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course PHY241
9/27 9, Ill try to get those last 4 done and submitted by the end of the day and submit it as part 2
ExperimentsSpace 6 magnets, three on each side, symmetric ...
see how different you can make the symmetry and still get a balanced oscillation
For the magnets on the rotating strap:
`qx001. How fast was each of the magnets moving, on the average, during the second 180 degree interval? All the magnets had the same angular velocity (deg / second), but what was the average speed of each?
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3cm from center 15.71cm/s
8cm 41.89cm/s
14cm 73.30cm/s
same distances from center on both sides
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`qx002. For each magnet, one of its ends was moving faster than the other. How fast was each end moving, and how fast was the center point moving?
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3cm mag, inside end:10.47cm/s,outside end:20.94cm/s
8cm mag, inside end:36.65cm/s,outside:47.12cm/s
14cm mag, inside end:68.07cm/s,outside:78.54
The center points velocities are in the above problem
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`qx003. What was the KE of 1 gram of each magnet at its center, at the end closest to the axis of rotation, and at the end furthest from the axis of rotation?
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Inside magnet:inside:55.13g*cm^2/s^2,center:123.4, outside:218.41
Middle magnet:inside:673.45g*cm^2/s^2,center:877.81, outside:1109.21
Outside magnet:inside:2318.81g*cm^2/s^2,center:2686.45,outside:3081.13
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`qx004. Based on your results do you think the KE each magnet is greater or less than the KE of its center?
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They should be the same because the center velocity is also the average of the of the velocities of the whole magnet
velocity is linear with distance from center; kinetic energy is not linear with velocity, so isn't linear with distance from center
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`qx005. Give your best estimate of the KE of each magnet, assuming its mass is 50 grams.
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3cm:6170g*cm^2/s^2
8cm:43890g*cm^2/s^2
14cm:134322g*cm^2/s^2
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`qx006. Assuming that the strap has a mass of 50 grams, estimate its average KE during this interval.
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38553.14g*cm*2/s^2
that's about double the correct result; right ballpark but not really a very good estimate
you should detail how you got your estimate; I can't tell you how you where your thinking coul could have changed to improve it if I don't know how you got it
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`qx007. (univ, gen invited) Do you think the KE of 1 gram at the center of a magnet is equal to, greater or less than 1/2 m v_Ave^2, where v_Ave is the average velocity on the interval?
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Wouldnt it depend on where the magnet is?
v_ave does depend on this, but the question asks about KE in terms of v_ave, whatever it is
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For the teetering balance
`qx008. Was the period of oscillation of your balance uniform?
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pretty close
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`qx009. Was the period of the unbalanced vertical strap uniform?
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no
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`qx010. What is the evidence that the average magnitude of the rate of change of the angular velocity decreased with each cycle, even when the frequency of the cycles was not changing much?
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Because it wasnt moving as much vertically(smaller angle)
not 100% clear, but probably right
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For the experiment with toy cars and paperclips:
`qx011. Assume uniform acceleration for the trial with the greatest acceleration. Using your data find the final velocity for each (you probably already did this in the process of finding the acceleration for the 09/15 class). Assuming total mass 100 grams, find the change in KE from release to the end of the uniform-acceleration interval.
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42393.61g*cm^2/s^2
thats from the first one that moved to the greatest
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For the experiment with toy cars and magnets:
`qx012. For the experiment with toy cars and magnets, assume uniform acceleration for the coasting part of each trial, and assume that the total mass of car and magnet is 100 grams. If the car has 40 milliJoules of kinetic energy, then how fast must it be moving? Hint: write down the definition of KE, and note it contains three quantities, two of which are given. It's not difficult to solve for the third.
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89cm/s
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`qx013. Based on the energy calculations you did in response to 09/15 question, what do you think should have been the maximum velocity of the car on each of your trials? You should be able to make a good first-order approximation, which assumes that the PE of the magnets converts totally into the KE of the car and magnet.
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?
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`qx014. How is your result for KE modified if you take account of the work done against friction, up to the point where the magnetic force decreases to the magnitude of the (presumably constant) frictional force? You will likely be asked to measure this, but for the moment assume that the frictional force and magnetic force are equal and opposite when the magnets are 12 cm apart.
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?
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`qx015. If frictional forces assume in the 9/15 document were in fact underestimated by a factor of 4, then how will this affect your results for the last two questions?
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?
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related questions are addressed in the 9/27 class notes as currently posted
`qx016. What did you get previously for the acceleration of the car, when you measured acceleration in two directions along the tabletop by giving the car a push in each direction and allowing it to coast to rest?
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`qx017. Using the acceleration you obtained find the frictional force on the car, assuming mass 100 grams, and assuming also a constant frictional force.
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`qx018. Based on this frictional force
How long should your car coast on each trial, given the max velocity just estimated and the position data from your experiment?
... this could be done with an inclined air track ...
... collision: release two cars simultaneously, one carrying two magnets and the other carrying one
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The following questions are for university physics students, though all but one are accessible to general college physics students, who are invited but by no means required to attempt them. Questions of this nature will be denoted by (univ; gen invited). Questions which actually require calculus are denoted (univ; calculus required). General College Physics students with a calculus background are invited to attempt these questions.
`qx019. (univ; gen invited) Looking at how v0 affects vf, with numbers: On a series of trials, a car begins motion on a 30 cm track with initial velocities 0, 5 cm/s, 10 cm/s, 15 cm/s and 20 cm/s. By analyzing the first trial in the standard way, the acceleration is found to be 8 cm/s^2. Using the equations of uniformly accelerated motion, find the symbolic form of the final velocity in terms of the symbols v0, a and `dx. Then plug the information common to all trials into this equation (i.e., plug in the values of `ds and a) to get an expression whose only unknown quantity is v0. Finally plug your values of v0 for the various trials into your expression, and obtain your values for vf. Sketch a graph of vf vs. v0 and explain as best you can, in terms of your direct experience with these systems, why the graph has the shape it does.
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It is a graph increasing at a constant rate because the v0 and vf are directly related if your v0 gets larger so will your vf with constant a.
the rate won't be constant
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`qx020. (univ; gen invited) Use your calculators to graph vf vs. v0, using the expressions into which you plugged your values of v0, and verify your graph.
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ok
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`qx021. (univ, calculus required) Should the derivative of vf with respect to v0 be positive or negative? Don't answer in terms of your function, your graph or your results. There is a good common-sense answer based on the behavior of the system and the nature of uniform acceleration.
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`qx022. (univ; calculus required) What is the derivative of vf with respect to v0? What does this derivative function tell you about the behavior of the system?
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`qx023. (univ; gen invited) Using the velocity and position functions for uniform acceleration, and the resulting equations of uniform acceleration, can you get an expression for the time required to achieve velocity v_mid_x in terms of v0, a and `dx?
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`qx024. (univ; gen invited) Using the velocity and position functions for uniform acceleration, and the resulting equations of uniform acceleration, can you get an expression for the velocity v_mid_t in terms of v0, a and `dx?
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`qx025. (univ; gen invited) Can you interpret the expressions for v_mid_x and v_mid_t to answer at least some of the open questions associated with the ordering of v0, vf, `dv, v_mid_x, v_mid_t and v_ave? Can you develop expressions that can be interpreted in order to answer the remaining questions?"
Good answers on most of the questions you answered, except that you aren't showing how you obtained your answers. See my notes.
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