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course PH
Accidentally sent two blank submit forms without even an access id hope that doesn't mess anything up.
That can mess things up, but it happens at least a couple of times every day and I usually catch it. It takes a minute to fix, but no big deal, as long as I catch it. Your note at the beginning was helpful.
Domino/Slope Tip
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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Slope = 2.7/30.5=27/305 ≈ 0.089
I can't find a difference in the thickness of my 3 dominos.
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Refer to the analysis in Class Notes of the cart-suspended mass-rubberband Chain 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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Running back through the calculations I find that if m=0.6 kg then the tipping point becomes 6 cm. So we end with a greater disparity btw predicted and observed, which means that the mass should be around 0.4 kg. In fact, my results seem to indicate that the amplitude is equal to the mass*10, e.g. m=0.5--> A= 5. Thus the mass must be 0.38 kg to have the observed tipping point.
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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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A=1/20*k*m
d(1/20km)= k d(1/20m)+m d(1/20k) 1/20 k dm+ 1/20 m dk
d(1/20km)/(1/20km)= dm/m + dk/k
dk = 0 ---> dA/A= dm/m
dm=20% ---> 5(0.2)= 1 ---> dm/m =1/5 = dA/A---> dA = ±1 ---> A= 5±1---> A_min = 4 cm
Very nearly explains for it with the dk = 0, but with dk=10% then yes.
dA/A= dm/m + dk/k = 0.2 + 0.1= 0.3 --> dA= 1.5 --> A_min= 3.5 cm
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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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Major assumption is RB behaving like a SHO
uneven/un-level surfaces btw cart wheel and board etc
As long as the incline is straight the slope will result in a constant parallel component of the cart's weight, won't affect the linearity of the force about the equilibrium position. It will affect the equilibrium position but not the motion about that position. If the slope changes, then this does affect the linearity of the restoring force and the motion, while harmonic, will no longer be simple harmonic.
friction between the cart and surface
Good. Since the cart changes direction, the direction of the frictional force changes, so the restoring force would not be symmetric.
RBs only stretch one way
The RB chain maintained tension throughout, exerting less force than the suspended mass when that mass was to the left of the equilibrium point, more force when the mass was to the right.
To the extend that the rubber band force is a linear function of the length of the chain, this would result in SHM.
Nonlinearity in that response would result in harmonic motion (the system does oscillate) but the motion wouldn't be simple harmonic.
friction in the pulley
weight of domino evenly distributed, i.e. symmetry in COG
Good. See my notes.
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