The purpose of this experiment was to demonstrate the uncertainty of experimental measurements. The free-fall times of two metal balls of varying weight were measured. This data was used to calculate the best estimate of these measurements and its consistency. Then, the acceleration due to gravity was determined using the data obtained. Procedure The heavier metal ball was used first. It was placed in the release mechanism of the electronic free-fall timer apparatus.
The receptor plate was placed right below the release mechanism and the release mechanism was placed on the stand so that the measured distance from the top of the receptor pad to the bottom of the ball was the specified length given, which was 90 centimeters. Once the timer was set to zero, the ball was released by loosening the thumb screw to start the timer; the timer ended when the ball hit the pad. The fall time was recorded in seconds in a table and was repeated for twenty trials.
The average time of the twenty trials was calculated using the following equation where xN is the fall time and N is the number of trials. Then , the standard deviation was determined using the equation , where x is fall time. The experimental value of the free-fall time of the heavy metal ball was, which is the best estimate i?? uncertainty. Another table was made to determine the number of trials that occurred for each value of time. A graph resembling a Gaussian distribution was plotted using this table where the number of trials occurred was a function of time value.
The acceleration due to gravity in cm/s2 was then calculated using the formula , where t is the average time and d is the specified distance. This process was repeated using the lighter steel ball using five trials only. The experimental value of the acceleration due to gravity was obtained by calculating the class average of g and ?. The percent error was calculated using the literature value of the acceleration due to gravity, which is 980 cm/s2, and the experimental value ( . A graph was plotted using the class results where the distance, y, was a function of tavg, x.
The experimental value was determined by multiplying the slope of the graph by two. . The percent error was calculated using experimental value attained from the graph as well. Data Table 1: Heavy Steal Ball Fall Time Trial # Tis.
The x(t) graph of the falling puck is a parabolic, concave-up curve and the points of the v(t) graph of the falling puck can be best described as a linear curve. For the position versus time graph, the points reveal a well-defined parabolic curve. However, the velocity versus time graph, it was more difficult to distinguish what curve it followed; instead of velocity increasing the same amount per second, the velocity fluctuated a few times, but generally followed an increasing fashion. The equation of the line of best fit (regression) was obtained.
The parameters obtained by fitting the program was significant because the acceleration of the puck on the horizontal plane (ax) is the slope of the x(t) graph, which was 0. 355 m/s2. Using this value, the experimental value of gravity was obtained, which was, 10. 6 m/s2. The graph of a(t) should look like a straight horizontal line, where One may expect to get better agreement for larger, rather than smaller values of ? because the larger the angle, the more it resembles a motion of a free-falling object, which falls perpendicularly from the horizontal.
Conclusion The motion of a puck sliding down an inclined plane, without air resistance, resembles a free-falling object and should have had a 9. 80 m/s2 acceleration due to gravity. However, there were possibly two dominant sources of error in this experiment: the table was not completely level, which may have effected the motion and the velocity of the puck, and there was a lot of glare from the sunlight in the video, which made it difficult to see the dot in the middle of the puck.
Therefore, there was random error due to the inaccuracy of the cursor tracking of the image of the middle of the puck. These were the probable causes of error in the experimental results. It can be concluded that the force acting upon the puck undergoing a two-dimensional projectile motion is gravity and its motion can be described in two different components independently, its horizontal and vertical motions.