Class 091014
Don't remove or overwrite **** or &&&&. You and I both need those marks to be able to separate your answers from the question. Your work would get less scrutiny if these marks aren't both present, and it will be harder for you when you want to review it. If any of these marks are missing I will likely ask you to reinsert any missing marks and resubmit.
if rb has tension equal to weight of dominoes, what happens
if double; if fourple, etc.
rb force * dist, dist of slide
draw vectors representing init vel of ball off ramp, etc. etc.
assign intro set 5; briefly introduce vectors in context of incline to show what they're good for
The Atwood machine
data
`q001. Give your raw data for the Atwood machine. This includes all directly observed quantities used in calculating your results.
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`q002. For one of your trials show in detail how you use your raw data to obtain the acceleration of the system for that trial.
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`q003. Give a table of acceleration vs. number of clips, one line at a time representing one trial at a time, with the number of clips then the acceleration for the trial separated by four spaces. At the beginning or the end of the table, insert another line giving the units of each column. Alternatively, you can copy a table made using a spreadsheet.
acceleration vs. number of clips:
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`q004. Is it possible to fit a reasonable straight line to the data? How much 'leeway' do you think you have in where to fit the line?
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`q005. Give the coordinates of two points on the straight line you think comes as close as possible, on the average, to the points of your graph. Use one point near each end of your line, rather that two points right next to one another.
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`q006. Between the two points you specified in your preceding answer, what is the rise, what is the run and what therefore is the slope? Be sure you specify the units of each of these quantities.
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`q007. How plausible is it that the actual acceleration vs. number of clips is in fact well represented by a straight-line graph, with the deviations of the individual points from the straight line being due mostly to experimental uncertainties?
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`q008. Specify the positive direction you chose for your system. This can be specified by stating which mass goes which way in your chosen positive direction, or by stating whether the pulley rotates in the clockwise or counterclockwise direction when the system is moving in your chosen positive direction.
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`q009. Suppose that each side of the pulley has a mass of 20 kg, and that each paperclip has a mass of about .2 kg (these masses are not realistic for the system we observed, being much greater than the masses we used in class). Pretending that these are the actual masses in your system:
How much force is exerted by gravity on each side of the system when 1 paperclip is added to one side?
Assuming the absence of friction, what therefore is the net force on the system?
What is the mass of the system?
What therefore should be its acceleration?
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`q010. Find the acceleration for the system in the preceding for 3 paperclips, and for 5 paperclips, added to the same side as before.
Sketch a graph of acceleration vs. number of paperclips and fit your best straight line to the graph.
How straight do you think your line is?
What is the slope of your line? (be sure you include units)
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`q011. For this series of examples, what is the mass of a single paperclip, as a percent of the mass of the entire system?
What percent of the acceleration of gravity is the slope of the graph you made for the preceding problem?
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`q012. From the slope of the graph you made for your experiment, can you conjecture the mass of a paperclip as a percent of the mass of the system?
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`q013. On your graph, what is the horizontal intercept of your straight line (i.e., if the line is extended, where does the line cross the x axis)?
What are the units and the meaning of this point?
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`q014. If the frictional force on the system is increased, would the acceleration of the system increase, decrease or stay the same?
What effect would this have on the points of your graph?
What effect would this have on the straight line that approximates your points?
What effect would this have on the x intercept of the straight line?
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Energy considerations
`q015. Going back to the example problem where each mass is 20 kg and each clip has mass .2 kg, let's assume that three clips are added to the mass on the left, so that the system accelerates in the counterclockwise direction.
We want to analyze the energy situation if the system moves .7 meters in our chosen positive direction.
What downward force is exerted on a 20 kg mass by gravity?
By how much does the gravitational potential energy of the 20 kg mass on the right therefore change as the system moves +.7 meters?
Answer the same for the 20 kg mass on the left.
Answer the same for the three clips.
What therefore is the PE change of the system?
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`q016. Assuming that no nonconservative forces act on the system, what therefore is its change in kinetic energy?
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`q017. The kinetic energy of the system is 1/2 m v^2, where m is the mass of the system.
Assuming it started from rest, its KE at the end of the interval will be equal to its change in KE.
What therefore is its KE at the end of the interval?
What is the mass of the system?
What therefore is its velocity at this point?
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`q018. How would your answers to the last two questions change if there is a frictional force of 3 N acting on the system?
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vectors
`q019. The figure on the board represented three vectors, one of magnitude 10 units at 305 deg, one of magnitude 8 units at 158 deg and one of 4 units at 80 deg.
According to our estimates:
Based on these estimates calculate the x and y components of the three forces.
What is the sum of all the x components?
What is the sum of all the y components?
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`q020. The actual percents are given by the sine and cosine functions as decimals. For example if the percents are 45% and -86%, the cosine function would give us .45 and the sine function would give us -.86.
For an angle of 305 degrees, use your calculator to find sin(305 deg) and cos(305 deg). (make sure you calculator is in 'degree' mode; using the sin/cos button find sin(305) and cos(305))
What do you get and how do the accurate values compare with our estimates?
Using the accurate values of the sine and cosine of 305 degrees, what are the x and components of the first vector?
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`q021. Use the same procedure to find the x and y components of the second and third vectors.
Give you results below, and include a brief explanation of your results.
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`q022. If you add up the x components of the three vectors, what do you get?
If you add up the y components of the three vectors, what do you get?
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Homework:
Your label for this assignment:
ic_class_091014
Copy and paste this label into the form.
Report your results from today's class using the Submit Work Form. Answer the questions posed above.
You should know everything in the first six problems of Set 5 in the Introductory Problem Set, which will give you a good, and not difficult, introduction to working with vectors. A link that should get you there is at http://vhmthphy.vhcc.edu/ph1introsets/default.htm .