ACCELERATION DUE TO GRAVITY
A.
OBJECTIVES The purpose of this lab is to permit the student to calculate a standard physical constant from experimental data.
B.
BACKGROUND All objects fall at the same acceleration caused by the pull of gravity unless the fall is balanced by air resistance. This acceleration is constant for all objects at the same elevation. On the average, it is calculated as 9.8 m/sec.2 The classical way to determine the acceleration due to gravity (g) is to observe a falling object and measure its velocity during adjacent intervals. An increase in the velocity means that the object is accelerating as it falls. On campus, there is equipment that fires a spark through a slip of paper as it moves through the instrument. The spark is timed to fire 60 times a second and is used as a timing device. If you measure the distance between marks, you know the distance it traveled in 1/60 second and so you can calculate the velocity (v = d / t). By calculating the velocity in two sequential intervals, you can then subtract the smaller from the larger to get their difference. The change in velocity, divided by the time of the interval, gives the ACCELERATION (a = (v – vo) / t). This is the acceleration due to gravity. A second way to determine the value of the acceleration due to gravity (g) is by using a pendulum. A swinging pendulum is actually falling as it swings. All that is necessary for the calculation is to know the length of the pendulum wire and the time it takes to make one complete swing. Below is the equation: g = 4p2 (L / T2)
p = 3.14
C.
EQUIPMENT 1. 2. Part 1: Simulated paper strip, metric rule, calculator Part 2: Playground swing, tape measure, stopwatch or watch with second hand
D.
PROCEDURES 1. Part 1 The narrow rectangle in figure 1 represents an actual paper that I dropped through our laboratory sparker at ORU. The bottom of the paper was weighted with a metal clip to cause it to fall freely. As it fell, sparks were sent through it every 1/60 second, making marks that are represented on figure 1 as +’s.
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a.
First, circle five consecutive marks. Starting from the end of the strip labeled “top,” measure the distance in meters from the first to the second mark. Then measure the distance from the second to the third, the third to the fourth, and the fourth to the fifth. Record these distance measurements in the chart below. Next, divide each distance by 1/60 second to determine the velocity of the falling paper through each interval. (NOTE: It is the same to multiply distance by 60 as it is to divide it by 1/60 and is easier to calculate.) Third, subtract the velocity of the first interval from the second, and record this difference in the chart. Also subtract the second from the third and the third from the fourth. Finally, divide each velocity difference by 1/60 second (that is, multiply by 60) to find the acceleration of the paper as it fell. Average the three values you got for acceleration due to gravity, and compare it to the expected value of 9.80 m/s2 using the experimental error formula. Base
b.
c.
d.
e.
Top + + + + + + + +
Distance (m)
Velocity (m/s)
Vel. Difference
Acceleration
Average Acceleration 2. Part 2
m/ss
Have a friend go with you to the park. (You can use the same friend as in Lab #7 if he or she is still your friend after that weigh in.) Have your helper get swinging as high as he or she can, and then have your friend stop pumping. Time the swing from its high point to the other high point and then back to where you started the timing. Record this time in seconds as the time period of the swing.
Measure the chains of the swing from the swing seat to the swivel attachments (in meters). If you don’t have a metric measure, multiply the total length in inches by 2.54 to get centimeters and divide by 100 to get meters. Repeat the timing of the swing two more times to get three values. Use the average of the three times, and plug it into the following equation along with the chain length. Be sure to use the square of the time. g = 4 p2 (L/T2) E. RESULTS AND CONCLUSIONS Include all your calculations and measurements in your lab report. Compare your experimental values to the accepted average value of 9.8 m/sec2. Use the following formula as you did in the probability lab: Experimental Error =
p = 3.14
Theoretical – Experimental x 100 Theoretical
What are some sources of error you can identify in this experiment? F. REVIEW AND PRACTICE Compare two pendulums by tying a weight (such as a large bolt) onto a string. Time how long it takes the pendulum to complete a full swing when the string is short and again when the swing is long. If you want to make the pendulum move faster, what should you do to the string length? How does the above discussion apply to a pendulum clock that is running slow? G. IMPORTANT NOTE Refer to Appendix B, “Analysis of Acceleration Due to Gravity Exercise,” on pp. 74-75 of this Study Guide. You must use this appendix to analyze the data from this lab as part of Assignment III. Students with General Education ePortfolios must submit a hard copy of this paper along with the rest of Assignment III and must submit this paper via ePortfolio to Dr. Enrique Valderrama. It should be uploaded under the main heading of “Intellectually Alert,” under the subheading of “Critical Thinking,” and under the section named “Acceleration of Gravity Measurement Lab Report (PSC 101L).” Students who do not have a General Education ePortfolio will simply submit a hard copy of this paper along with the rest of Assignment III. For more information, consult Appendix C, “About ePortfolio,” on pp. 76-80 of this Study Guide and Appendix D, “Acceleration of Gravity Measurement Lab Report Rubric,” on pp. 81-83 of this Study Guide.
laboratory report should contain the following sections: (1) Hypothesis, (2) Procedures,
(3) Observations and Results, and (4) Conclusions. Make certain you include all four headings with at least a short paragraph for each. In addition, tables, graphs, and answers to questions may be necessary in the latter two sections.
HYPOTHESIS
Scientific research should contain a preliminary statement of the expected outcome of the experiment. This can include predictions of the specific experiment or the general anticipated result. If you are merely doing an observation and have no idea of the outcome, you cannot make an actual hypothesis. Instead, make a short statement of the purpose of the observation. However, if you have preconceived ideas of the outcome, include them in this section, and then see how they compare to the results.
PROCEDURES
Even though you are told what to do, write a paragraph of the specific steps you actually took in doing the experiment or observation. Because you are coming up with your own equipment, your procedures will be of particular interest.
OBSERVATIONS AND RESULTS
This is where you should make a detailed statement of the outcome of your experiment. Record all your pertinent observations in a clear, readable form. Arrange your data in tables (such as measurements and calculations you make). Answer any questions asked in this Study Guide, marking these clearly so that they can be easily found.
CONCLUSIONS
Your conclusions should include a comparison between the outcome of the experiment and your initial predictions made in the hypothesis. In cases where you are attempting to recreate a physical constant, compare your number to the accepted value, using the formula for experimental error:
Experimental Error Equation
If you find a large difference in your results from the expected value or if your anticipated observations are not the same as your actual observations, try to identify possible sources of error or reasons for the difference in the hypothesis and results
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