Experiment to Calculate Acceleration of Mass and Velocity of Free-Falling Object

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Recommended: Experiment to investigate gravity using free fall apparatus

Experiment 4: Free Fall

Objective: To calculate the acceleration of a mass as it falls toward earth’s surface and calculate the average velocity when measuring the total distance that the mass moved during some period of time. We had to determine the acceleration due to gravity and compare it to the standard value of 980 cm/s2. Then plot the velocity versus time, find the slope which in turn will provide the experimental value of g. (Air resistance wasn’t considered for the mass in free fall).

Theory: According to Newton’s second law acceleration is produce when a force acts on a mass. The greater the mass the greater amount of force needed. This law gives us an exact relationship between force, mass and acceleration. Which can be expressed as:

F=MA or FORCE =MASS times ACCELERATION

For free falling objects, the net external force is just the weight of the object:

F=W

Substituting into the 2nd law equation gives:

a = W / m = (m*g)/m=g

The average, or standard, value of g is 9.8 m/s2 or 980 cm/s2

Galileo Galilei first proposed that all free falling objects fall with the same acceleration nearly 400 years ago. He used a ball on an inclined plane to determine the relationship between the time and distance traveled. When measuring total distance that an object moves during some period of time, you can calculate the average velocity:

=

where ∆d is the total distance (final distance minus initial, or ) and ∆t is the total time (final time minus initial, or - ) For the case of a falling object, = = since di =0 and t1=0 ∴ =

If an object moves in constant acceleration you can fi...

... middle of paper ...

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Then we used the calculated slope and the accepted value of 980 cm/s2 to calculate the experimental error:

Experimental value – accepted value = 100%

Accepted value

1000 – 980 = 20 = .02 off by 2%

980 980

Conclusion: The objective of the lab was met, because for each trial the acceleration remained constant during each trial. There was no external force such as a vacuum used during this free fall to effect weight of the object nor was air resistance not considered in this free fall object. The gravitational acceleration equals the acceleration of the object. Regardless of the weight or size all objects free fall with the same acceleration until it hits the ground unless it is acted upon by another force. The values were compared to the theoretical values and the percent error of 2% shows the experiment was successful.

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