Materials Included In Kit

Additional Materials Required

Prelab Preparation

Cut the sandpaper into 1 cm x 10 cm strips.

Safety Precautions

Be sure students quickly capture the ball if it leaves the track. Wear safety glasses. Please follow all laboratory safety guidelines.

Lab Hints

• Enough materials are provided in this kit for 30 students working in groups of three or for 10 groups of students. Both parts of this laboratory activity can reasonably be completed in two 50-minute class periods. The prelaboratory assignment may be completed before coming to lab, and the data compilation and calculations may be completed the day after the lab.
• A 2-inch ring clamp (Flinn Catalog No. AP8230) on a support stand is a good way to hold the upper end of the track in place. The track can be inserted through the ring from the bottom and its height easily adjusted by raising the clamp or pulling more track through the ring. If ring clamps are not available, students may tape the track to the support stand, a classroom chair, table leg, wall, etc.
• A paper or plastic cup may be placed at the end of the track to catch the marble if it rolls off the end. Alternately, a “fence” may be created with two or three books to keep the marble from rolling across the floor.

Teacher Tips

• Consider adding a cost factor to the design challenge in Part B for any materials used other than the marble and track. For example, assign a monetary value to each 1 cm x 10 cm sandpaper strip. Additionally, masking tape may be cut into 10-cm strips and attached to the edge of a table or wall cabinet for ease of access, with a cost per piece. Provide cups or other objects that students may use to raise the level of the track. Students must then keep track of expenses for these materials.
• Students may research the difference between circular loops and clothoid (teardrop-shaped) loops. The radius at the bottom of a clothoid loop is larger than at the top. Roller coaster passengers are traveling faster and experiencing greater force at the bottom than the top of a loop, so the larger radius at the bottom of the clothoid loop creates a safer ride.
• Students should know how to determine speed, given the distance and time.
• All groups may have a successful roller coaster design. Consider giving special recognition in various categories. Some suggestions follow.
  — Marble that stops closest to the end 
  — Fastest ride 
  — Highest loop or hill 
  — Greatest average speed (different than fastest ride, depending on ride length or where marble stops) 
  — Most creative stopping method 
  — Least amount spent for supplementary materials (if assigning monetary values—see first tip)

Answers to Prelab Questions

1. Figure 1 represents a section of a roller coaster track. If a marble were rolling along the track, at which point would the marble
   1. have the most potential energy?

      W

   2. be gaining kinetic energy and losing potential energy?

      Z

   3. have the most kinetic energy?

      X

   4. have the greatest speed?

      X

   {14062_PreLab_Figure_1}
2. A 15-g marble is raised to the top of a roller coaster track 0.5 m high.
   1. Use Equation 1 from the Background section to calculate the potential energy of the marble. Remember: 1000 g = 1 kg.
      {14062_PreLabAnswers_Equation_1}
   2. The marble is released and travels down the first slope of the track. Neglecting friction, how much kinetic energy does the marble have when it reaches the bottom of the slope?

      At the bottom of the slope, all the PE the marble had at the beginning would be converted to KE, 0.07 J.

   3. The marble traveled the entire length of the 3-meter track in 1.2 seconds. What was the marble’s average speed?

      v = d/t = 3 m/1.2 s = 2.5 m/s

   4. When testing a roller coaster design, why is important to only make one change at a time before running the next trial?

      Only one change should be made at a time in order to determine the effect of that change on the motion of the marble. If more than one change is made, any difference before and after might be the result of any of one of the changes or of a combination of variables.

Sample Data

Part A.
Mass of steel marble: 16 g
Mass of glass marble: 5 g

Diagram of Track from Part A Part B. Final Test
Marble: Glass Roller Coaster Track Diagram for Part B

Answers to Questions

Design Challenge

1. Which marble will you use for your roller coaster? Be prepared to give a reason for your choice.

   Students may choose the heavier steel marble for more kinetic energy. The heavier marble, however, may slide more if the initial slope is fairly steep, creating more friction and reducing the marble’s speed.

2. Did any part of Part A contribute to inconsistencies in the way the marble traveled along the track? If so, how can more consistency be achieved?

   Students may discover that a consistent release of the marble is critical. In addition, vibrations in the track or tape pulling loose may affect the results.

3. How does the speed of the marble change as it goes around a loop or up and down a hill?

   As the marble travels upward, its speed decreases. As it enters the downward side of the loop or hill, it accelerates until it reaches the bottom.

4. How might the answer to the above question help determine where the special features should be located along the track?

   If a loop or hill is near the end of the track, the marble will be traveling at a fast speed coming out of the loop or at the bottom of the hill. This would make it more difficult for the marble to stop before it reaches the end of the track.

5. What are some possible ways to slow the marble down before it reaches the end?

   Placing strips of tape, sticky side up, or strips of sandpaper along the final stretch of track would create more friction. The end of the track may be raised up, as the marble would lose kinetic energy as it traveled up the slope.

6. Why is it important to draw and label your design with accurate measurements and to record observations and any adjustments made during testing?

   Keeping track of all data during testing is important to ensure consistent results. Accurate data leads to a better analysis of the results to determine the best possible solution to the design challenge. Thorough recording of adjustments made and the results will avoid repeating the same unsuccessful attempts. If the track must be taken down and rebuilt the next day, accurate data collection will ensure the track is constructed the same way.

Post-Lab Questions and Calculations

1. Record your marble choice in the space above the data table for Part B.
2. Give an explanation for your marble choice.

   During the Introductory Activity trials, the glass marble gave more consistent results than the steel marble, so it was chosen for a greater chance of success each time.

3. Calculate the initial potential energy of the marble and record in the column A of the data table. Show your work.

   PE = mgh = 0.005 kg (9.8 m/s²) x 0.55 m = 0.027 J

4. Record the time of the marble ride for each trial in the final test in column B.
5. The total length of the track is 12 feet. Determine the total length of the track in meters if 1 ft = 0.305 m. Record the total length in meters in column C.
   {14062_Answers_Equation_1}
6. Record where the marble stopped from the end of the track for each trial in column D.
7. Calculate the actual distance the marble traveled until it stopped for each trial. Record in column E.

   3.66 m – 0.04 m = 3.62 m

8. Calculate the average speed of the marble for each trial. Fill in column F.

   v = d/t = 3.62/2.25 = 1.63 m/s

9. Most roller coasters move the cars to the top of the first hill using motors and gears run by electric energy. In this activity, what contributed to the marble’s initial potential energy?

   The initial potential energy was transferred to the marble by the work done in lifting the marble to the top of the track.

10. A group of students made a sketch of their roller coaster design (Figure 4). Predict whether or not the marble will make it around the loop without leaving the track and explain your prediction in terms of the marble’s energy.
    {14062_Answers_Figure_4}

    The marble will not make it around the loop since the top of the loop is higher than the starting height of the track. The starting height determines the maximum amount of energy the marble has. The conservation of energy principle states that the marble cannot gain any energy as it travels along the track, unless more work is done to give it more energy.

References

“Roller Coaster Physics: STEM in Action.” Teaching Channel. www.teachingchannel.org/videos/teaching-stem-strategies (accessed January 2016).

Introduction

The roller coaster is a popular thrill ride at amusement parks. In order to make roller coasters fun as well as safe, a great deal of science, technology, engineering and math is required. Design and build a model roller coaster that sends a marble on a fast, fun and safe ride.

Concepts

• Kinetic vs. potential energy
• Friction
• Conservation of energy
• Engineering design

Background

Work is the act of using a force to move an object through a distance. In order to reach the highest point on a roller coaster, energy (work) must be used. The energy expended to raise a roller-coaster car to a higher position is “stored” in the car—the car now has potential energy (PE). The potential energy of the roller-coaster car is related to its weight and height, and is equal to the mass (m) in kilograms of the car multiplied by the acceleration due to gravity (g, 9.8 m/s²) multiplied by the relative height (h) in meters of the car above the ground (Equation 1). The unit of energy is the joule (J).

In this activity, a rolling marble will simulate a roller-coaster car. When the marble rolls downward along the track, its potential energy is converted into kinetic energy, or energy of motion. Kinetic energy (KE) is related to the mass (m) in kilograms (kg) and speed (v) in meters per second (m/s) of the object (Equation 2). The marble’s kinetic energy is converted back into potential energy as it rolls up the track. This is due to the conservation of energy principle. The conservation of energy principle states that energy cannot be created or destroyed—energy can only be converted from one form to another. Therefore, the initial potential energy the marble has at the release point will be completely converted into kinetic energy at the bottom of the roller coaster (neglecting frictional forces). Each time the marble rolls up the track, its potential energy increases and its kinetic energy decreases, but the total amount of energy remains the same (Equation 3). As the marble rolls down the track, its height decreases. Therefore its potential energy also decreases, and its kinetic energy increases as gravity causes the marble to accelerate. Friction is a force that opposes motion. As the marble rolls along the track, friction occurs where the two surfaces come in contact with each other. The track exerts a friction force in the opposite direction as the motion of the marble. Friction causes some of the marble’s kinetic energy to be converted to heat energy, which is not useful with respect to the marble’s motion. If the track were long enough at the bottom, eventually all the kinetic energy of the marble would be converted to an unrecoverable form and the marble would stop. In general, rougher surfaces experience more friction than smooth surfaces and an object that rolls along a surface experiences less friction than it would if it were sliding across the same surface.

Experiment Overview

The purpose of this activity is to build a roller coaster out of the materials provided. The lab begins with an introductory activity to determine the starting height needed for a marble to travel through a loop without leaving the track. The results will be used to design a fast, yet safe roller coaster ride that meets all the design criteria and constraints given by the instructor.

Materials

Prelab Questions

1. Figure 1 represents a section of a roller coaster track. If a marble were rolling along the track, at which point would the marble
   1. have the most potential energy?
   2. be gaining kinetic energy and losing potential energy?
   3. have the most kinetic energy?
   4. have the greatest speed?

2. A 15-g marble is raised to the top of a roller coaster track 0.5 m high.
   1. Use Equation 1 from the Background section to calculate the potential energy of the marble. Remember: 1000 g = 1 kg.
   2. The marble is released and travels down the first slope of the track. Neglecting friction, how much kinetic energy does the marble have when it reaches the bottom of the slope?
   3. The marble traveled the entire length of the 3-meter track in 1.2 seconds. What was the marble’s average speed?
3. When testing a roller coaster design, why is important to only make one change at a time before running the next trial?

Safety Precautions

Be sure to quickly capture the ball if it leaves the track. Wear safety glasses. Please follow all laboratory safety guidelines.

Procedure

Part A. Introductory Activity

1. Obtain the 6-foot piece of foam pipe insulation and note the scored line running along the length.
2. Using the scored line as a guide, cut the insulation in half lengthwise with a plastic knife (see Figure 2).
   {14062_Procedure_Figure_2}
3. Use masking tape to connect the two halves of the pipe together to make one 12-ft long U-shaped track. Make sure the seam where the two pieces meet is smooth so it does not interfere with the motion of the marble as it rolls along the track.
4. Attach one end of the track to a support stand so the end is 0.3 m above the floor. The vertical distance from the beginningof the track to the floor is the rise.
5. Form a loop by curling part of track. The top of the loop should be less than 0.3 m above the floor.
6. Tape the bottom of the loop to the floor.
7. Measure the horizontal distance in meters from the starting point to where the track touches the floor. This horizontal distance is the run (see Figure 3). The rise over the run (rise/run) is the slope of the first part of the track.
   {14062_Procedure_Figure_3}
8. Measure the horizontal distance in meters from the beginning of the run to the bottom of the loop.
9. In a notebook or separate sheet of paper, construct a data table to record the rise, run, distance to the loop and distance from the floor to the top of the loop.
10. Extend the remainder of the track along the floor in a straight line, taping where needed to keep it in place.
11. Place a barrier at the end of the track so the marble does not roll across the floor (e.g., a paper or plastic cup or two or three books to make a “fence”).
12. Obtain one glass marble and one steel marble.
13. Measure and record the mass of each marble.
14. Choose one marble, glass or steel, and release it from the top of the track.
15. Note whether or not the marble makes it around the loop, and if it stays on the track the entire time.
16. Repeat steps 14–15 with the other marble.
17. Make adjustments as needed in the rise, run, or diameter of the loop in order to achieve success. Success is defined as the marble traveling down the slope and around the loop while remaining in contact with the track at all times for a minimum of five trials.
18. Once success has been achieved with either marble or both, draw and label a diagram of the track, including measurements of the rise, run, distance to the loop and height of the loop for Part A on the Roller Coasters Worksheet (use Figure 3 as a guide).

Part B. Design Challenge

The challenge is to design and construct a roller coaster with two special features, either two loops or a loop and a hill. The roller coaster must meet the following criteria and constraints.

• The ride must be safe—the marble must remain in contact with the track at all times during each of three trials.
• The marble must stop at or near the end of the track without falling off. It cannot “crash” into a barrier, but must slow down and come to a stop as close to the end as possible.
• Masking tape may be used to keep the structure of the track in place.
• Other objects may be used to raise the level of the track at any point.
• Masking tape or sandpaper strips, available from the instructor, may be used to provide more friction on the track.
• The time of the ride from the release of the marble to when it stops must be measured.
• The distance from the end of the track where the marble stops must be measured.

Form a working group with other students and discuss following questions to aid in the experimental design.

1. Which marble will you use for your roller coaster? Be prepared to give a reason for your choice.
2. Did any part of Part A contribute to inconsistencies in the way the marble traveled along the track? If so, how can more consistency be achieved?
3. How does the speed of the marble change as it goes around a loop or up and down a hill?
4. How might the answer to the above question help determine where the special features should be located along the track?
5. What are some possible ways to slow the marble down before it reaches the end?
6. Why is it important to draw and label your design with accurate measurements and to record observations and any adjustments made during testing?

Student Worksheet PDF

14062_Student1.pdf