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course Phy 241
October 2 around 1pm.
Lab activitiesNotes:
Include concise explanation: Whether specifically requested or not, all responses should include a brief explanation or description beginning on the line following other requested information. Abbreviations and incomplete grammar are acceptable; if you go too far with this I'll let you know, but I don't want to keep typing demands reasonable.
Reporting data:
• Data consists of what you observed, not what you concluded or how you got from observations to conclusions.
• Data should be presented in the specified format. If no format is specified, give a succinct data report in the form of a table.
• Unless otherwise specified, data should consist of numbers, with a subsequent note on the meanings and units of the numbers.
• Basic rule: Don't bury your data in a paragraph of explanation. It's OK if it appears that way within your explanation, as long as there's a succinct data summary.
Explaining your analysis:
• Typically the explanation of your analysis will include some combination of symbolic and numerical results in a sample calculation of one result.
• Other results should be reported in specified format; if no format is specified a list or a table would be appropriate.
1. Projecting point on CD onto paper on tabletop.
`qx001. Your points will lie along (or close to) an x axis perpendicular to the line you sketched on your paper. With the origin at the center point, what were the positions of your points corresponding to theta = 0, 30, 60, 90, 120, 150 and 180 degrees? Report as 7 numbers separated by commas in the first line, with brief explanation starting in the second line.
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6.2, 4.8, 3.3, 0, -3.35, -4.35, -5.35
Looking at my lab where we marked the dots, made the dot furthest from the center 0 degrees , 2nd dot from center 30 degrees and so on. I then added up the distances apart from the center to get the positions of the points I got in line 1, since I measured them in class in cm. I made this into quadrant one and two so the positions in quadrant two will be negative, if I say that’s the x-axis.
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`qx002. What were the coordinates of your points corresponding to theta = 180, 210, 240, 270, 300, 330 and 360 degrees?
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-5.5, -4.5, -3.5, 0, 3.5, 5, 6
To be a “coordinate,” then for example the first one would be (0, -5.5). On this set, I used quadrant three and four to do the thetas >180 degrees.
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`qx003. Suppose the disk rotated with a constant angular velocity, with an actual object moving along the tabletop just below the point on the disk. How would the velocity of that object change as the disk rotated through one complete revolution? Sketch (on your paper) and describe (below) a graph representing the velocity vs. clock time behavior of that point. Include an explanation connecting your results to your data.
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I don’t understand these next 3 problems. What data would I use? I’m confused on when it says “an actual object moving along the tabletop just below the point on the disk.” ???
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`qx004. For the same object as above, sketch a graph representing the acceleration vs. clock time behavior of that point. Describe your graph and include an explanation connecting your results to your data.
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`qx005. For the same object, sketch a graph representing the net force on the object vs. clock time for one revolution of the disk. Describe your graph and include an explanation connecting your description to your data.
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We'll talk about this in class. It won't give you any trouble once you understand what 'an actual object moving along the tabletop just below the point on the disk' means.
... describe r, v and a vectors ...
2. Quick collision experiment
`qx006. In the first line below give the landing positions of the 'straight drop', uninterrupted steel ball, the marble, and the steel ball after it collides with the marble, separated by commas.
In the second line, report the horizontal displacement of the uninterrupted steel ball, the marble, and the steel ball after it collides with the marble, separated by commas.
Starting in the third line give the units of your measurements and a brief explanation.
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2.5, 21.5, 21.5, 11
64, 19, 53.5
I measured in cm. What I did was look at my marks on my paper and had measured them in class from the edge of the table to wherever the points were to get my “landing positions.” Knowing horizontal displacement is just the change in x, I considered that the long ramp was 30cm long and the short ramp was roughly 15cm and so I added 45cm to my distances, except for the marble one, since it started at the end of the ramp. Lastly, I subtracted 2.5cm from what I got for that, since where the ball was “just dropped” was 2.5cm, which had to be close to the edge of the paper.
The ramp lengths don't apply to the constant-acceleration interval of the fall. That interval runs from the instant the ball loses contact with the ramp and ends at the instant the ball first contacts the floor (before the force of the floor has had time to affect its velocity).
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`qx007. Assuming that the time of fall was .4 seconds, what do you conclude was the velocity of each object at the instant it left the end of the last ramp? Report three numbers separated by commas in the first line, in the same order used in the preceding question. Units, explanation, etc. should start in the second line.
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160, 47.5, 133.75
Units are “cm/s.” I took the 3 distances in the preceding question and divided that by 0.4 seconds to get my velocities. (ex. 64cm/0.4s=160cm/s)
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`qx008. In the collision, the velocity of the steel ball changed, as did the velocity of the marble. What was the change in the velocity of each? Report number in the first line, brief explanation in the second.
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-26.25, 47.5
Units are “cm/s.” I subtracted the velocities of the steel ball calculations and since the marble started from rest, you subtract 0 which would be the same velocity as above.
Your velocities are all off by the same amount, so the differences in velocity aren't affected; these results are very likely correct, based on your data.
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3. Motion of unbalanced vertical strap
`qx009. The original vertical strap system oscillated about an equilibrium position with one end lower than the other. Why do you think the equilibrium position had that end lower?
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I think since you had 2 magnets on each end, one had to be more near the end of the strap than the other for it to end up lower than the other. If the magnets were perfectly symmetric to each other on both ends, it should’ve worked out that no side would be lower than the other.
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`qx010. What changed about the behavior of the system when a couple of #8 nuts were added to the higher end? What is your explanation?
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It spun and almost went all the way around, because it was ABOVE the center of mass.
Think in terms of energy conservation. It didn't get all the way back to its original position because some force dissipated a bit of its energy.
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`qx011. Would it have been possible to balance the system at a position where the end with the #8 nuts was higher? Would it have been challenging to do so? Explain.
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It IS possible, however not as easy as 1-2-3. You would have to change the system and where the center of mass would have to be located.
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`qx012. Did the frequency of oscillation of the system appear to be constant?
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Yes and no. It seemed constant while it first started swinging then when it got to a point where it was slowing down, and then it wasn’t.
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4. Balancing the styrofoam rectangle
`qx013. Was the styrofoam rectangle easiest to balance when the paperclip was inserted along an axis through the point below its center of mass, at a point above its center of mass, or at the point of its center of mass? Why do you think it was so?
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It was easiest to balance when the paperclips, in the side, were inserted BELOW the center of mass. Because when you try to insert them AT or ABOVE the center of mass, it just swings downward. While inserting them below “stops” it from trying to swing. It just balances.
It doesn't just balance, though it can and will. It first oscillates about the balance point, with what appeared to be a fairly constant frequency of oscillation.
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`qx014. At which positions of the paperclip did the system oscillate? At which positions did it appear to oscillate with constant frequency? At which positions did it appear to oscillate with nonconstant frequency?
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I’m not sure about this question; however, I saw that when the paperclips were inserted AT the center of mass, on mine, it came to a slight “tilt”. When they were inserted ABOVE the center of mass, it almost did a complete oscillation around.
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5. Two cars with repelling magnets
`qx015. Why do you think the two cars traveled different distances when released?
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??Is this referring to when you did the experiment with ONE car and jerked the magnet back/slowly came near it??? I’m confused because it says “Two cars with repelling magnets”???
It was a quick demo I did, near the end of the lab period, at the front table. Two cars, with magnets, were released and moved apart. It was clear that the more massive car (which had dominoes strapped to it) moved through the lesser distance.
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`qx016. Which car do you think exerted the greater force on the other?
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See above.
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6. Graphs
`qx017. The graphs you were given in class depict coasting distance, in centimeters, vs. separation in centimeters, for a 120-gram toy car whose acceleration due to friction is 15 cm/s^2 (plus or minus an uncertainty of 10%). Sketch four tangent lines to the first curve, spaced equally from near one end of the curve and the other. Find, with reasonable accuracy, the coordinates of two points on each tangent line, and use these coordinates to find the approximate slope of each tangent line. In the first line below, report your four slopes. In the second line report the x and y coordinates of the two points used to find the slope of the third tangent line, reporting x and y coordinates of the first point then x and y coordinates of the second, using four numbers separated by commas.
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-20, -15, -9.4, -5.4
[(4, 40) and (2, 80)], [(5.5, 20) and (2.5, 65)], [(8,4) and (1.5, 65)], [(9.3, 10) and (2.4, 47)]
(3.5, 50), (4,43), (4.3,40), (5.5,28)
I’m not sure if I did this right but what I did was draw 4 tangent lines, that “kissed” the curve, on the 1st graph using a ruler, made an estimate of where the tangent POINT was (3rd line answers) and then took the two ends of the tangent line I drew (2nd line answers) and found the slope (1st line answers).
I can scan my graph and let you see how I did this if you want me to.
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`qx018. Each centimeter of coasting distance corresponds to very roughly 2000 g cm^2 / s^2 of energy lost to friction. That energy came from the potential energy of the magnets at the given separation. So the vertical axis of your graph can be relabeled to represent the energy lost to friction, and hence the potential energy of the magnet system. For example, 20 cm on the vertical axis corresponds to 20 cm of coasting distance, each cm corresponds to 2000 g cm^2 / s^2 of potential energy, so the 20 cm coasting distance corresponds to 20 * 2000 g cm^2 / s^2 = 40 000 g cm^2 / s^2 of potential energy. The number 20 on the vertical axis can therefore be cross-labeled as 40 000 or 40 k, representing 40 000 g cm^2 / s^2 of PE. You should be able to quickly re-label the vertical axis of your graph.
Using the relabeled vertical coordinates, find the y coordinates of the two points you used to find the slope of your third tangent line, then report the x and y coordinates of those two points as four numbers in the first line below. In the second line report the rise and run between these points, and the slope. In the third line report the units of the rise, the units of the run and the resulting units of the slope. Starting in the fourth line explain what you think the rise means, what the run means, and what you think the slope means.
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[(4, 80k) and (2, 160k)], [(5.5, 40k) and (2.5, 130k)], [(8,9k) and (1.5, 130k)], [(9.3, 20k) and (2.4, 97k)]
(80k/-2=-40), (90k/-3=-30), (121k/-6.5=-18.6), (77k/-6.9=-11.2)
RISE units= “k” and RUN units=”cm” and SLOPE units=”g*cm^2/s^2 or k*cm^2/s^2”
The RISE means the energy lost to friction/PE of the magnet system. The RUN means the separation between the two magnets, in cm. The SLOPE tells us the change in PE/change in s, which tells us the FORCE!
The 1st line is the end points of the 4 tangent lines I drew, with the new y-axis coordinates. The 2nd line is finding the slope.
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`qx019. Report the slopes of all four of your tangent lines, in terms of your relabeled coordinates, as four numbers in the first line below. You can easily and quickly find these four slopes from the slopes you previously reported for the four tangent lines. Starting in the second line report very briefly how you found your slopes.
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-40, -30, -18.6, -11.2
My slopes for the previous tangent lines didn’t have the re-labeled y-axis. After re-labeling, you see that using “k” that the y-axis units just double. Therefore your slopes will also double or just be multiplied by 2.
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`qx020. University Physics Students: Find the derivative of the given y vs. x function y = 88 x^1.083 (this is a simple power function with a simple rule for its derivative) and evaluate at each of the four tangent points. Give the derivative function in the first line, in the second line the values you got at the four points, and in the third line compare your values to the slopes you obtained previously.
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Derivative of y= (95.304x^0.083)
y = 88 x^1.083
when you say 'Derivative of y= (95.304x^0.083)' you would be talking about the derivative of the function y= (95.304x^0.083). What you mean, however, is
'the derivative of y is (95.304x^0.083).
You could write this clearly as
'Derivative is y' = (95.304x^0.083)'.
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`qx021. University Physics Students: What is the specific function that describes PE vs. separation for the magnet system? What is the meaning of the derivative of this function?
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When we did this on the board in class, we said PE(s)=k/(s-0.5)^3. We said that force is the derivative of PE wrt position (s). We also said that the change in PE=(-F) of magnet * change in position, which concludes that the slope of PE vs. s is the FORCE.
F(s)=k/(s-0.5)^3 was a function presumed to model the force exerted by a rubber band.
PE(s) was an integral of this function.
However neither applies to the magnet system.
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Good work. See my notes and we'll clarify more in class.
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