Place one piece of tape on the ground (starting point) and one on the rim of the wheel (the rider). Roll the wheel away from the starting point (see figure below) and stop the wheel in at least 16 different positions, including points at which the rider is at the top of the wheel and bottom of the wheel.
At each position, measure the distance from the starting point to the bottom of the wheel (x) and the height (h) of the rider. Care should be taken to make sure that the wheel rolls in a straight line, and that the wheel makes at least one complete rotation.
so, did you do this? You should have created a cycloid.
To conduct the experiment and gather the required measurements, follow these step-by-step instructions:
1. Find a suitable location with a smooth and flat surface to perform the experiment.
2. Mark the starting point on the ground using a piece of tape.
3. Measure the height of the rider, denoted as "h," from the ground to a reference point. Ensure the measurement is consistent throughout the experiment.
4. Place another piece of tape on the rim of the wheel, which will act as a reference point for measuring the position of the rider.
5. Position the rider on the wheel at the starting point with the reference tape aligned with the starting point tape on the ground.
6. Begin rolling the wheel away from the starting point, making sure it rolls in a straight line. You can push it or allow gravity to propel it, depending on the setup.
7. Once the wheel reaches a new position, carefully stop it from rolling. At each stopping point, ensure that the reference tape on the wheel lines up vertically with the starting point tape on the ground.
8. Measure the horizontal distance, denoted as "x," from the starting point to the bottom of the wheel. This distance represents how far the wheel has traveled.
9. Measure the height of the rider at the new position, ensuring that the measurement is taken from the ground to the same reference point used in step 3.
10. Record the values of x and h for each stopping point, keeping track of which position corresponds to which measurements. Aim to obtain at least 16 different positions, including points where the rider is at the top and bottom of the wheel.
11. Repeat steps 6 to 10 until you have completed at least one full rotation of the wheel, ensuring that the wheel rolls evenly and consistently.
12. After gathering all the measurements, analyze the data. You can plot the x and h values on a graph, with x on the x-axis and h on the y-axis. This will allow you to observe any patterns or relationships that may exist between the two variables.
By following these steps, you will be able to conduct the experiment and obtain the necessary measurements to study the relationship between the position of the rider on the wheel and the horizontal distance traveled.