endobj Pendulum 2 has a bob with a mass of 100 kg. !Yh_HxT302v$l[qmbVt f;{{vrz/de>YqIl>;>_a2>&%dbgFE(4mw. >> The pendulum was released from \(90\) and its period was measured by filming the pendulum with a cell-phone camera and using the phones built-in time. This method for determining g can be very accurate, which is why length and period are given to five digits in this example. Recall from Fixed-Axis Rotation on rotation that the net torque is equal to the moment of inertia I = \(\int\)r2 dm times the angular acceleration \(\alpha\), where \(\alpha = \frac{d^{2} \theta}{dt^{2}}: \[I \alpha = \tau_{net} = L (-mg) \sin \theta \ldotp\]. We measured \(g = 7.65\pm 0.378\text{m/s}^{2}\). The period of a simple pendulum depends on its length and the acceleration due to gravity. This experiment uses a uniform metallic bar with holes/slots cut down the middle at regular intervals. The period of a pendulum (T) is related to the length of the string of the pendulum (L) by the equation:T = 2(L/g). 27: Guidelines for lab related activities, Book: Introductory Physics - Building Models to Describe Our World (Martin et al.
PDF Experiment 9: Compound Pendulum - GitHub Pages Using the small angle approximation and rearranging: \[\begin{split} I \alpha & = -L (mg) \theta; \\ I \frac{d^{2} \theta}{dt^{2}} & = -L (mg) \theta; \\ \frac{d^{2} \theta}{dt^{2}} & = - \left(\dfrac{mgL}{I}\right) \theta \ldotp \end{split}\], Once again, the equation says that the second time derivative of the position (in this case, the angle) equals minus a constant \(\left( \dfrac{mgL}{I}\right)\) times the position. For the precision of the approximation sin \(\theta\) \(\theta\) to be better than the precision of the pendulum length and period, the maximum displacement angle should be kept below about 0.5.
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pendulum). What should be the length of the beam? << Note that for a simple pendulum, the moment of inertia is I = \(\int\)r2dm = mL2 and the period reduces to T = 2\(\pi \sqrt{\frac{L}{g}}\). Retort stand, boss head, and clamp, string and mass bob, Stopwatch, rulerif(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physicsteacher_in-box-4','ezslot_5',148,'0','0'])};__ez_fad_position('div-gpt-ad-physicsteacher_in-box-4-0'); Record the data in the table below following the instructions in the section above. /F9 30 0 R A typical value would be 2' 15.36" 0.10" (reaction time) giving T = 1.3536 sec, with an uncertainty of 1 msec (timing multiple periods lessens the effect reaction time will have on the uncertainty of T). %PDF-1.5 1 Objectives: The main objective of this experiment is to determine the acceleration due to gravity, g by observing the time period of an oscillating compound pendulum. /MediaBox [0 0 612 792] Apparatus . In order to minimize the uncertainty in the period, we measured the time for the pendulum to make \(20\) oscillations, and divided that time by \(20\). Even simple pendulum clocks can be finely adjusted and remain accurate. The relative uncertainty on our measured value of \(g\) is \(4.9\)% and the relative difference with the accepted value of \(9.8\text{m/s}^{2}\) is \(22\)%, well above our relative uncertainty. The period is completely independent of other factors, such as mass. PDF Measurement of acceleration due to gravity (g) by a compound pendulum