Lab 6

Abstract: We used applications of constant acceleration to find the gravitational acceleration constant, g, and also proved Newton?s Second Law as well. We achieved this with ink-jet records and frictionless air tracks. Our results were that g = 9.57 m/s2 and that M = 550 g. Our relatively small errors can be attributed to human mistakes, especially in analyzing ink-jet records after trials. This lab will prove to teach many useful strategies such as how to use constant acceleration to one?s advantage in real-world applications. Objectives: In this lab, we will use an ink-jet timer to determine position, velocity, and acceleration as functions of time. We will also utilize the properties of constant acceleration to find the gravitational constant, g, and prove Newton?s Second Law, force equals mass times acceleration. Procedure: PART ONE: Tilt track with two wooden blocks and measure height and length of the right triangle made. Then make an ink-jet record of the cart accelerating down the frictionless track. Record data from ink-jet imprint and remove blocks. Clean up area. PART TWO: Make sure the track is level and using a nylon string, connect the air track cart over a pulley to a hanger. Then test four trial runs in which the hanging mass accelerates down the track and add mass to the hanger in increments of 50 grams. Record data from ink-jet imprints and replace masses. Clean up area. Results: See lab sheets attached. Measurements from Part One: Height of blocks, A = 8.19 cm Length of track, B = 216 cm Acceleration, a = 0.3629 m/s2 ?A = 5 x 10-5 m ?B = 5 x 10-3 m Measurements from Part Two: Mass increments = 0.05 kg, 0.15 kg, 0.25 kg, 0.30 kg g = 9.81 m/s2 Data Analysis: See graphs attached. Part One: Determination of g ? A=8.19cm B = 216cm The calculated gravitational acceleration: The calculated error in g: Part Two: Newton?s Second Law ? The slope of a vs. F: The experimental error for our measured system mass: The significance of the slope in Part Two is that it is the inverse of the total mass of the system. The y-intercept represents the acceleration when force approaches zero. Newton?s Second Law has been verified to within our experimental error as the total mass of the cart system is 550 grams. Discussion and Conclusion: To sum up, in part one, we measured position through ink-jet recorders to find velocity and acceleration. In part two, we measured slope as an inverse function between acceleration and force. Through these experiments, we were able to prove that though the net force and acceleration vary, the accelerated mass in each experiment will stay the same. Our errors for the gravitational acceleration constant and the total mass of the system are 0.015 m/s2 and 0.01 kg, respectively, which can be accounted for through human error. Possible reasons for the errors include imprecise measurements of height and length, and calculations from ink-jet sheets. This lab has helped verify that the gravitational acceleration is indeed around 9.8 m/s2 and that Newton?s Second Law holds true.