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Lab Report Acceleration Of Gravity

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When a 0.067 kg metal ball was dropped from rest, the average acceleration due to gravity (g) was 7.33 m/s2(Appendix A Table 1) and the time was recorded as well as the displacement. The kinematic equation of motion for displacement, g=2(x-vot) /t2(Appendix A, figure 1), was used to solve for acceleration. The variable g represents the acceleration of gravity in free fall, x represents the total distance traveled by the ball, t represents time, and vo represents the initial velocity of the ball. The ball was was dropped slightly above the photogate, therefore the exact initial velocity of the ball was not 0 m/s at xi. The initial velocity at xi was estimated by dividing the diameter of the metal ball by the time it took for the ball to pass …show more content…

To determine the acceleration of the ball, the equation g = 7(v2)/10h was derived (Appendix B figure 1) using conservation of energy principles. The variable v represents the final velocity of the ball at the bottom of the ramp and h represents the height of the ball at rest above the table. In measuring the velocity of the ball and height of the ramp there were inaccuracies that could have affected the calculated accelerations for the ball. The accuracy of the height measurement was limited by the meter stick because a meter stick is only accurate to +/- 0.001 m. With a height of 0.070 m, the meter stick would have contributed a significant measurement tolerance. Additionally, friction was not included in conservation of energy calculations. In rolling down the ramp, part of the ball's initial potential energy was converted to heat energy due to friction. Because the loss of energy due to friction was not accounted for in the derived equation, an average acceleration of 7.21 m/s2 differs slightly from the actual acceleration due to gravity that the ball experienced. Additionally, conservation of energy principals do not account for the effects of air resistance on the metal ball. Therefore the actual acceleration of the ball due to gravity would have differed slightly from 7.21m/s2. The accepted value for …show more content…

To determine the acceleration of the pendulum, the equation for the period of a pendulum was used. Acceleration was derived so that g = L / (T / 2)2 (Appendix C Figure 1). The variable L represents the length of the pendulum to the center of mass, T represents the period of the pendulum, or the time of a full swing, and g represents the pendulum’s acceleration due to Earth’s gravity. In measuring the length of the pendulum, measuring tolerances occurred. The length of the pendulum was found to be 0.450 m, however because a meter stick was used, this measurement is inaccurate by +/- 0.001 m. Furthermore, L represents the distance to the center of mass of the pendulum. L was measured as the distance from the top of the string to the center of the pendulum mass. The string’s mass was considered negligible in calculations for L, but because it had a small mass, the center of mass was not exactly at the center of the pendulum weight. This added additional measurement errors and inaccuracies in the calculations for finding g. Air resistance, which is affected by surface area, drag, and velocity, was not accounted for in the calculations. However, the effects of air resistance are negligible because of the small surface area, drag, and velocity of the pendulum. Due to these sources of error, the average acceleration for

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