Sample Report On Motion In One Dimension

Introduction

In this experiment, the positions of the burn marks were measured. These were then used to determine the time instants during at which the average velocities occurred. The data was then used to construct a graph of velocity against time instant. The experimental value of acceleration due to gravity was then determined from the gradient of the graph and compared to the theoretical value of acceleration due to gravity.

Data

The data shown below were obtained from the experiment
Data analysis
The graph of velocity against instantaneous time is as shown in the figure below.
Calculations
The percent difference between the experimental value of acceleration due to gravity and the theoretical value, 9.792ms-2 was determined as follows:
Percent differenced%=experimental value-theoretical valueTheoretical value*100
d%=987.882-979.2979.2*100
d%=0.89%

Discussion

The experiment was aimed at determining the value of acceleration due to gravity. A weight was used as the body in motion. In order to examine changes in velocity of the weight, as it drops towards the ground, a sparker and a paper tape were used. The sparker produces sparks at regular time intervals that make burn marks on the tape. Since the tape is joined to the weight that moves towards the ground under the influence of force of gravity, the burn marks are formed at different positions on the paper tape. The distance between any two consecutive burn marks increases as one move from the first mark to the final mark. Larger distances between any two consecutive burn marks observed near the final mark indicate that the weight covered larger distances per unit time as it got nearer to the ground. Since the distances between any two consecutive marks increased from the first mark to the last mark, the weight was moving at an increasing speed.
All bodies in the state of free fall move with increasing velocity. Their acceleration is equal to the acceleration due to gravity. Acceleration due to gravity varies slightly from one part of the earth surface to another. In this case, the value of acceleration due to gravity is highest at the poles where the distance from the center of the earth to its surface is shortest. In other words, magnitude of the force of gravity influences the magnitude of acceleration due to gravity.
The slope of the velocity versus time graph indicates the rate of change in velocity of the weight as it falls towards the ground. Consequently, it represents acceleration due to the force of gravity pulling the weight towards the center of the earth. The percent difference between the experimental value obtained from the experiment and the given value for acceleration due to gravity was found to be 0.89%.
The experimental value of acceleration due to gravity was found to be accurate. In this case, the experimental value was found to be 9.9 ± 0.4 m/s2. Considering the error, the experimental value lies between 9.5 m/s2 and 10.3 m/s2. Since the given value, 9.792ms-2 also lies within this range; it follows that the experimental value is accurate. Consequently, this experiment was conducted successfully.
The experimental value in this experiment differs from the given value due to various errors. Both random and systematic errors were involved. Some of the likely sources of random errors include the following: changes in the properties of the tape or the weight during the experiment and changes in the air resistance to the movement of the weight. Systematic errors could have been caused by slight inaccuracies of the meter rule used in taking the positions of the marks. As a result, a consistent slight variation from the actual values occurred.
The errors led to the obtaining of the values for instantaneous time that slightly deviate from the actual values. Consequently, other values calculated from the values of the instantaneous time also deviated from the actual values.

The experiment was successful since the error recorded is within the acceptable range.

Conclusion
This experiment sought to determine the value of acceleration due to gravity. In this case, the experiment found that acceleration due to gravity is 9.87882 ± 0.44118ms-2. This value deviated slightly from the theoretical value since the error covers the given value. Therefore, the experimental value is accurate. In conclusion, the experiment was successful.