Any object that is dropped close to the surface of the Earth has the same acceleration, 9. 8 meters per second every second, denoted as g. As the height of the falling object increases, so does the acceleration of that object. By varying the height of the fall of a ball, and observing the time it took the object to fall, we verified that g, the acceleration of a freely falling object, is approximately 9. 8 meters per second every second. This can be determined using the slope of a height vs. time squared graph, where the slope of the line is equal to g/2. ?y = 1/2 g(? t)2 (1).
Method We set up an apparatus, called a Pasco Free-Fall Adapter, to hold a metal ball at five different measurements of height, and obtain precision timing for the ball being dropped. Once the ball was released, the time it took to fall the measured distance was collected and recorded. The height h and the time t of the freely falling object are related by the following formula: h = 1/2 gt2 (2) By using the relationship between height and time, as stated above, and plotting the data on a graph, we were able to determine the acceleration of the gravitational field strength g.
Equipment error was also found and taken into consideration. Analysis And Results Once the ball was released, the time it took to fall the measured distance was collected and recorded in the table that follows.
The ball was dropped from five different heights, measured with a meter stick, five trials at each height. Table 1 Height, Error due to equipment, in the value for the acceleration, can be determined using the following formula. ?g = g [? h/h + 2? t/t] / g (100%) (3) The expected uncertainty is denoted by ? g, g is representative of the experimental value of acceleration, h and ? h is a measured height and the uncertainty in the measured height respectively, and t and ?t is the average time and difference in measured times respectively.
Table 2 Height (m) Expected Uncertainty Acceleration (%) 2. 00 m + or – 0. 299 % 1. 80 m + or – 0. 441 % 1. 60 m + or – 0. 435 % 1. 40 m + or – 0. 471 % 1. 20 m + or – 0. 538 % A linear graph of height versus time squared with a constant slope, shows that the acceleration of a freely falling object is considerably constant with the theoretical data given. The slope and y-intercept of this graph (Figure 1) were found to be 4. 89 meters per second squared, and 0.
001 meters respectively. Using the slope of the graph, the gravitational acceleration was determined to be 9. 79 m/s2. This experimental value is in fact consistent with the theoretical value of gravitational acceleration. Questions 1. ) “Little g” is a measure of the gravitational field strength: 9. 79 N/kg at Loyola University New Orleans. Are the magnitude and direction of “g” constant over the surface of the earth? Explain! The gravitational acceleration g, is not constant everywhere on Earth, but depends on many factors.
Such factors include: the distance to the center of the Earth, the irregular distribution of land above or below sea level, as well as the rotation of the Earth. Discussion Gravitational acceleration g = 9. 8 m/s2 is experienced by every falling object on Earth. This is only true when ignoring the drag force or air resistance acting on an object. The gravitational acceleration of a freely falling metal ball was established by computing the time of fall of the ball from an identified distance above the surface. The experimental value of g was determined to be 9. 79 m/s2, no more than an error from the anticipated theoretical value of 0.
6 %. This experiment proves that a freely falling metal ball can ignore the drag force exerted upward on it, as well as verifies the acceleration of gravity to be approximately 9. 8 meters per second every second. Sample Calculations Sample calculations for average time, average time squared, and expected uncertainty in the value of acceleration.