# Atwood's Machine Experiment - Carleton University...

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Carleton University Laboratory Report Course #: PHYS 1007 Experiment #: 4 Atwood’s Machine Experiment Jennifer Armstrong 101030095 Date Performed: Tuesday, November 8 th , 2016 Date Submitted: Tuesday, November 22 nd , 2016 Lab Period: L9 Partner: Ayelet Lustgarten Station #: 35 TA: Stephen
Purpose This experiment uses a pulley system with magnetization (Atwood’s Machine) in order to evaluate 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 inertia The 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 = 2 mhA                Equation 1. A σ g = g σ m m 2 + σ h h 2 + σ A A 2     Equation 1. B = -2bhrA     Equation 1. C σ = σ b b 2 + σ h h 2 + σ r r 2 + σ A A 2     Equation M = m 1 + m 2 + 10 m washer     Equation 1. E σ M = σ m 1 2 + σ m 2 2 + 100 σ m washer 2     Equation 1. F 1
Where m 1 is the mass of mass 1, m 2 is the mass of mass 2, m washer is the mass of one washer, and σ m is 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, I r 2 =(80 ± 1 ) g, M is total mass, σ M is total mas error, and σ I r 2 is 1. Welch’s consistency test is used to evaluate the consistency of the known value of gravity (9.8 m/ s 2 ). It is given by the following equation; Where t is consistency, x 1 is the known value, x 2 is the calculated value, σ 1 is error of known value, and σ 2 is error on experimental value. Error calculations are used in this experiment in order to ensure the measurements taken are a ccurate 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
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