Merrily we roll along Name Period Date Lab partners Overview Measuring motion of freely falling objects is difficult because they acclerate so fast. The speed increases by 9.8 m/s every second, so Galileo tried slowing it down by tilting the motion closer to horizontal, on a plane inclined at a small angle. Objects still accelerate, but much more slowly. This lab will help you toward an understanding of acceleration in free fall. For best results, measure accurately with meter stick and stopwatch. Materials Meter stick, stopwatch, aluminum ramp, wood block, steel ball, padded target. Procedure 1. Set up a ramp, with the 0 mark against the padded target on the wall. Give it a slight slope, supported by a meter stick on edge, located under the 1 cm mark. You will release the ball from 6 different spots, as shown in Data Table A below. These points divide the ramp into 6 equal segments. 2. Divide up the jobs. You need a ball releaser, a timer, a recorder, and a data processor. During the lab, rotate jobs so everyone tries each job. On the timer s command, release the ball from each starting mark 3 times. When you release it, don t use your hand directly! You ll get more consistent results if you block the ball with a ruler, then release it by moving the ruler down slope, parallel to the ramp. The timer stops her watch when she sees it hit the bottom. Don t wait for the sound (that will cause too much delay). Record the results below. If one trial is very different or has an error, ignore it and try again. Calculate averages. Data table A. Shallow angle, equal distances 0 Average Speed 3. The data processor should graph the distance vs average time for data table A. Note there is no (0,0) data point. If distance is on the vertical axis, the slope will be the speed! Use the prepared axes Mr H will provide. Include a title, names and date, uniform numerical scales, labeled axes including units, and data points connected with straight lines. Overall, these data usually produce a line that is slightly curved.
4. Increase the ramp angle by replacing the meter stick with a wooden block, also at 1 cm. Record the results for this in table B. For each distance, calculate average speed. Data table B. Steep angle, equal distances 0 Average speed 5. On the same graph paper, add data points and a line for data table B, in a contrasting color. Label the lines A and B. 6. Let s try arranging the starting lines differently. This time, release the ball at the spots shown in table C below. These were chosen because each is a multiple of the same distance (7 cm) The distances represent 7 x 1 2, 7 x 2 2, 7 x 3 2 and 7 x 4 2. This sequence of squares is significant, as Galileo discovered 0 years ago in making these same kind of measurements. Measure times for 3 of each, calculate average times and enter them into table C. Data table C. Steep angle, square-sequence distances Trial 1 Trial 2 Trial 3 Average time 7 t 1 = t 1-0= Time differences Time in natural units Natural time squared 28 t 2 = t 2-t 1= 63 t 3 = t 3 t 2=
Analysis 7. To complete data table C, let s use Galileo s method of looking at the data. Lacking a watch, he used his pulse to time events on the ramp. If you measured carefully, the time differences should be roughly similar. Calculate an average of the time differences: sec. We ll call this average one unit of natural time. 8. Divide your average times in table C by the natural time unit, round to the nearest whole number and enter the results in the last column. This procedure smoothes out the irregularities in your data. You should notice a pattern of integers, where the pattern of t 1, t 2, t 3 matches up with natural times of 1, 2, 3 Do you see that the distances (left column) have something to do with squares of the natural time (right column)? This is an insight that should help you appreciate our modern statement of accelerated motion, that shows d varying directly with the square of t: d = ½ a t 2. 9. Prepare a graph of the data table C, showing distance as a function of natural time SQUARED (last column on the table). This usually makes a straight line.. Explain in words: what is speed? What is velocity? What is acceleration? 11. What happens to the speed of the ball as it rolls down the ramp? What evidence from your lab results proves that your answer is correct? Be specific by naming the data table and columns you are talking about. 12. Think about speed in comparing your results for curves A and B. Slope of the line shows speed (distance/time). How did speeds compare? Why were they different? 13. Think about acceleration in comparing A and B. Bending of the line upward shows acceleration (change in speed). How did accelerations compare? Why were they different? 14. Examine your table C. What is the relationship between distance (first column) and time in natural units (last column)? See step 6 if you need a reminder.
15. Instead of releasing the ball along the ramp, suppose you simply dropped it on the ground. It would fall about 5 meters during the first second (do you see how this number was calculated?). How far would it freely fall in 2 seconds if you dropped it? See step 8 if you need a reminder. In 5 seconds? In seconds?
DATA SHEET Data table A. Shallow angle, equal distances 0 Average Speed Data table B. Steep angle, equal distances 0 Average speed Data table C. Steep angle, square-sequence distances Trial 1 Trial 2 Trial 3 Average time 7 t 1 = t 1-0= Time differences Time in natural units Natural time squared 28 t 2 = t 2-t 1= 63 t 3 = t 3 t 2=