Falling in a Gravitational Field



Abstract

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For this laboratory report, several objects were dropped from the same height and observed to note how they fell, and how long each object took to hit the ground. The following considerations were made towards competition of the lab report: Do the objects fall at the same rate? Having conducted the experiment, it was noted that acceleration of objects tend to be same at the same rate despite their densities and sizes. This is due to free-fall, which is caused by the presence of gravitational pull. What if the objects are different sizes, does that make a difference?  When objects of varied sizes were used during the laboratory experiment, it was noted that it did not make any difference.

Falling in a Gravitational Field

Questions One: The acceleration due to gravity calculated this way works well for objects near the Earth’s surface. How would you have to change the above equation if the object was 100,000 meters above the ground?

The acceleration (g) due to the gravitational force is basically calculated when the objects are close to the surface of the earth. However, when having an object released from over one hundred thousand, 100,000, meters from the ground’s surface, the equation of gravity will have to change.

g = GM/R2

From the above equation, M is the total Mass of the body, G is a constant for the gravitational pull, and R is the earth’s radius. This is usually used when the body is very close to the ground. When talking of the earth, g is approximated to be 9.8 m/s2 (Sharan, 2009). When, for example, the radius of the earth is increased by one hundred thousand meters, most definitely the above Newton’s equation will change for the gravitational pull. In that case, the distance from the earth’s center increases, and this will definitely cause a much weaker pull of the earth’s gravity. Basically, the farther a given body is placed from a big body the weaker g becomes.

Question Two: How does air resistance alter the way we perceive falling objects?

From experiments, assuming that the earth’s entire surface had no air or atmosphere, a body released at whatever height will accelerate downwards at a constant rate of g (9.8m/s2). However, this will not happen due to the presence of atmosphere. In that case, any falling object will face air resistance depending on its fall (Sharan, 2009). This results in terminal velocity at which no acceleration since the upward and downward forces at play are equal. This hence causes variation of fall as the case with a feather and a heavy material. It is because of this resistance that objects tend not to fall at equal rates. Without atmosphere, objects would all fall downwards at equal rates.

Question Three: Is the force acting on a massive object larger than that acting on a less massive one? How can you verify this without taking any measurements?

            The second Newton’s law can be used in addressing this scenario. Going by this law, once force is placed on a given body or object, it will definitely accelerate or change its direction. Again, the acceleration will directly be proportional to the amount of force that has been applied on the body. Once the mass of the same object or body is increased, then the object’s acceleration tends to decrease. On the other hand, an increase of force advances the acceleration directly (Sharan, 2009). From this explanation, a larger body will experience a larger force in comparison with a small-sized body. Without any measurements involved, this experiment can be done by having two objects, one large and the other small, and applying equal forces to push them. The smaller object attains a higher acceleration since it is acted by smaller force. This is the reason why a larger body attains a lower acceleration due to the bigger force acting on it.

References

Sharan, P. (2009). Spacetime, Geometry and Gravitation. New York: John Wiley and Sons.


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