INSTRUCTIONS – READ THESE FIRST 1. 2. 3. 4. You have all three hours for the exam. This is an open book exam. You are allowed to use all the available resources. Part A is completely optional. Upon opening the Excel file (which will have four separate sheets), save it as “[Your last name] Final270L”. 5. Also open up a Word document with a similar naming convention. Here you can enter all answers, paste plots, etc. All plots must be properly labelled. 6. When finished, email me the documents along with any hand-written work (take a picture). Part A – Tutorials (20 points) 1. Block A of mass m and block B which has a mass of 2m are connected by a string of negligible mass that runs over a frictionless pulley. The coefficient of kinetic friction between the incline and block A is 𝜇𝑘 . The blocks are released from rest when block A is at location C. Determine the change in the kinetic energy of block A as it moves from C to D which is a distance L up the incline. Assume that block B is still off of the ground when A gets to location D. Answer should be in terms of 𝑚, 𝐿, 𝜃, 𝜇𝑘 and g. (10 points) 2. Two blocks are on a frictionless, level table. Both blocks have mass m and the left block is moving with speed v to the right towards the stationary block. Attached to the stationary block is a massless spring with spring constant k. What is the maximum distance the spring gets compressed? [Hint: When the spring becomes maximally compressed, how will the two blocks be moving with respect to one another? Hint 2: You’ll need to consider both conservation of momentum and conservation of mechanical energy. (10 points) Part B – Lab exam (60 points) 1. (10 points) The weights of each member of two different sports teams at USD were measured. In both teams, 30 athletes were weighed. Those weights are given in the Excel spreadsheet labeled as “Question 1.” Which team (team red or team blue) has a larger average weight? According to the criterion used in the lab manual, is the difference in the average weight of the two teams significant? Be quantitative in explaining why or why not. Conclusions must be drawn using a plot. 2. (15 points) Emily designs an experiment to test the effect of temperature on reaction time (t) and asks her friend Beth to help her. Emily sits in a chair and places her forearm on a table. Beth stands beside Emily and holds a meter stick over Emily’s hand. Without warning, Beth drops the meter stick and simultaneously exclaims: “catch!” Emily closes her hand to catch the ruler as quickly as she can. Emily conducts two versions of this experiment. The first experiment is done at a comfortable temperature of 70 °F. In the second experiment, she cranks up the thermostat to a sweltering 95 °F. Listed in the Excel spreadsheet “Question 2” are the two data sets Emily collected for her “reaction distance (x)” (how far the ruler fell before Emily caught it over many trials). Ignoring air resistance, the theoretical free-fall time t for a meter stick that falls through a 2 1/2 distance x after being released from rest is given by the function 𝑡(𝑥) = ( ) 𝑔 𝑥1/2 , where 𝑔 = 9.8 𝑚/𝑠 2 is the magnitude of the acceleration due to gravity. According to the criterion used in the lab manual, is there a significant difference in Emily’s reaction time for the two experiments? Explain. You need to propagate the uncertainty in the reaction distance (x) to time (t) and then plot for drawing any conclusions. 3. (20 points) You are reading a biophysics paper on the molecular motor protein kinesin and decide to explore some of the data presented in the paper further yourself. In the paper, you see a table for how the measured velocity of a kinesin motor varies with the concentration of ATP in solution. The uncertainties are listed as well in separate columns (all the data is in the spreadsheet “Question 3”). You want to see if a power law of the form 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = (constant) × (ATP 𝑐𝑜𝑛𝑐)n is consistent with the data for some value of n. One of your lab partners suggests trying the power law n = 1/3. Another lab partner suggests n = 3. a. Which value of n (3 or 1/3) is a more reasonable guess? Explain why. Include a plot of velocity versus ATP concentration (with error bars) which you should use to justify your answer. b. Is the data consistent with a power law for the value of n that you chose? Use the graphical approach to test if the data is consistent with this power law (include the plot in your answer). Do not forget error bars. How do you obtain the “constant” value from the plot? Include the value in the report. c. What, if anything, can you conclude regarding the dependence of ATP concentration on the speed of kinesin? 4. (15 points) Below you will find one highly questionable paragraph (in red) from a hypothetical report on project 3. Identify and explain what is done incorrectly. If you can, suggest how the authors could fix the errors. There are (at least) two glaring errors that you need to find. The errors need not be quantitative or mathematical in nature but they should be more significant than just grammatical or spelling errors. In this lab, we addressed the question: “other than roundness, what properties influence the acceleration of an object as it rolls down a ramp?” We found that the hollowness of a rolling object has a large influence on the object’s acceleration down the ramp. We found that the solid cylinder we used, which had a mass of 2.45 kg, rolled down with a larger acceleration (𝑎 = 1.60 ± 0.2 m/s 2) than the hollow sphere we used with a mass of 1.13 kg (𝑎 = 1.32 ± 0.2 m/s2). For both objects, we measured the acceleration of the object down the ramp 15 times. The accelerations of each object were significantly difference since the difference in the two mean accelerations (0.28 m/s2 ) was greater than either of their uncertainties (0.2 m/s2). Weight of Team Red Players (lbs) 147.28 129.5 165.92 111.96 130.48 149.96 145.22 116.72 142.12 140.12 124.36 135.18 151.05 141.22 152.21 136.38 137.91 126.06 139.68 112.03 154.07 140.19 164.61 154.7 126.7 132.82 131.01 143.66 156.35 156.86 Weight of Team Blue Players (lbs) 171.2 165.69 165.47 180.2 135.6 170.31 192.83 141.48 147.07 188.3 159.03 159.71 158.57 139.6 166.75 156.38 190.56 152.38 139.72 171.9 137.9 149.68 132.47 154.43 165.37 155.59 187.73 120.78 173.43 152.99 70 °F reaction distance (cm) 13 9 17 19 18 11 10 13 16 19 22 18 16 15 21 16 19 21 28 27 95 °F reaction distance (cm) 22 12 17 13 14 16 17 14 12 14 24 19 13 12 14 21 10 11 28 10 Concentration of ATP (µM) Uncertainty in conc (µM) 12 44 79 105 130 3 5 8 8 10 Velocity (nm/s) 0.21 0.38 0.43 0.50 0.49 Uncertainty in velocity (nm/s) 0.03 0.04 0.05 0.05 0.05
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