Measuring g using
a simple pendulum

The aim of this experiment was to find out a value for g (the
gravitational force of the earth at sea level) using a simple pendulum and a
video recording camera. For this experiment a value for g of 10.016N ± 0.5N was
obtained, which is within the range of the accepted value for g (9.81 N in
Edinburgh)1

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Background
Physics:

Gravity exerts a force on all objects, this force is directly
proportional to the mass of the object. The forces is measured in Newtons (N)
or Acceleration (ms-2). The constant of this force is the
acceleration due to gravity, or “g”. The value for g on Earth has been calculated
to be 9.81N and this value remains fairly constant for a few thousand feet
above the Earth’s surface.

One method that can be used to approximate this value of g is a
simple pendulum. A bob mass attached to the end of a string and pulled to the
side through a very small angle, the bob is let go and oscillates back and
forth. The motion produced is simple harmonic motion, where the mass oscillates
around the centre point with an acceleration proportional to its displacement
and always against the displacement vector.

To start2 we
will define the displacement as arc length “s”, figure 1 shows that the force
on the mass (m) is tangent to s and therefore equals -mgsin?. The weight (mg)
has both components mgcos? along the string and mgsin? tangent to arc s. The
tension of the string removes the component mgcos? parallel to the string. This
results in a restoring force towards the equilibrium point at ? = 0.

The displacement (s) is directly proportional to ?. When ? is
expressed in radians, and is small, the arc length of a circle is proportional