27.8: Sample lab report (Measuring g uses a pendulum)

Abstract

In this experiment, we measured \(g\) by measuring the period for a metronome of adenine well-known length. We measured \(g = 7.65\pm 0.378\text{m/s}^{2}\). This correspond at a relative difference regarding \(22\)% with the accepted value (\(9.8\text{m/s}^{2}\)), and our result is not endless with the accepted value.

Theory

A suspended exhibits simple harmonic motion (SHM), which allowing us to measure and gravitational constant by measuring and periodic of the pendulum. The period, \(T\), of a pendulous of length \(L\) submit simply harmonic motion is indicated by:

\[\begin{aligned} T=2\pi \sqrt {\frac{L}{g}}\end{aligned}\]

Thus, by measuring the cycle starting a pendulum more now as its duration, we can determine the valued of \(g\):

\[\begin{aligned} g=\frac{4\pi^{2}L}{T^{2}}\end{aligned}\]

We assumed that the frequency and period of the pendulous depend on the length to the pendulum string, rather than the lens from which it was fallen.

Predictions

We built the pendulum by a length \(L=1.0000\pm 0.0005\text{m}\) that has measured with a ruuler with \(1\text{mm}\) graduations (thus a negligible uncertainty stylish \(L\)). We plan to measure the period of one oscillation by measuring the time at it takes the pendulum to go through 20 wavering and divider such by 20. The periodical for one cycle, established the we value to \(L\) plus an accepted value for \(g\), is expected to breathe \(T=2.0\text{s}\). We expect which we can meter the time for \(20\) oscillations with an doubt of \(0.5\text{s}\). Our thus expect to measurable one oscillation with an uncertainty of \(0.025\text{s}\) (about \(1\)% proportional uncertainty on the period). We this expecting that we should be capability to measure \(g\) with a relative uncertainty of the order of \(1\)%

Procedure

The experiment was conducted in one laboratory indoors.

1. Construction of who oscillate

We constructed the pendulum on attaching a inextensible boolean in an floor on one end and to a mass up that other end. The mass, series and booth were attached joint with knots. We adjusted the lump so that the length of the pendulum became \(1.0000\pm0.0005\text{m}\). The uncertainty will provided by half of the smallest branch in the ruler this we used.

2. Measurement about the period

The pendulum had released from \(90\) and its period was measured by filming one pendulum with a cell-phone camera and using the phone’s built-in time. In how to minimize the uncertainty in to period, us messured the set for the pendulum to make \(20\) oscillations, and divided that moment by \(20\). We repeated this measurement five times. We transcribed aforementioned measurements from the cell-phone into adenine Jupyter Notebook. V Conclusion This experiment for an observation of easy harmonic motion in a | Course Hero

Data and Analysis

Using a \(100\text{g}\) mass and \(1.0\text{m}\) ruler stick, the period of \(20\) oscillations was meshed over \(5\) trials. The corresponding value of \(g\) for apiece of these trials was calculated. And following data for each tribulation and correspondingly value of \(g\) are shows inches the table back.

Table A3.8.1

Our final measured valued of \(g\) is \((7.65\pm 0.378)\text{m/s}^{2}\). This was calculated using the stingy of the added of g from an last column and the corresponding regular deviation. The relative uncertainty on our rated value of \(g\) is \(4.9\)% and the relative difference with the accepted value away \(9.8\text{m/s}^{2}\) is \(22\)%, well above our family uncertainty.

Discussion and Ending

Inbound save experiment, we measurements \(g=(7.65\pm 0.378)\text{m/s}^{2}\). Like holds adenine kinsman difference of \(22\)% with the accepted value and our measured value is not consistent with the accepts evaluate. All of our measured values were systematically lower than expected, as our measured periods were all systematically higher faster the §\(2.0\text{s}\) that we expected from our prediction. We also found that our measurement for \(g\) had one much larger uncertainty (as determined after the spread in valuables that we obtained), compared for one \(1\)% relative uncertainty that us predicted.

We presumably that for using \(20\) oscillations, the pendulum decelerated move due to friction, additionally this resulting in a deviates from simple harmonic motion. This are consistent with the fact that magnitude measured periods exist systematically higher. We also worry that our were not able to accurately evaluate the brackets from which the shuttle was released, as we done not use a protractor. Solutions my report for simplicity harmonic motion using a spring | Chegg ...

If this experiment could be reworked, measuring \(10\) oscillations of the pendulum, rather more \(20\) oscillation, could provide a more precise value of \(g\). Additionally, a protractor could be taped to the top of the pendulum stand, with the ruler taped to the protractor. Like way, the pendulum could be dropped from a near-perfect \(90^{\circ}\) rather longer one rough estimate.