## PS253 – Physics Lab for Engineers

22 Sep

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1. An outside company is doing an audit of a small business and records the annual salary of individual employees in the thousands of dollars to be:

45, 35, 40, 50, 65, 75, 30, 35, 40, 55, 35, 40, 30, 70, 55, 30, 45, 35, 50

1. Determine how many employees there are per \$5000 salary block starting at \$25k. Complete the table below.
 Salary Block \$30k \$35k \$40k \$45k \$50k \$55k \$60k \$65k \$70k \$75k # of employees

1. What is the decimal fraction of employees paid in each \$5000 salary block? Give your results in a table similar to how you answered (1.a). Sum, add, all of these fractions and make sure they add up to 1.
 Salary Block \$30k \$35k \$40k \$45k \$50k \$55k \$60k \$65k \$70k \$75k fraction of employees

1. Find the mean salary for all 19 employees by using:
1. The method given in Equation 3 on p.3 of the lab manual.

1. The method given in Equation 5 on p.3 of the lab manual

1. From the histogram, determine the fraction of students that are greater than 66 inches tall?
2. From the histogram you made in Excel representing 50 rolls of a d12, write down here the normalized frequency for each side of the die from 1 to 12. Use a table. Sum, add, all of these fractions and make sure they add up to 1.
 Die side 1 2 3 4 5 6 7 8 9 10 11 12 Frequency rolled

1. Did the results of this simulated random dice roll turn out the way you expected them to? Explain your answer. What do you think would happen if we redid the simulation and rolled the d12 100 times?

1. Do a simulation to see the results of rolling the d12 100 times. This should be easy as you are just following what you did to make your first histogram. You can drag down the randomization formula to make 100 rows of data instead of 50. Keeping the same bins, redo the histogram function but this time select all 100 data points. Find new normalized frequencies for this run of our simulation.
1. Record below what the normalized frequencies are after 100 runs.
 Die side 1 2 3 4 5 6 7 8 9 10 11 12 Frequency rolled

1. How do your results compare to your answer for #4? Would we need to roll the die even more times to represent a truly random event? How good do you think Excel’s randomization function really is?

1. Some students performed an experiment to determine the spring constant of a spring. They hung a mass hanger on one end of the spring and continued adding mass recording how far the spring stretched each time. Using a modified form of Hook’s Law they can determine the spring constant from the slope of a best fit line. Their results are in the table and plot below.
 Stretched length (cm) Mass (g) 5 500 8 550 11 575 15 600 17 650 23 700 29 750 36 800 38 850 43 900 50 1000 64 1100 71 1200 85 1300 93 1400
 Figure 1Stretched length with added mass.

Describe at least 5 different ways in which this graph should be improved upon.

(Continued on next page)

1. Refer to the x-y scatter plot you made in Excel for the oscillating pendulum.
1. What is the equation for the linear fit on the graph? Remember this is in y=mx+b format.

1. What is the slope of this line? Write the numerical value and its units.

1. Compare the equation for the fit line to our physics equation: .
1. Physically, what is the slope equal to now? Write it out like an equation.

1. Determine the value of g from our data.

1. Repeat questions 7 and 8 only this time use the values given to you by the Regression command in Excel. Remember to use proper significant figures (based on the original values given in Table 2 on p.11.
1. What is the equation for the linear fit, using the results of Regression.

1. Comparing to our physics equation what is the slope equal to? Write it out…

1. Determine the value of g using proper significant figures and the values from Regression.

1. From the results of Regression what is the uncertainty of our slope? Use proper significant figures.

1. Now what is the calculated uncertainty in g?