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course PHY 231
1:47 pm 9/9/2014
Ball Ramp:predictions :
The ball will undergo constant acceleration while gravity is the only force acting on it. Raising the height will increase acceleration and velocity and decrease the time interval. For each trial acceleration will increase by a constant factor. Velocity will increase at an exponential rate.
Using dice each height is raise. In order to find the slope I aligned dice as a measurement to calculate the run of the ram.
M = Rise/Run
Hc = Half Cycles (unit of time)
d = dice (unit of distance)
Height 1: slope= 1/36 (1 di)
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The slope is calculated from raw data. The raw data should have been provided. However this result seems clear.
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The length of the pendulum should also be reported, or alternatively the calibration of this pendulum (the number of half-cycles in 30 cycles of the standard pendulum).
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Time = 6 hc
Velocity = 36/6 = 6d per second
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The calculation would read 36 d / (6 hc) = 6 d / hc, or 6 d per hc.
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Acceleration = (6-0) / (6-0) = 1d per hc per hc
Height 2: slope = 1/18 (2 dice)
Time = 4 hc
Velocity = 36/4 = 9 per hc
Acceleration = 9/4 - 2.25 d per hc per hc
Height 3: slope = 1/12 (3 dice)
Time = 3
Velocity = 36/3 = 12 per hc
Acceleration = 12/3 = 4d per hc per hc
Height 4: slope = 1/9 (4 dice)
Time = 2 hc
Velocity = 36/2 = 18 per hc
Acceleration = 18/2 = 9d per hc per hc
As expected, an increase in height leads to an increase in velocity and acceleration. For each trial the velocity increased at a fairly consistent rate and with limited data cannot be confirmed as exponential. Acceleration doubles for each increase in height. The consistency of the increase slopes assisted in relating the data to its previous; however, relating the slope to the acceleration is difficult with limited data and imprecise measurements. What is apparent is the increase in slope yields a higher rate of acceleration.
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If you extrapolate this doubling for each domino, what sort of acceleration would you expect for, say, 10 dominoes, and how long would it take the ball to reach the end of the ramp?
Is this realistic?
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The number of pendulum counts will not have increased by exactly a whole number for each additional die.
However by varying the length of the pendulum, it would be possible to get very close to a whole number of counts on each trial.
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Very good. I've inserted a few notes, but except for a couple of omissions your report and analysis are very good.
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