• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

SHM: determining acceleration due to gravity

Extracts from this document...

Introduction

Student Name: WONG Wing Yan

Class and class no. : 6G2 (22)

Date of experiment: 25th March, 2009

Experiment 5 – SHM: determining acceleration due to gravity

Objective

In this experiment, we are going to study the simple harmonic motion of a simple pendulum. The acceleration due to gravity (g) can be estimated by the following set-up.

Apparatus

  • Retort stand and clamp
  • String 1.5m long
  • Protractor
  • Pendulum bob
  • G-clamp
  • Metre ruler
  • Stop watch

Setup


Theoryimage11.pngimage10.pngimage09.pngimage03.pngimage47.pngimage04.pngimage02.pngimage14.pngimage45.pngimage48.jpgimage02.pngimage13.pngimage46.pngimage49.gifimage34.pngimage07.pngimage44.pngimage08.pngimage12.pngimage05.pngimage23.pngimage06.pngimage00.pngimage01.png

A simple pendulum can perform a simple harmonic motion as shown in figure 2. The acceleration due to gravity can be determined if we know the period (T) of the SHM and the length of the string (image55.pngimage55.png).image15.png

image16.pngimage19.pngimage18.pngimage17.png

image20.pngimage21.pngimage22.png

image24.png

image26.pngimage25.pngimage27.png

image28.pngimage29.png

image30.pngimage31.png

image32.pngimage33.pngimage35.png

image37.pngimage36.png

        A light string with its upper end fixed and lower end attached to a pendulum bob mass m is shown. When the string is held to make and angle image65.pngimage65.png with the vertical, the bob displaces an arc length image71.pngimage71.png.

...read more.

Middle

 (e.g. < 10image52.pngimage52.png), we have sinimage51.pngimage53.pngimage53.png and therefore sinimage54.pngimage54.png. Hence, it becomes:

image56.png

As the bob continues to move, it performs a simple harmonic motion with angular velocity (image57.pngimage57.png) and it has an acceleration (image58.pngimage58.png). By comparing it with the equation, we have:

image59.png

However, the period can be shown as follows:

image60.png

image61.png

image62.png

Note that period of the simple harmonic motion is independent of the mass.

Procedure

  1. The apparatus was set up as shown in Figure 1.
  2. The bob was moved to a height so that the attached string was taut and an angle of 10image52.pngimage52.png was made with the vertical.
  3. The period (t1) for 20 complete oscillations was measured and it was recorded in the following table.
  4. Steps 2 and 3 were repeated for another measurement of period (t2).
  5. Steps 2 to 4 was repeated by shortening the length of the string by 5 cm each time for measuring further 7 sets of data.
  6. The graph of the square of the period (T2) against the length of the string (image55.pngimage55.png) was plotted.
  7. A best-fitted line was drawn on the graph and the slope was measured.
  8. The acceleration due to gravity (g) was calculated from the equation, its slope is given by:

image63.png

image64.png

Precautions

...read more.

Conclusion

Conclusion

        In this experiment, we try to study the simple harmonic motion of a simple pendulum. By looking for the value image82.pngimage82.png , we can estimate the acceleration due to gravity (g).

We compare the experimental value to theoretical value and find that the experimental one is a bit smaller than the theoretical value, which is due to the error of this experiment.

It is also clear to period is independent of the mass of the body. From the equation :

image83.png

we can know the relationship between T and image55.pngimage55.png, which is image84.pngimage84.png.

image38.png

image39.png

image41.pngimage40.png

image43.pngimage42.png

We can improve the experiment by measuring the angle carefully but not larger than 10image52.pngimage52.png. We can also reduce the surface area of the weight, then we can reduce the air resistance. The time for more periods of oscillations (like 40 periods) could be taken for minimizing the measurement error. A more precise result could be obtained.

Reference

  • New Way Physics for Advance Level – Book1(Mechanics) ; Manhattan Press (H.K.) LTD, page 263-265
  • http://en.wikipedia.org/wiki/Simple_harmonic_motion

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Mechanics & Radioactivity section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Mechanics & Radioactivity essays

  1. Peer reviewed

    Aim:To find out whether or not the angle of the ramp affects the acceleration ...

    3 star(s)

    trolley each time; but in this case the angle will remain the same all the way through but the weights will change. Mini-Plan: Aim: To find out whether mass affects the acceleration of an object travelling down a ramp. Prediction: I am certain that the added mass will not affect the acceleration of the trolley.

  2. Determination of the acceleration due to gravity (g) by free fall.

    There is a positive correlation, which shows that the experiment was carried out fairly accurately each time the experiment was done and a reading was taken. Conclusion: The obtained value of the acceleration due to gravity has been calculated to 10.00ms-2.

  1. Carry out an experiment of simple harmonic motion using a simple pendulum and determine ...

    Results Length/m Time/s Time/s Av. time/s T/s (L/m( 0.2 17.60 18.76 18.18 0.91 0.45 0.3 22.13 22.03 22.08 1.10 0.55 0.4 25.1 25.31 25.21 1.26 0.63 0.5 27.94 28.00 27.97 1.40 0.71 0.6 30.44 30.47 30.455 1.52 0.77 0.7 32.44 32.56 32.5 1.63 0.84 0.8 34.91 34.88 34.89 1.74 0.90

  2. Objectives: To determine the center of gravity of a body of irregular shapes

    To ensure that the surfaces of the boards are smooth surface, we can use sand paper to make the surface of the board smoother. On top of that, the holes A, B and C on the paper are very small, it is very difficult for us to draw line from

  1. Experiment to find the acceleration due to gravity using free fall.

    = u/t + 1/2 a We know that intital velocity is Zero so: s/t� = 1/2 a This rather conveniently allows us to find the acceleration due to gravity by simply doubling the gradient.

  2. OCR B Advancing Physics Physics Practical Investigation Coursework Investigating Simple Harmonic Oscillations

    Damped Oscillations The above experiment was repeated with a constant volume of water in the plastic cylinder, covering the mass, acting as a damping force. As above, both the maximum amplitude and resonant frequency were recorded in three trials and the average calculated, removing any anomalous results.

  1. Experiment to Find Acceleration due to Gravity

    As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together. Conclusion I have concluded from my results that the gravitational field strength of the earth is 9.8 N/Kg. This is only accurate to two significant figures because of the limitations of quality and accuracy of the experiment.

  2. Physic lab report - study the simple harmonic motion (SHM) of a simple pendulum ...

    = 90�), and the acceleration graph should lead the velocity by also a quarter of the cycle. This can be illustrated by the fig. 2(a), (b) and (c). Fig. 2(a): Graph of displacement x against time (Suppose the motion starts at the point where lower amplitude is obtained)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work