Your analysis is correct--you've done all the calculations correctly, following the right procedures.
However your data are not accurate. There is very little difference in the periods of those pendulums, while there is a very significant difference in the times necessary to travel down that ramp.
You need to watch the clips again and revise your data. If you have trouble hearing the synchronization of the pendulum with the sounds on the clip, you might instead use the Timer program.
Before you modify any calculations, send me your revised times on the ramps and a description of how you got them.
Phy 201
Experiment #5
Determination of the acceleration of gravity using acceleration vs. slope.
Rise (cm) Run (cm) Slope (cm) # Periods Pend. Length (cm) Time of each oscillation (sec)
1.26 44 0.028636 2 27.5 1.048809
2.04 44 0.046364 2 26 1.019804
1.69 44 0.038409 2 27 1.03923
0.95 44 0.021591 2 28.2 1.062073
To figure out the slope, I did rise/run, then I used Time = 0.2 sqrt (L) formula to figure out the time interval for each cycle of the pendulum. Using the time for each cycle and then multiplying it by how many cycles it took for the car to roll down the ramp give me the total time in seconds that it took the car to roll.
Cycles per second Distance Traveled (cm) vAve(cm/s) vf (cm/s) Acceleration (cm/s^2)
2.0976177 44 20.976177 41.952354 19.99999993
2.0396078 44 21.572775 43.14555 21.15384606
2.078461 44 21.16951 42.33902 20.37037035
2.124146 44 20.714207 41.428414 19.5035624
For the vAve, I divided the distance traveled (‘ds) by the time (‘dt). Then I doubled the vAve to get the final velocity of the car. For acceleration, I used the equation (vf-v0) / ‘dt. Since the initial velocity is zero, the spreadsheet only shows vf/’dt for the acceleration.
x – intercept = -0.277822301
y – intercept = 18.13420454
Slope = 62.896
Though I’m not entirely sure if I did this right, but to change the slope by 1, the change in acceleration would have to be 0.02(cm/s^2). To figure this out, I just added numbers onto the two highest acceleration points (changing all the points on the graph by an equal amount does not change the slope any) until the slope increased by 1 up to 63.896cm/s.
I feel that my time for each ramp slope is pretty accurate. I used the pendulum as a timer and changed the length of the pendulum to get an even 2 cycles for every ramp height. This made my times for each oscillation fairly similar and that helped keep the overall results relatively linear.
Here are my answers to the specified questions. I did as instructed in the paragraph on the assignments page contrary to what you have now specified.