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course Phy 201
12/3 11 amSlope at which domino tips:
At what slope does your thickest domino tip?
You might well have dominoes of two or even three different thicknesses. How many different thicknesses do you have?
Test a domino having each of these thicknesses similarly.
Briefly report your results and how they were obtained:
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Using the board as demonstrated in class, I first used my finger to make the board level then judged at what slope the domino tipped when placed in the center of the board.
Small domino tipped with a slope of 2 cm/30 cm
Thickest domino tipped at a slope of 4.5 cm/30 cm
Based on my results, the thicker domino obviously tips at a greater incline than that of the smaller domino.
Your slopes are therefore about .07 and .15.
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Refer to the analysis in Class Notes of the cart-suspended mass-rubberbandChain system we've been observing in class.
The cart system in was assumed in that analysis to have mass .5 kg, which resulted in the conclusion that the domino should tip when the amplitude of the oscillation is greater than 5 cm. This was in contrast to the observation that the tipping point occurred at an amplitude of about 3.8 cm. If the actual mass of the cart system is .6 kg, how does this affect our analysis and our comparison with the observed tipping amplitude?
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We would assume that if the mass is actually .6 kg then the domino would tip when the amplitude of oscillation is greater than 6 cm.
The assumption that the two are proportional is OK as a starting point, but it needs to be validated.
If the mass is actually .6 kg, this affects our predication the angular frequency omega and therefore the maximum acceleration omega^2 * A.
What angular frequency omega is predicted if the mass is .6 kg?
What acceleration did we predict in our previous analysis would cause tipping?
What amplitude is necessary to make omega^2 * A equal to this acceleration?
How does this compare with your assumed amplitude of .6 cm?
Do you think the 'tipping' amplitude is indeed proportional to the mass of the cart?
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We estimated the 2 m/s^2 'tipping acceleration' based on data that had an uncertainty of +- 10%, and the estimated mass of the system, which we might consider to be uncertain by +-20%. Are these uncertainties sufficient to explain the discrepancy between the observed tipping amplitude (3.8 cm) and the predicted tipping amplitude (5.0 cm)?
University Physics students should do a symbolic solution, finding the expression for A in terms of the 'tipping acceleration', k, and m then calculating and applying the differential of this expression. For the moment consider our value of k to be accurate, with negligible uncertainty (ain't so, but for simplicity assume it).
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General College Physics students may simply use the appropriate maximum and/or minimum values of 'tipping acceleration' and mass, along with the given value of k, to calculate the predicted 'tipping amplitude'. If you're unsure what this means, start by assuming 10% greater 'tipping acceleration' and 20% greater mass, and calculate the resulting amplitude necessary to tip the domino; determine by what % this differs from the result .05 m obtained in the notes.
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We assumed k to be 20 Nm in class so that is what I’ll use for calculating my results if needed.
If tipping accel is 10% greater than the 2 m/s^2 as found in class then it is 2.42 m/s^2 and the mass at 20% is .6 kg. Our omega becomes 7.5 rad/s A=2.42 m/s^2/(7.5 rad/s)^2=.04m
If tipping accel is 10% less it is 1.98 m/s^2. And the mass at 20% less is .4 kg. Omega becomes7.07 rad/s. Then A=1.98 m/s^2/(7.07 rad/s)^2=.039 m
If accel is 10% less and mass is 20% more then A=.035 m
If accel is 10%more and mass is 20% less then A=.048 m
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It was observed that when the system was released from the opposite side of the equilibrium point, the tipping point occurred at about 5.3 cm from equilibrium. How does this observation affect our faith in the assumptions we made in the analysis? (hint: start by identifying and listing the assumptions).
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Based on my calculations, if they are accurate, then our assumptions are slightly on the high side but not by much.
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Good overall. Check my notes and let me know if you have questions or want to make additional modifications (do so only if you think they would be beneficial to you).
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