Lab Report 11 - Physics Laboratory Report PHY 158 M11...

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Physics Laboratory Report PHY 158 M11 Rotational Dynamics This report is worth 142 points ______________________________ This section is completed by the student Student Name: _________________________________________ Partner’s Name(s): _______________________________________ Date: __________________ TA name: __________________Section: ____________ _______________________________ This section is completed by the TA: VI-1 (44) :_______________ VI-2 (53):________________ VI-3 (45): _______________ Report Grade:_________________ TA Signature: __________________
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VI (1) I tabulated the data of Section V-1. This data included the total mass, m t , the angular acceleration of the slotted pulley, α pulley , and the linear acceleration which I calculated using Excel, a . m t (g) α pulley (rad/s 2 ) a (cm/s 2 ) 15.3 0.20 0.476 15.3 0.15 0.357 15.3 0.21 0.500 15.3 0.18 0.428 15.3 0.18 0.428 15.3 0.18 0.428 15.3 0.18 0.428 20.3 0.25 0.595 20.3 0.25 0.595 20.3 0.25 0.595 20.3 0.25 0.595 20.3 0.24 0.571 20.3 0.25 0.595 20.3 0.24 0.571 25.3 0.32 0.762 25.3 0.30 0.714 25.3 0.30 0.714 25.3 0.31 0.738 25.3 0.31 0.738 25.3 0.31 0.738 25.3 0.31 0.738 30.3 0.38 0.904 30.3 0.36 0.857 30.3 0.34 0.809 30.3 0.34 0.809 30.3 0.37 0.881 30.3 0.37 0.881 30.3 0.37 0.881 35.3 0.44 1.047 35.3 0.45 1.071 35.3 0.41 0.976 35.3 0.41 0.976 35.3 0.42 1.000 35.3 0.44 1.047 35.3 0.43 1.023
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Example calculation for a : a = α pulley r slotted = ( 0.20 rad s 2 ) ( 2.38 cm ) = 0.476 cm / s 2 r slotted = radius of the slotted pulley = 2.38 cm I used Excel to plot a vs. m t . 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 1.2 f(x) = 0.03x - 0 a vs. mt Data Linear (Data) mt (g) a (cm/s2)
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Then, I used LINEST in Excel to calculate the slope s , uncertainty in the slope σ s , the intercept b and the uncertainty in the intercept σ b . From these values, I calculated I D,exp and σ ID,exp . a = m gr 2 I D, exp s = gr 2 I D, exp r = radiusof the step pulley = 1.5 cm I D, exp = g r 2 s I D, exp = ( 980 cm s 2 )( 1.5 cm ) 2 0.028832 cm / gs 2 I D, exp = 76477.5 gcm 2 76477.52497 g cm 2 ( 10 3 kg 1 g ) ( ( 10 2 ) 2 m 2 1 cm 2 ) = 0.00764775 kg m 2
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I D, exp = 0.00764775 kgm 2 σ ID, exp = ( ( ∂ I ∂ s ) 2 ( σ s ) 2 ) 1 2 ∂I ∂s = gr 2 s 2 σ ID, exp = ( ( gr 2 s 2 ) 2
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