Physics Lab4 - Lab 4: Rigid Pendulum Muhammad Usama Arabi...

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Lab 4: Rigid Pendulum Muhammad Usama Arabi 5267668 PHY1322_LAB Conducted Monday March 14 th 2011 Submitted Monday March 21 th 2011 1. Purpose
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The purpose of this experiment is to determine an experimental, gravitational acceleration g . This constant will be calculated experimentally using the mechanics of a physical and torsional pendulum. The literature value of gravitational acceleration on earth is 9.81 m/s 2 , for this experiment to be truly successful, the gravitational acceleration must be calculated within 1% of the literature value. 2. Theory Rigid Pendulum Equation: This equation is typically used to calculate the theoretical period of oscillation T using the following terms: I - moment of inertia (kg/m 2 ) M - mass of the oscillating pendulum (kg) h - height of the pivot point from the center of mass (m) T - period of oscillation (s) Derived formula for g: Use equations (2) and (3): Rearrange for the torsional constant C: The modified equations (2) and (3) are equated by the torsional constant to obtain equation (4): Use the given moment of Inertia of the bar, equation (5), and sub it into equation (4): Use the parallel axis theorem to determine the exact moment of inertia of the rigid pendulum:
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Now we must substitute this equation into the initial Rigid Pendulum equation and derive and expression for g : 3. Procedure For procedure please refer to 4 page 2 in the Physics Laboratory Manuel for First year Science Students. 4. Results 4.1 Masses and dimensions Table 1: Masses and dimensions M (kg) 1.8405 ± 0.0001 M bar (kg) 1.8578 ± 0.0001 h (m) 0.498 ± 0.005 L (m) 0.605 ± 0.005 b (m) 0.01915 ± 0.00005 3.2, 3.3, 3.4, 3.5 Table 2.1: Time of Oscillation Trial t (for 50 oscillations) t o for 25 oscillations) t bar (for 25 oscillations) 1 80.5 ± 0.5 162.7 ± 0.5 102.7 ± 0.5 2 79.7 ± 0.5 160.9 ± 0.5 102.4 ± 0.5 3 80.1 ± 0.5 162.2 ± 0.5 101.9 ± 0.5 Average 80.1 ± 0.5 161.9 ± 0.5 102.3 ± 0.5 Table 2.2: Period of Oscillation
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Trial T (for 50 oscillations) T o for 25 oscillations) T bar (for 25 oscillations) 1 1.61 ± 0.01 3.25 ± 0.003 2.05± 0.005 2 1.59 ± 0.01 3.22± 0.003 2.05± 0.005 3 1.60 ± 0.01 3.24± 0.003 2.04± 0.005 Average 1.60 ± 0.01 3.24 ± 0.03 2.05 ± 0.005 Sample Calculation for T : Calculating g: Calculating the error of g: To determine the error associated with g , we must isolate the different terms for simplicity. There is no error associated with the constants; 4, 12 and, so we can disregard them for the error calculation:
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Physics Lab4 - Lab 4: Rigid Pendulum Muhammad Usama Arabi...

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