Procedure Set up apparatus as illustrated in Fig 3.7 with the ‘picket fence’ above the light gate. Drop the ‘picket fence’ vertically through the light gate. Plot a graph of velocity versus time using the data logger and calculator; note the slope of the graph. Repeat the process a number of times, recording the slope of the graph on each occasion.
Graph The velocity of the falling ‘picket fence’ is calculated for you, based on the time taken for each of the opaque bands of the ‘picket fence’ to travel through the light gate.The width of this band is known.The calculator returns a value
for velocity using the equation: velocity
displacement (width of opaque band) time
. The velocity (v) for each of the
opaque bands is calculated in this way. The time (t) at which each of these velocities is measured is calculated by noting the time interval from when one opaque band enters the light gate and when the next opaque band enters.
Use Graph
Acceleration due to gravity can be calculated from the graph. If the velocity is on the y-axis and time on the x-axis, then acceleration due to gravity is the slope of the line of best fit (g slope).
Explanation
Based on the first equation of motion; given that the acceleration (a) equals acceleration due to gravity (g) we get:
v u atQv gt u
Using the equation of the line y mx c; given that c u, it is clear that acceleration due to gravity is equal to the slope.
Precautions Repeat the process a number of times and find an average for the acceleration. Make sure the ‘picket fence’ falls vertically through the light gate, otherwise the widths of the bands will appear bigger than they really are.
Note
This method of calculating acceleration due to gravity is perfectly acceptable as a ‘mandatory experiment’.However, the ‘g by free-fall apparatus’ is more likely to be asked in the Leaving Cert.
Weight WEIGHT
Weight (W) is a force equal to the product of mass and acceleration due to the gravity.
WEIGHT
W mg W weight m mass g acceleration due to gravity
As weight is a force, it is a vector quantity and is measured in newtons. It is directed towards the centre of the planet.
