Determination of Gravity

Through the use of a simple pendulum it is possible to determine the acceleration due to gravity, g, within the Earth's gravitational field.   A simple pendulum consists of a "bob" (a mass) attached to a string which is fastened such that it is free to swing or oscillate in a plane.    Because most of the mass is concentrated in the bob, we can ignore the mass of the string and its effects on the pendulum.

Four physical properties of the simple pendulum need to be considered:
(1) The length, L, of the pendulum is the distance from the center of the bob to the point where the string is attached
(2) The mass, m, of the pendulum bob
(3) the angular displacement (how far out from center) of the bob
(4) the period, T, of the pendulum's oscillation (the time it takes to the bob to swing from point A to B and back to A.

 Do not cut the string. Release the clamp and slide the string through to the required length.
The lengths that will be used in this experiment are indicated on the string.
When the pendulum is pulled to one side and released, it will oscillate back and forth with a period of oscillation, T.
Equation (1) shows the relationship between the period, T, the length, L, the angle of displacement and the acceleration due to gravity, g.

T= period, the time it takes to move from A to B and back to A
L= the length of the string from where it’s attached to center of bob
g= gravity

    to determine the square root of  L/g ... 
 

To observe the period of the pendulum, time several swings (four or five is recommended) and determine the average period.
Take the time and divide it by the number of swings, then enter this value into the data table.
 Repeat this three times.
Also, timing is generally more accurate if you start the pendulum oscillating before you begin timing.
It is also best to use the lowest point in the swing of the pendulum as your reference point. Use the stand's vertical rod as a reference.
Measure the period of oscillation for 3 trials for each of the three lengths.
Record the data for L = 1 m in Table 1. Record the data for L = 0.7 m in Table 2. Record the data for L = 0.4 m in Table 3. Be sure that the angle of displacement for each trial is the same (20 degrees off center).
 
 

Table 1 Trial Length (L)  Period (T) 
1. 
1 meter
 
2. 
1 meter
 
3. 
1 meter
Average Period
 
 
Table 2
Trial Length (L)
Period (T)
1. 
0.7 meter
 
2. 
0.7 meter
 
3. 
0.7 meter
 
Average Period
 
 
 
 
Table 3
Trial Length (L)
Period (T)
1. 
0.4 meter
 
2. 
0.4 meter
 
3. 
0.4 meter
 
Average Period
 
Problem
    Calculate the value of g using equation for each of the three pendulum length

                                                                                         Table 4

Length (L) acceleration (g)
1 meter
0.7 meter
0.4 meter
2. Compare the calculated values of g with the standard value of g, 9.8 m/s/s. Calculate the percent error in your results, using the equation: ((9.8 m/s/s - g) / 9.8 m/s/s) * 100
 
 
 

3. Equation (4) is valid for determining the acceleration due to gravity. Based on your results what factors might have affected the outcome if your results for g do not match 9.8 m/s/s?