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To determine the acceleration of free fall (g) using a simple pendulum. To achieve this I must research background information provided in the specification.

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Introduction

Chris Horswell                                                                      1st December 2002

Determine the Gravitational Field Strength (g)

at the Earths Surface, Using a Pendulum.

Aim: -

        To determine the acceleration of free fall (g) using a simple pendulum. To achieve this I must research background information provided in the specification.

        In my specification I am provided with the Periodic Time equation: -

L = Length - Measured in metres (m)

g = Gravity - Measured in Metres per second (ms  )

T = Periodic Time - Measured in second (s)

Background information

        “This was produced by Galileo in 1632. He was inspired by a swinging lamp, strung form the ceiling of the Cathedral in Pisa; using his pulse as a stopwatch, he calculated that the oscillations of the lamp remained constant even when the oscillations were dying away.”

It was acting like a Pendulum.

A pendulum consists of a mass hanging from a string and fixed at a pivot point. Once released from an initial angle, the pendulum will swing back and forth with Periodic Motion.

  1. ‘a’ to ‘b’ to ‘c’ to ‘b’ to ‘a’ = 1 oscillation.
  1. at points ‘a’ and ‘c’ = greatest potential energy.
  1. at point ‘b’ = greatest kinetic energy.

This is a diagram showing the motions of the pendulum and forces acting on it. It shows where the bob passes once swinging and the Simple Harmonic Motion it follows. Also shown above is where the greatest potential and kinetic energy is. We shall refer back to this later in our preliminary work.

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Middle

Using an Electronic timer.

This is the use of an electromagnet, a ball bearing and a trapdoor. The timer starts when the ball bearing is released from the electromagnet and then stops when it enters the trap door. Using the Displacement equation : -

S = Displacement

t = Time taken

U = Initial velocity

a = Acceleration  

Substituting in common factors (Gravity, Height and initial velocity) : -

With this we can find out the gravity by adding the height of the ball bearing from the trap door, and the time taken.

Using a ticker-tape timer.

This method shows the acceleration of a mass with small dots. The dots increase distance apart as the mass falls.  After this we separate the dots into 5 dot intervals, which represents 0.1 of a second.

If we then line these 5 dot intervals in a row it displays as a bar chart then  by measuring the gradient : -

We can find the acceleration of the mass (Gravity)

Using a light gate.

 This is set up so the object falls through the set of light gates. Setting the light gates at different lengths apart give more accurate reading. To use this method a computer is needed and the information can be converted into metres per second instantly but equations can be used

also: -

Putting this into the equation for Acceleration we can work out gravity: -

But

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Conclusion

Constant and Varying Factors

Constant Factors: -

  1. Pendulum/Bob
  1. Number of oscillations
  1. Fiducial marker

Varying Factors: -

  1. Length of pendulum

I shall be measuring the time it takes for 10 oscillations to occur using a stopwatch (seconds)

Prediction.

I predict that I shall get the value of 9.81ms   . I predict this because from research and common knowledge Galileo produced this almost 300 years ago and has become a legend since. But I cannot expect my results to show exactly 9.81ms   ,this is because of human error with the fiducial point, and air resistance with the bob.

Safety

The usual safety precautions should be enforced, safety goggles, long hair should be tied back and stools and bags under the desk. Extra precaution should be taken when walking about the lab as there are swinging weights about.

ApparatusDiagram

  1. Clamp and Stand
  2. 2.5 metres of thread
  3. 2 pieces of slated wood
  4. Pendulum / Bob
  5. Stool
  6. Stop watch
  7. 2 metre sticks
  8. Protractor
  9. Card and felt pen

Method

  1. Set up as Diagram
  2. Draw vertical line on card to make your fiducial point.
  3. Let pendulum hang vertically to elign the fiducial point.
  4. Once prepared, hold protractor at the top of the string and measure the pendulum out to 10º
  5. Let go of pendulum and start stopwatch when u see it pass the fiducial point. (you may want to let it swing back and forth a couple of times to regulate the oscillations)
  6. Once the pendulum has oscillated 10 times, stop the stopwatch and record the time.
  7. Repeat 2 more times and record results.
  8. Change length to 1.80 metres and repeat
  9. Repeat for the other lengths until you have collected all your data.
  10. Plot on Graph and work out the gradient

...read more.

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