Lab Report: Measuring the Acceleration due to Gravity, g.

Experiment: Determining the Acceleration due to Gravity. 

The aim of the Experiment 

The experiment aims to find the acceleration due to gravity (g) of an object using a motion detector and Logger Pro. 

Theory 

The rate of change in velocity is referred to as gravity. When an object falls, its velocity increases, this rate of change in speed is what is referred to as acceleration. Buoyancy or frictional forces are neglected when determining g. This acceleration is because of the force of gravity between Earth and the object. The Theoretical value of acceleration is 9.8m/m 2 . This value can be determined experimentally using various methods. In this experiment, a motion detector and a LoggerPro will be used to find g. 

Equipment Used 

Motion detector, 

Vernier LabPro interface and Cable, 

Table Clamp, 

Aluminum rods (Long and short), 

Right angle clamp, and 

Rod. 

Procedure 

The detector was set up as shown in the diagram below. 

The LoggerPro software was then started. The ball was then dropped and the values for its acceleration recorded. Twenty trials were carried out. The data obtained are as shown below. 

D ata Obtained 

The results obtained from the experiment are as tabulated below 

The graph below shows the acceleration of the ball from drop #17 in the fit data  

Data Analysis and Discussion 

The acceleration due to gravity is obtained using the formula shown below; 

Therefore, by multiply the accelerations tabulated in the table above, we get the values for g. The average value can be obtained by diving the sum of g for the 20 runs and then dividing it by 20. The average deviation is then calculated. The percentage error was calculated by multiplying 100 by the difference between the experimental and theoretical value of g. All these calculation were done using excel and the results obtained are shown below. 

We found that the average experimental value of g (9.5+/- 0.1) m/s^2 was off from the accepted value of 9.80 m/s^2 by 0.3 m/s^2, which is 3%. We compute gravity, g, from the acceleration data using the relation a  2 = g . We estimated the percent error by subtracting our average experimental value of g, (9.5+/- 0.1) m/s^2, from the accepted value of g, 9.8 m/s^2, and multiplying that by 100%. This resulted in a 3% fractional error. From the data shown in the table below, we find  

g = 9.5 +/- 0.1 m/s^2 

The true did not fall within our range of experimental values. 

Conclusion 

To sum up, the objective of the experiment was met. The motion detector was used to plot the x-t graph of a ball falling freely. The experimental g was determined and was found to be 9.5 + 0.1 m/s 2 . This value is less than the theoretical value (9.8m/s 2 ). This error was due to assumptions as well as errors introduced while carrying out the experiment and determining the experimental g. First, we neglected the air resistance. We assumed that there was no air resistance for consistency purposes. However, this is never the case. Air resistance slows the motion of an object, thus, slowing down the acceleration of the object. This makes the experimental value of g to be less than the theoretical value. Had we considered air resistance the experimental value of g would have been approximately 9.8 m/s 2 . Another error was round off errors. This error was introduced as a result of rounding off all the experimental data obtained. The initial velocity of the object doesn’t affect the experimental outcome of g because the object will still accelerate at the same rate when released from a certain height regardless of its initial velocity. Overall, the experiment was successful. 

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