and accelerations, to speed and energy. Many physical principles can be studied using the simple model rollercoaster. In this Lab we will look at several of them, to include position, velocity, acceleration, vectors, potential energy, kinetic energy (and the exchange between the two over the course of a roller coaster ride), collisions, and friction.

Procedure

Two Roller Coasters—We will look at two different kinds of roller coasters. One group will work with one roller coaster; the second will work with the other. Although the roller coasters look very different, the procedure for each is the same.

• With the string and the meter stick, make the measurements specified on the Data Sheet, measuring the height with respect to the tabletop on which the structure rests. (Measurements include: height of highest hill, height of secondary hill(s) if any, height of lowest point on track, total track length, number of loops (if any), loop radius for each loop…can you think of others?)
• With the stopwatch, take five measurements, from the starting point at the base of the first hill, until it returns to the starting point or the end-of-the-line. Average these and record the average value on the Data Sheet.
• Designate three to six points along the ride for which you will measure distances and time intervals (it would be a good idea to include valleys adjacent to hills to enable comparison between the potential energy at the top of each hill to the kinetic energy in each valley immediately following each hill).
• Each person will have a stop watch and will take a designated point on the track
• All persons will start their stop watches at the base of the first hill
• The first person will stop his/her watch when the nose of the train reaches Point A, then measure the distance from the starting point to Point A
• The next person will stop his/her watch when the train reaches Point B, then measure the distance from the starting point to Point B. Each successive person will do likewise.
• The instant velocity can be (approximately) found by taking the distance interval between A and B and dividing this by the time interval between the same two points.
• Record these data in the first column of the table, as well as the average train speed along each interval (in cm / sec).
• You will record the kinetic energy (K.E. = ½ mv²) for each interval a little later in the lab.
• At least two pairs of photogates attached to smart timers are found along the roller coasters. Run the ride an additional time and record the values for speed and acceleration
• At a predetermined point on each track, we will use two different means to measure the force of impact should the roller coaster come to a complete stop.
• The first method involves a ping pong ball. Let the train run into the ball and watch the ball carefully, marking the location where it lands and recording the range. We can then use the range equation, neglecting air resistance, to find the initial velocity of the ball, then the energy of the impact on the ball.
• The second method involves a simple pendulum. We can easily measure the pendulum’s swing and find the initial collision velocity from that.

Data Sheet for Roller Coaster Activity

Name of Roller Coaster (circle name): Rippin’ Rocket Screamin’ Serpent

Height of Highest Hill (cm):

Height of secondary hills (cm):

Height of Valleys (lowest point) adjacent to each hill (cm):

Total Track Length (cm):

Number of Loops:

Diameter of Loops (cm):

Number of propelling Motors:

Total Ride Time:

Record any additional measurements you may find useful here:

Travel times (fill in table for three to five measurements):

Interval	Distance (cm)	Time (s)	Average Speed (cm / s)	K. E. (J)
Point A to B
Point B to C
Point C to D
Point D to E
Point E to F

Total mass of train (g):

Potential Energy of Train at top of each Hill:

Kinetic Energy of Train at bottom of each Hill:

Impact of Roller Coaster on Ping Pong Ball:

· Location of Impact

· Range of Flight

· Initial Velocity

· Force of Impact

Maximum Angle of Pendulum After Impact:

· Location of Impact

· Amplitude of Swing

· Initial Velocity

· Force of Impact

Results and Conclusion

Compare this real life “scale model” with the simulated model you played with earlier. What are some advantages and disadvantages of using each to design a roller coaster in real life? Name some successes or failures and how you would incorporate this exercise in a science or mathematics classroom setting.