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Freely falling body definition

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Objective: To measure the acceleration of a freely falling body (g) fairly precisely using a Picket Fence and Photogate.

Materials: LabQuest, LabQuest App, Picket Fence, Vernier Photogate, clamp or ring stand.

Procedure The Photogate was fastened rigidly to a ring stand so the arms could extend horizontally, and so that the entire length of the Picket Fence was able to fall freely through the Photogate. A soft – landing surface was placed beneath to avoid damaging the Picket Fence. The Photogate was connected to DIG 1 of LabQuest and a new file was chosen from the file menu.

The free fall data was then calculated by holding the top of the Picket Fence and dropping it through the Photogate, it being released from ones grasp completely before it entered the Photogate. The Picket Fence was carefully released so that it did not touch the sides of the Photogate as it fell and remained vertical. When the Picket Fence had completely passed through the Photogate, a graph of distance vs time and velocity vs. time appeared on the screen and a photograph taken of it. To establish the reliability of the measurement, repeat Steps 3–6 five more times. Drops in which the Picket Fence hit or missed the Photogate were not used. The slope values were recorded in the data table.

Diagram showing the apparatus for this experiment

Analysis.
Trial 1 2 3 4 5 6
Slope (m/s2) 9.82 9.72 9.78 9.79 9.83 9.79

Average = 9.82 + 9.72 + 9.78 + 9.79 + 9.83 + 9.79 / 6 = 9.788 (m/s2)
Minimum Maximum Average
Acceleration (m/s2) 9.72 9.83 9.788

Acceleration due to gravity, g 9.79 * 0.1 m/s2

Precision 1 %

2. The distance vs. time graph is a parabola.
3. If an object is moving with constant acceleration the shape of its velocity vs time graph is a linear line.
4. Results are in the table above.
5. Precision = ( 0.1 / 9.79) *100 = 1%
6. The accepted value for gravity (g) is 9.80 m/s2. This value is within the range of the experimental results, therefore, agreeing with the accepted value.

Discussion: All objects, regardless of mass, fall with the same acceleration due to gravity assuming that there is no air resistance. Objects were thrown upward or downward and those released from rest are falling freely once they are released. Any freely falling object experiences an acceleration directed downward, regardless of the direction of its motion at any instant.

The altitude affects the acceleration due to the gravity because the closer you are to the centre of the earth the greater gravity. Gravity decreases with altitude since the greater the altitude means greater distance from the centre of the earth. The picket fence fell through a short distance close to sea level, the acceleration due to gravity remained constant throughout the entire fall through the photogate.

Each equidistant black line on the picket fence passed through the gate in shorter and short time increments because it was accelerating. Air resistance did have an effect on the falling fence but it was so minute, it did not affect the data. If air resistance was large enough to affect the data, the acceleration due to gravity would be less than 9.8 m/sec2. Other things that could cause a change in the experimental value of acceleration would be if the fence fell askew while in the photogate.

This would cause an insignificant decrease in distance between black lines ultimately causing a change in acceleration. Since we are neglecting air friction and assuming that the free-fall acceleration does not vary with altitude over short vertical distances, the motion of a freely falling object is equivalent to motion in one dimension under constant acceleration. For an object falling down only under the influence of gravity can be graphically analyzed with a displacement versus time graph shown by a parabolic curve describe.

Conclusion

The results of the experiment confirmed the theory that objects will fall with a constant acceleration equal to 9.8 m/s2. The purpose of the experiment was to verify the acceleration due to gravity which was done to 1%. The percent difference is so low shows that our experimental value is very close to the accepted value of acceleration due to gravity.

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