### Measuring proportional to its radius (L in this case)

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

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

to its radius (L in this case) by s = L? (when ? is roughly