how can i determine experimentally the acceleration due to gravity?

Question

in a lab we used a dynamic cart photogate smart timer etc

Answer 1

Determination of acceleration was first accomplished by Galileo in an experiment using the tower of pisa as the lab.
He found it to be constant. However since he did not have sensitive instrumentation to measure time , he could not detect that acceleration is not a constant in reality.
Since the changes of the value of acceleration is very small at near to the Earth surface.

An experiment can be made to detect the change of acceleration (Acceleration is defined as the Gravity field) .
It can be done by dropping a ball from a certain height and by using a stroboscope light and taking a photograph. The variayion in the distance that the ball falls relative to the flashing time of the stroboscope, the value of acceleration can be calculated. This is similar to the Galileo experiment except the stroboscope is a more accurate timing device.

The Experiment in the prevous answer Using the pendulum only gives acceleration as a constant or average. This is what Galileo had assumed.

Therefore we can conclude that Gravity field is variable as a function of the relative distance to the Center of mass of the Gravitational mass(the Earth)and the square of the Time at that particular distance.

Answer 2

You can also use a 'simple pendulum' - this is just a weight tied onto a piece of string.

You swing the pendulum at a small angle ( less than 30 degrees) and time 30 oscillations - then divide the total time for the 30 oscillations by 30 to give the time for 1 oscillation.

You should do this for several different lengths of string.

The equation used is-:

Time period of 1 oscillation = 2 * pi * (sqrt (length of string / acceleration due to gravity))

Re-arranging-:

Acceleration due to gravity = 4 * pi^2 * length of string / Time Period^2

You can get quite an accurate answer using this method, as we use this for Foundation year and 1st year undergraduates in laboratory sessions.