Experiments to measure the acceleration of a falling object
There are various methods to measure acceleration due to gravity. At Higher level all rely on one of the equations of motion.
The measurements required will depend on the equation used.
Watch this video to see the procedure for one method, which uses the equation \(s = ut + \frac{1}{2} a t^{2}\).
How to measure the acceleration of a falling object using a timing plate.
An alternative experiment involves using two light gates.
Use of the equation \(v=u+at\) requires:
- length of mask (falling object) \(l\) (in metres)
- time to cut first light gate \(t_1\)(in seconds)
- time between light gates \(t_2\)(in seconds)
- time to cut second light gate \(t_3\)(in seconds)
Question
In this method, does the acceleration measured depend on how far above the light gates the object is dropped from?
No, the acceleration due to gravity is constant. Providing the object does not build up too much speed and air resistance is not a factor the acceleration measured should be the same.
The equation can be used with similar apparatus capable of measuring the time to fall over a height \(s\). If the initial velocity \(u\) is zero, the equation simplifies to\(v=at\).
Question
If the time \(t\) taken to fall from various heights \(s\) is measured, how could a graph of the results be analyzed to determine the acceleration due to gravity \(g\)?
The results should be plotted on an s-t (velocity) graph with \(s\) on the y-axis and \(t\) on the x-axis. The gradient of this graph will be \(陆g\)
Question
Would it be possible to use the equation \(v^2=u^2+2as\) to determine g? If so what measurements should be taken and how could the results be analyzed graphically?
Yes, drop an object at rest from different heights \(s\)and measure the final velocity \(v\). As \(u = 0 \) the equation simplifies to \(v^2=2as\). Plot \(v^2\) against \(s\) and the gradient will be \(2_g\)