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# Determinating of acceleration due to gravity by timing a simple pendulum

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Introduction

Physics Laboratory Report The number and the name of the experiment:Experiment 4- Determinating of acceleration due to gravity by timing a simple pendulum The date of experiment:18 / 1 / 08 Objective * To investigate the relationship between the period and the distance of pendulum bob from the ground * To measure the acceleration due to gravity from the experiment Apparatus * A piece of string at least one meter long * retort stand and clamp * stop-watch * a pendulum bob * g-clamp / heavy stuff(for fixing the stand) * two coins * a table * a chair The diagram of the setup Procedure 1. Attach the pendulum bob to one end of the light string and nail the string to the coins, and place the coins onto the stand. 2. Set the pendulum bob to swing through a small arc of about 200 3. Measure the time for the bob to complete 20 oscillations. 4. Repeat the timing. Record the results in the table. ...read more.

Middle

Table of data distance of the bob from the ground/m Time for 20 oscillations Period of oscillation T / s (Period)2 T2 / s2 t1 t2 t3 t4 Mean t 0.30 50.77 50.86 50.95 / 50.86 2.54 6.47 0.35 50.00 50.01 50.07 / 50.03 2.50 6.26 0.40 49.16 49.16 49.17 / 49.16 2.46 6.04 0.45 48.37 48.28 48.28 / 48.31 2.42 5.83 0.50 47.33 47.38 47.38 / 47.36 2.37 5.61 0.55 46.66 46.55 46.64 / 46.62 2.33 5.43 0.60 45.71 45.71 45.68 / 45.70 2.29 5.22 0.65 44.84 44.83 44.88 / 44.85 2.24 5.03 0.70 43.92 43.92 44.00 / 43.95 2.20 4.83 0.75 42.94 43.00 43.03 / 42.99 2.15 4.62 Theory When the string makes an angle ? with the vertical, the displacement of the bob is the arc length given by x = (H-d)?......(1) and the restoring force acting on it is along the tangent, given by F = -mgsin?......(2). See Fig c, the net force causes the bob to accelerate towards the equilibrium position, given by F = ma = -mgsin?......(3). ...read more.

Conclusion

The sources of errors in the experiment Ans:The pendulum does not oscillate exactly in vertical plane / The reaction time of the observer when he starts timing for beginning and the stopping of the oscillation will cause the human error and lead to the inaccurate reading of time / there exists friction where the string is nailed to the coins and affects the mechanical energy of the pendulum bob system. 3. Suggest improvement to the experiment Ans:Using motion sensor rather than timer to record the oscillation of pendulum bob which is the simple harmonic motion 4. Discuss how the value of H can be determined Ans:By the equation T� = (H-d), we know the value of T�,and d, so we can solve the value of H. Conclusion From the experiment, we obtain that the acceleration due to gravity (g) is 9.69 � 2.24, the period of the oscillations of the pendulum varies inversely as the distance of the pendulum bob from the ground. It is very difficult to carry out the mechanical experiment accurately as many errors must be existed. ?? ?? ?? ?? ...read more.

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