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course Phy 121
2/5 11
Experiment 2 Phy 121 Cecil WellsA steel ball ( approx. 1.7 cm dia.) was rolled down an inclined ramp ( a 29.9 cm length of metal shelf standard ). The slope of the ramp was calculated by dividing the rise by the run of the ramp. The measured rises and runs and the calculated slopes are shown in the following table:
Rise ( cm) Run ( cm) Slope ( cm)
0.7 29.9 0.023
1.4 29.9 0.046
2.1 29.9 0.070
2.8 29.9 0.094
The time required for the ball to reach the end of the ramp, from rest, was observed three times for each incline. The average times were calculated by adding the three observed times and dividing by three. The measured heights of the ends of the ramp, the observed times and the calculated average times are shown in the following table:
Heights of ends
of ramp ( cm) Time required ( sec) Average time ( sec)
0 and 0.7 2.046875
2.125
2.0625 2.0781
0 and 1.4 1.4375
1.5625
1.484375 1.4948
0 and 2.1 1.28125
1.28125
1.265625 1.27604
0 and 2.8 1.09375
1.078125
1.078125 1.08333
The average velocity was calculated for each slope by dividing the ramp length ( the distance the ball traveled) by the average time required. The average velocities are shown in the following table:
Slope ( cm) Average velocity ( cm/sec)
0.023 14.4
0.046 20.0
0.07 23.4
0.094 27.6
The average velocities were plotted on a graph with the slope on the y- axis and the average velocity on the x- axis. The line connecting these points was very close to straight which makes the graph linear.
Since the ball starts from rest ( 0 initial velocity) on a straight ramp, the final velocity is expected to be twice the average velocity. The rate of velocity change for each slope was calculated by dividing the final velocity by the average time required. These calculations are shown in the following table:
Slope (cm) Final velocity ( cm/ sec) Rate of velocity change ( cm/ sec) this rate will be in cm/s^2
0.023 28.8 13.9
0.046 40 26.8
0.07 46.8 36.7
0.094 55.2 51
These points were plotted on a graph with the slope on the y- axis and the rate of velocity change on the x- axis. A straight line was fitted to these points and the rise and run of this line was estimated to be 3 cm and 51 cm, respectively. 3 divided by 51 gives a slope of 0.059 cm for this line.
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@& The graph is of rate of vel change vs. slope, so rate would be on the vertical axis and slope on the horizontal.
If you use a straight line best fit to your points the slope will not be 51 cm/s^2. That would be the slope of a line from the origin to the point (.094, 51 cm/s^2), but the origin is not linkely to be a point the straight line.
Plot a good straight line and use points from the line, not data points, to get your slope. I estimate that the slope will be in the rough neighborhood of 600 cm/s^2, and this will be a very good result.
You can just submit this note, along with the values in your final table and your calculation of the graph slope.*@