Determination of the Acceleration due to Gravity on the Earth’s Surface

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Determination of the Acceleration due to Gravity on the Earth’s Surface

I will be investigating the acceleration due to gravity on the Earth’s surface using an experiment based on this effect. The acceleration due to gravity is constant for all objects, as it is defined by the strength of the gravitational field strength of the object, and not the mass of the object it is pulling.

Therefore, in a vacuum, all objects will accelerate at the same rate due to gravity. This only applies in a vacuum, as air resistance plays a significant role as a frictional force. The Earth’s acceleration due to gravity (also referred to as Standard Gravity, or simply g) is 9.80616ms2 (according to ), or 9.81ms-2 to three significant figures.

The weight of an object is its downwards force, which is given by the equation:

F = mg

Where F is the downwards force, or weight; m is the mass of the object; and g is the gravitational field strength of the body attracting it (this is simply g on Earth; standard gravity).

When forces are taken into account, frictional forces play a part in determining the resultant force. The downwards force of the body is constant, as the mass does not change as the body falls. However, air resistance increases with velocity, in the case of freefall under gravity. This means that the acceleration will steadily decrease as the body moves faster, since the resultant downwards force would be less.

In Figure 1, as the velocity increases, the air resistance arrow would grow, showing that the air resistance would increase as well. Eventually, it will equal the weight arrow and the air resistance will equal the weight. This would mean there would be no more acceleration, and the body will have reached a terminal velocity.

In a vacuum, there would be no air resistance, so the body will not decrease its acceleration. Therefore, this would give the most accurate value for standard gravity.

I predict that the g value I will receive from my experiment will be lower than 9.81ms-2, since air resistance will affect the results taken. The actual effect will depend on the weight, and therefore, the mass of the object which will be used to measure g.

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Several methods can be used to measure the value of standard gravity.

Pendulum

This method involves allowing a pendulum to oscillate freely, recording the time taken for each oscillation.

The length of the string used to make the pendulum, and the angle of the drop will also have to be measured, in order to calculate the value of g.

This equation () is used to determine g from the data we can measure. Here, l is the length of the pendulum, and T is the time taken for one oscillation.

Equipment

  • Stopwatch
  • Pendulum, of a ...

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