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Carleton UniversityLaboratory ReportCourse #:PHYS 1007 Experiment #: 4Atwood’s Machine Experiment Jennifer Armstrong101030095Date Performed:Tuesday, November 8th, 2016Date Submitted:Tuesday, November 22nd, 2016Lab Period:L9 Partner:Ayelet LustgartenStation #:35TA:Stephen
PurposeThis experiment uses a pulley system with magnetization (Atwood’s Machine) in order toevaluate the acceleration due to gravity and to evaluate the frictional torque of the system.Theory The purpose of this experiment is to use data collected from Atwood’s experiment in order to evaluate the acceleration due to gravity and compare it to the known value, as well as calculate the frictional torque. The value of the acceleration due to gravity is given by the equation;Its error is the approximation of the total error on the overall value of gravity. It is given by the equation;Where g is acceleration due to gravity, m is mass, h is height, and A is rotational inertiaThe frictional torque is the frictional force experienced by the pulley. It is given by the equation;Its error is the approximation of the total error on the overall value of torque. It is given by the equation;Where ⊺is torque, b is y intercept on Figure 1, h is height, r is radius of pulley, and A is rotational inertia, and σ isthecorresponding error .The total mass of the machine is required for the calculation of gravity. It is given by the equation;Its error is the approximation of the total error on the total value of mass. It is given by the equation;g=2mhA Equation 1. Aσg=g√σmm2+σhh2+σAA2Equation 1. B⊺= -2bhrA Equation 1. Cσ⊺=⊺√σbb2+σhh2+σrr2+σAA2EquationM=m1+m2+10mwasherEquation 1. Eσ M=√σ m12+σ m22+100σ mwasher2Equation 1. F1
Where m1is the mass of mass 1, m2is the mass of mass 2, mwasheris the mass of one washer, and σ mis the error of each value.The value of rotational interia in the system is given by the equation; Its error is the approximation of the total error on the rotational interia. It is given by the equation;Where A is rotational interia, Ir2=(80± 1) g, M is total mass, σMis total mas error, andσIr2is 1.Welch’s consistency test is used to evaluate the consistency of the known value of gravity (9.8 m/s2). It is given by the following equation; Where t is consistency,x1is the known value, x2is the calculated value, σ1is error of known value, and σ2is error on experimental value. Error calculations are used in this experiment in order to ensure the measurements taken are accurate and account for errors in the experimental process. Inefficient statistics and statistical error are used, in addition to reading error, to find the error on an individual calculation. Reading error is found by taking the smallest decimal and go one decimal to the right by one half to account for discrepancies in measurement. Inefficient statistics and statistical