Procedure: There are 13 steps. Step 1: Set up a ramp with the angle of the incline at about 10° to the horizontal, as shown in Figure A
Step 2: Divide the ramp’s length into six equal parts and mark the six positions on the board with pieces of tape. These positions will be your release points. Suppose your ramp is 200 cm long. Divide 200 cm by 6 to get 33.33 cm per section. Mark your release points every 33.33 cm from the bottom. Place a stopping block at the bottom of the ramp to allow you to hear when the ball reaches the bottom. Step 3: Use either a stopwatch or a computer to measure the time it takes the ball to roll down the ramp from each of the six points. (If you use the computer, position one light probe at the release point and the other at the bottom of the ramp.) Use a ruler or a pencil to hold the ball at its starting position, then pull it away quickly parallel to incline to release the ball uniformly. Do several practice runs with the help of your partners to minimize error. Make at least three timings from each position, and record each time and the average of the three times in Data Table A. Step 4: Graph your data, plotting distance (vertical axis) vs. average time (horizontal axis) on an overhead transparency. Use the same scales on the coordinate axes as the other groups in your class so that you can compare results. Step 5: Repeat Steps 2–4 with the incline set at an angle 5° steeper. Record your data in Data Table B. Graph your data as in Step 4. Step 6: Remove the tape marks and place them at 10 cm, 40 cm, 90 cm, and 160 cm from the stopping block, as in Figure B. Set the incline of the ramp to be about 10°.
Step 7: Measure the time it takes for the ball to roll down the ramp from each of the four release positions. Make at least three timings from each of the four positions and record each average of the three times in Column 2 of Data Table C. Step 8: Graph your data, plotting distance (vertical axis) vs. time (horizontal axis) on an overhead transparency. Use the same coordinate axes as the other groups in your class so that you can compare results. Step 9: Look at the data in Column 2 a little more closely. Notice that the difference between t2 and t1 is approximately the same as t1 itself. The difference between t3 and t2 is also nearly the same as t1. What about the difference between t4 and t3? Record these three time intervals in Column 3 of Data Table C. Step 10: If your values in Column 3 are slightly different from one another, find their average by adding the four values and dividing by 4. Do as Galileo did in his famous experiments with inclined planes and call this average time interval one “natural” unit of time. Note that t1 is already listed as one “natural” unit in Column 4 of Table C. Do you see that t2 will equal—more or less—two units in Column 4? Record this, and also t3 and t4 in “natural” units, rounded off to the nearest integer. Column 4 now contains the rolling times as multiples of the “natural” unit of time. Step 11: Investigate more carefully the distances traveled by the rolling ball in Table D. Fill in the blanks of Columns 2 and 3 to see the pattern. Step 12: You are now about to make a very big discovery - so big, in fact, that Galileo is still famous for making it first! Compare the distances with the times in the fourth column of Data Table C. For example, t2 is two “natural” time units and the distance rolled in time t2 is 22, or 4, times as great as the distance rolled in time t1. Step 13: Repeat Steps 6–10 with the incline set at an angle 5° steeper.Record your data in Data Table E
Conclusion: In this lab, we learned how to measure the distance and the relationship of distance and time by rolling a metal ball down different measurements of incline. We learned how to graph velocity and acceleration using this data.