Gravitational Acceleration and the Pendulum

Activity 1 : Gravity and the pendulum procedure

Objective : Experimental measurement of the acceleration under gravity (g ) at the Earth 's surface by Gravity and Pendulum method

Materials : Ruler , Clip , Machine Nuts , Non-stretching String , Stop Watch

Procedure

1 . A large clip was bent into an S ' shape and tied to one end of a non-stretching string approximately 160 cm . The other end of the string was securely tied to the bottom of a tall doorway , such that the clip was hanging in the air and was free to swing

2 . Five (5

) machine nuts were hung on the bottom part of the clip .3 . Length of the string from the attaching point to the bottom of the clip (L ) was measured and recorded in table 1

4 . The nuts were pulled back about 6-7 cm and then allowed to swing freely

5 . After 2-3 swings were over , the stop watch was started at when the nuts were at one extreme end of the swing

6 . The pendulum was watched carefully and 20 complete oscillations were counted . The stop watch was stopped the moment 20th oscillations were complete

7 . The time for 20 oscillations was recorded in the table 1 corresponding to the length of the pendulum

8 . The length of string was shortened by approximately 5 cm and the new length was measured and recorded in the same table

9 . Time for 20 oscillations were again measured in the same manner and recorded in the table 1 corresponding to the new length of the pendulum .10 . The procedure was repeated for 10 different length of the pendulum

Data Table 1

Sl . No . Length of Pendulum (cm ) Time of 20 swings (s

1 161 .3 51

2 155 .2 50

3 150 .4 49

4 144 .3 48

5 140 .0 47

6 135 .1 47

7 129 .7 46

8 124 .5 45

9 120 .1 44

10 114 .7 43 11 . The data was typed in an Excel worksheet and the time for just one oscillation i .e . time period (T ) was obtained by dividing the by 20 . This was done for each of the length of the pendulum

12 . The time period T was squared and T2 was plotted against length (L of the pendulum , keeping T2 on y-axis and L on the x-axis . Linear trend line was imposed on the plot and the slope of the best fit line was obtained

Results

1 . T2 versus L plot is shown in figure 1

2 . Slope of the best fit line is : Slope 3 .9035 s-2

3 . Acceleration due to gravity on the Earth 's surface was calculated as 4 . The percent error for the experimental measurement from the accepted value of g 9 .8 m /s2

9 .80 100] /9 .80 3 .06

5 . The error involving human reaction time was minimized by counting period of oscillation of 20 swings instead of just one and then dividing the time of oscillation by 20 . Dividing by 20...