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4. Using the uncertainties in this experiment a student found that the lower and upper bounds of g are 9.4 m/s2 and 9.9 m/s2, respectively. Report g as in Equation 8.

4. Using the uncertainties in this experiment a student found that the lower and upper bounds of g are 9.4 m/s2 and 9.9 m/s2, respectively. Report g as in Equation 8.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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4. Using the uncertainties in this experiment a student found that the lower and upper bounds of g are 9.4 m/s² and 9.9 m/s, respectively. Report g as in Equation 8. 2
Transcribed Image Text:4. Using the uncertainties in this experiment a student found that the lower and upper bounds of g are 9.4 m/s² and 9.9 m/s, respectively. Report g as in Equation 8. 2
Equating Newton's Second Law with his Law of Gravitation we get Gm,m2 Gm2 or canceling m,: a = R- If we are standing on the surface of a large, spherical body like Earth, then R is the radius of the large body and we call a the acceleration of gravity, which we denote as: GM R2 Equation 5 Experimental Procedure Since the mass and radius of Earth are relatively constant (they actually vary a little in location and time), Equation 5 predicts that the acceleration of gravity on Earth's surface is constant (we can also verify this experimentally by noting that the velocity versus time plot is linear, and/or the distance versus time plot is parabolic). Ifan object is dropped from rest, then the initial velocity is zero and Equation 2 reduces to: 1. at2 Equation 6 Noting that a g. we can write: 2y Equation 7 To measure the distance and time we will use a powerful, but extremely common piece of technology: the cellphone. We will analyze the video of a falling object using a computer program that can identify position and time and automatically perform numerous data analyses. Using the uncertainties in the measurements of distance and time we can calculate a lower and upper bound of the acceleration of gravity. By averaging the upper and lower bounds we obtain g, and dividing their difference by 2 we obtain Ag: we can write: gtAg Equation 8 The relative uncertainty can be expressed as: Ag RU = x 100 Equation 9 Once we determine the acceleration of gravity using Equation 8, we can compare it to the theoretical value (Equation 5) by computing the percent error. 9eneorygexpl Percent Error = x 100 Equation 10 9cheory
Transcribed Image Text:Equating Newton's Second Law with his Law of Gravitation we get Gm,m2 Gm2 or canceling m,: a = R- If we are standing on the surface of a large, spherical body like Earth, then R is the radius of the large body and we call a the acceleration of gravity, which we denote as: GM R2 Equation 5 Experimental Procedure Since the mass and radius of Earth are relatively constant (they actually vary a little in location and time), Equation 5 predicts that the acceleration of gravity on Earth's surface is constant (we can also verify this experimentally by noting that the velocity versus time plot is linear, and/or the distance versus time plot is parabolic). Ifan object is dropped from rest, then the initial velocity is zero and Equation 2 reduces to: 1. at2 Equation 6 Noting that a g. we can write: 2y Equation 7 To measure the distance and time we will use a powerful, but extremely common piece of technology: the cellphone. We will analyze the video of a falling object using a computer program that can identify position and time and automatically perform numerous data analyses. Using the uncertainties in the measurements of distance and time we can calculate a lower and upper bound of the acceleration of gravity. By averaging the upper and lower bounds we obtain g, and dividing their difference by 2 we obtain Ag: we can write: gtAg Equation 8 The relative uncertainty can be expressed as: Ag RU = x 100 Equation 9 Once we determine the acceleration of gravity using Equation 8, we can compare it to the theoretical value (Equation 5) by computing the percent error. 9eneorygexpl Percent Error = x 100 Equation 10 9cheory
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