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# Determination of the acceleration due to gravity (g) by free fall.

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Introduction

Monjoor

Determination of the acceleration due to gravity (g) by free fall

In this experiment we will determine the acceleration of gravity g by measuring the time of fight for balls dropped from a known height. I also verify that the acceleration due to gravity does not depend on the mass of the ball.

The falling body in this experiment will be a metal ball, which falls freely from the catch at the top of the apparatus to the pad below it. The apparatus is designed to record the time of flight for the ball. When the ball is in the catch, it forms part of an electrical circuit. When the ball is released, the circuit breaks and the timer start. The pad acts as a switch, such that when the ball hits it the timer is stopped.

Knowledge:

Any object, which is moving, and being acted upon only be the force of gravity is said to be "in a state of free fall." This definition of free fall leads to two important characteristics about a free-falling object:

• Free-falling objects do not encounter air resistance.
• In the absence of air resistance, all objects in free-fall near the surface of the Earth will experience the same uniform acceleration

Gravity:

Middle

2

0.3

0.2273

0.2221

0.2226

0.2226

0.0495

0.4

0.2614

0.2615

0.2615

0.2614

0.0683

0.5

0.2979

0.2979

0.2972

0.2975

0.0885

0.6

0.3307

0.3311

0.3316

0.3311

0.1096

0.7

0.3601

0.3602

0.3617

0.3605

0.1299

0.8

0.3867

0.3976

0.3895

0.3897

0.1518

0.9

0.4144

0.4149

0.4147

0.4146

0.1718

1.0

0.4375

0.4384

0.4374

0.4377

0.9195

I acquired the results for 8 different heights of the free fall experiment. I took three readings of each value and took an average for each the times. I then divided by 3 to get the average reading for the time. This should influence the accuracy of my results.

g is the acceleration due to gravity so the calculation of g is be acquired by measuring an object in free-fall and then measure its time and height through the following equation of Motion:

S = ut + ½ at2

Where:

s = height / displacement m (meters)

u = initial velocity ms-1

v = final velocity ms-1

a = acceleration due to gravity ms-2

t = time s (seconds)

Initial velocity of the steel ball is 0 (ms
-1) so,

S = 0 + ½ gt2

S = ½ gt2

Therefore Where

g = acceleration due to gravity (ms-2)

h = distance the ball falls through (m)

t = time taken to fall (seconds)

This equation shows that g can be easily determined by measuring free fall time’s t as a function of height h. Therefore, we can determine the acceleration of gravity

Conclusion

-2

The percentage error value of 14.1%percent is unsatisfactory. This high percentage error indicates experimental errors.

The percentage difference for the experiment can be calculated as:

% Difference = The accepted value - The value measured      X       100

The accepted value

% Difference = 9.81-10.00 x 100 = ± 1.93%
9.81

##### Improvements:

In order to improve on the experimental procedures, I could use an apparatus with a higher degree of accuracy such as a meter rule with the marks of millimetres standing out more so that the measurements will be more accurate.  In addition, because of the fact that the error in the measurement of t (time) was doubled because it was squared in the formula and it would make severe errors in the value of g. For example, if t were too big it would make t2 much bigger than it really is, and hence would decrease the value of g. I can improve on this by implementing better techniques and equipment, however in turn these are very difficult to eliminate and the experiment would need to be repeated. Given more time I would have repeated the whole experiment and maybe taken 5 or more readings of each height to make my results more reliable. I also could have used a pendulum experiment to measure g (gravity) although this experiment is more difficult to carry out and therefore more likely to cause experimental errors. Measuring the time taken for oscillations to occur from the pendulum will do this.

Determination

Of the

Acceleration due to

Gravity (g)

By free fall

###### Monjoor Ahmed

This student written piece of work is one of many that can be found in our AS and A Level Mechanics & Radioactivity section.

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