Experiment 4
The Acceleration of Gravity
Objective: To measure g, the gravity acceleration, by measuring the period of oscillations of a simple pendulum
Equipment:
A computer with Internet connection, a calculator (The builtin calculator of the computer may be used.), paper, and pencil
Theory:
The Earth gravity exerts a measurable force on every object in its vicinity. This force is proportional to the mass of the object. The proportionality constant is the acceleration of gravity "g = 9.8m/s^{2} " that is to be verified in this experiment. The gravity acceleration g varies with elevation from the Earth surface; however, within a few thousand feet above the Earth's surface, it remains fairly constant. In this experiment, a simple pendulum will be used to measure "g." A simple pendulum is made of a long string and a tiny metal sphere, steel or preferably lead (higher density). The period of oscillation of a simple pendulum, T, may be found by the formula
As the first formula shows, the stronger the gravitational pull (the more massive a planet), the greater the value of the g of that planet, and therefore, the shorter the period of oscillations of a pendulum swinging on that planet. If the pendulum has a steel ball, and a magnet is placed underneath the arc where it travels back and forth as it swings, the pace of oscillation does change and it swings faster. Swinging faster results in a shorter period T. Symbol g is in the denominator. A greater g means a smaller T.
Procedure:
You may need to add the following Website to your Java exception list: http://www.phy.ntnu.edu.tw/
To do this, follow the path (Windows operating system),
Start → All Programs → Java → Configure Java → Security (use High) → Edit Site List … → Add → Type in the site URL (http://www.phy.ntnu.edu.tw/).
Note: The applet you open has an error in it. The correct unit for the length of pendulum is (cm) and not (m) as shown in the applet.
Click on the following link: http://www.phy.ntnu.edu.tw/oldjava/pendulum30/pendulum.html . A swinging pendulum appears. By changing the length of its string, you can change its period of oscillation, T. Period, T is defined as the time of one full oscillation. In this applet, the small hanging mass always swings from its rightmost position. This can be used as a reference point or state for counting the number of oscillations. To measure T, measure the time for 25 or 50 oscillations (swings) and then divide that time by 25 or 50.
Select a length of L = 115cm (1.15m) or as close to 115cm as you can. This can be done by the mouse. Hold the tiny hanging mass and move it with the mouse to get the desired length for the pendulum. As soon as you release the mass, swinging starts along with the applet's timer turned on simultaneously. Reset the time to zero by clicking on the "Reset" button and reselect the length when needed.
Practice the applet a few times. When you are ready, as soon as the pendulum starts moving count ZERO. As soon as it is back to the right again, count 1, next time 2 and so on. At the 25th occurrence, for example, if you click on the applet and hold, you can record the elapsed time from the timer.
Calculate the time of one oscillation or the period T by dividing the total time by the number of oscillations you counted.
Use your calculated T along with the exact length of the pendulum L in the above formula to find "g." This is your measured value for "g." for trial 1. Record the values of total time, period, and this measured g in the first row of Table 1.
Repeat the above procedure for 3 more cases. Choose 3 other values for L between 125cm and 158cm and record them in Table 1 in rows 2, 3, and 4.
Run each case for a different number of oscillations, but not less than 25.
Record your measured time and the corresponding # of oscillations and calculate "g" in each case. In each case you should get "g" close to its accepted value of 9.81 m/s^{2}.
Calculate the mean value of "g" and record it in the space provided. This is your overall measured value for "g."
Find a %error on "g" knowing that the accepted value is 9.81 m/s^{2}.
Data:
Given: g_{accepted} = 9.81 m/s^{2}.
Measured:
Trial  Length (L) [meters]  Total time of oscillations (t) [seconds]  Number of Oscill. (N)  T = t /N [seconds]  g = 4π^{2 }L /_{T}2 
1  1.15  
2  
3  
4  

Mean "g" : 
Calculations:
Comparison of the results:
Provide the percent error formula used as well as the calculation of percent errors.
Conclusion:
State your conclusions of the experiment.
Discussion:
Provide a discussion if necessary.
Question:
If this experiment were conducted aboard a Boeing 747 at 35,000 ft, would different results be obtained? If so, why?