course Phy 121
Experiment 3Figure 1. First ramp average velocities vs. second ramp average velocities and the resulting rectangles and slope. Line of best fit in black, sketched line in blue.
Length of First Ramp (cm) First Ramp Average Velocities (cm/s) Second Ramp Average Velocities (cm/s)
10 9.09 2.26
15 9.68 3.82
20 9.62 6.69
25 11.85 8.87
30 11.15 13.57
35 12.54 17.58
40 13.25 21.98
45 14.52 26.01
50 15.67 32.05
Table 1. First ramp average velocities in cm/s vs. second ramp average velocities in cm/s at each length of the first ramp (in cm)
The slope of the constructed line would consist of 2.5. The sketched line, however, does not pass through the origin of the graph (refer to Figure 1). If the constructed line passed through the origin of the graph, it would show a steadier slope. According to Figure 1, the second ramp represents greater average velocities. This should be so, because as the velocity of the first ramp increases, the second ramp velocity should also increase and its final velocity should be nearly double its average velocity according to the hypothesis that when an object accelerates uniformly from rest, its final velocity will be double its average velocity. When considering the initial velocity of the ball on the first ramp, the average velocity of the ball on the first ramp and the final velocity of the ball on the first ramp, the initial velocity would be the least, whereas the final velocity would be the greatest (the ball starts at a lower velocity then what it finishes with). To place in order the velocities of both the first ramp and second ramp would be as follows:
The initial velocity of the ball on the first ramp
The final velocity of the ball on the first ramp
The initial velocity of the ball on the second ramp
The average velocity of the ball on the second ramp
The final velocity of the ball on the second ramp
Figure 2. Velocity of a ball in cm/s vs. clock time in seconds.
We should suspect that the average velocity on the second ramp should be double that of the first ramp because as the ball accelerates down the ramp its velocity increases twice as much as that of the first ramp moving at a uniform acceleration. This experiment does a good job at validating this hypothesis because it represents that at uniform acceleration, the velocity of a ball is double that of its initial velocity.
Measuring the uncertainty of the 30 cm distance did not pose too much of an issue, in fact the uncertainty was approximately +-.1 seconds of 2.69 seconds (2.68 sec < Δt < 2.70 sec represent the minimum and maximum values for which the actual time should lie). This is an appropriate value for the uncertainty in my opinion because throughout the trials at 30 cm, I could have nudged the ball accidentally, or started the clock at slightly different times. The uncertainty value was not substantial; however, therefore the results were not massively affected. If the actual time had equaled the minimum value of 2.68 seconds, the average velocity would have differed only slightly; 11.20 cm/s. On the other hand, if the actual time had equaled the maximum value of 2.70 seconds, the average velocity would have been 11.1cm/s. As a result, the minimum average velocity could have been 11.1 cm/s and the maximum average velocity could have been 11.2 cm/s.
Figure 2. Velocity of ball vs. clock time representing uncertainty blocks for first ramp. Black dot represents average velocity at 30 cm.
If a straight line were to be constructed, it would most likely not pass through every block.
Measuring the uncertainty of the 30 cm distance on the second ramp also did not pose too much of an issue, the uncertainty was approximately +-.2 seconds of 2.21 seconds (2.19 sec < Δt < 2.23 sec represent the minimum and maximum values for which the actual time should lie). This is an appropriate value for the uncertainty in my opinion because throughout the trials at 30 cm, I could have nudged the ball accidentally, or started the clock at slightly different times. The uncertainty value was not substantial; however, therefore the results were not massively affected. If the actual time had equaled the minimum value of 2.19 seconds, the average velocity would have differed only slightly; 13.69 cm/s. On the other hand, if the actual time had equaled the maximum value of 2.23 seconds, the average velocity would have been 13.45 cm/s. As a result, the minimum average velocity could have been 13.45 cm/s and the maximum average velocity could have been 13.69 cm/s.
Figure 3. Velocity of a ball vs. clock time for second ramp and its uncertainty blocks. Black dot represents average velocity at 30 cm.
If a straight line were to be constructed, it would most likely not pass through every block.
Throughout this lab, timing could have posed a slight issue. If distance measurement errors were taken into consideration, this might have also posed a problem. It would probably not be more significant than that of time because both effect the velocity overall.
I can accept labs in this format, but I need you to modify them slightly by inserting a row of '^' symbols at the beginning, and a row of '&' symbols at the end of each of your responses.
Please resubmit and make this revision on subsequent submissions.