Prediction: I know that due to Newton’s laws; when something is in free fall its acceleration should be constant. However, due to air resistance an object in free fall will eventually reach a terminal velocity. This is because, as the object hits particles of air, the force of the air against the falling object will increase until it is the same as the force of the object. At this point the object will not be accelerating as it is falling at a constant speed:
As the ball only falls 95cm at maximum, it is unlikely that it will have reached its terminal velocity, but I should be able to prove that the acceleration decreases due to air resistance, I expect that the acceleration will decrease proportionally compared to time.
Data: The data I am using is as follows (with added averages)
Investigation: I have drawn a graph of the average time against the distance and it shows a very gentle curve, this shows that the ball’s velocity is changing because the velocity is the gradient of the graph. The gradient increases as the time increases, this means the velocity is increasing as the time increases. An increase in velocity means acceleration.
If there was a constant acceleration one would use the a SUVAT equation, the most appropriate for this is:
S = ut + 1/2at^2
‘U’ is the initial velocity, but the initial velocity in this experiment is zero because the ball is stationary. Because ‘u’ is zero, then zero multiplied by any number will also be zero. The equation can therefore be simplified to:
S = 0 + 1/2at^2 or S = 1/2at^2
Therefore if the acceleration is constant then the distance must be proportional to the time squared.
I will therefore draw a graph of the distance against the time squared to see if there is a linear relationship.
This graph shows a slight curvature, indicating that the acceleration is not constant. To investigate further I will work out the average velocity of the ball in each test and plot a velocity-time graph. To work out the velocity used the equation: Velocity = Distance / Time
The velocity-time graph shows a gentle curve, this indicates that the acceleration is not constant. The acceleration the change in velocity over the time taken, this is the gradient of the graph. Since the gradient decreases as the time increases we can say that the acceleration decreases as the time increases, which proves there is air resistance. The final result shows a larger gradient in proportion to the rest of the graph, because of this I will treat it as an anomalous result and not include it when calculating the acceleration.
From this graph I can extract the acceleration between each test to see exactly how it changes.
I worked out the acceleration by using the equation:
Acceleration = Change in Velocity / Time Taken
The table shows that the acceleration is decreasing as the time increases, which shows the presence of air resistance in the experiment. However the second result appears to be anomalous as well because it does not fit with the pattern.
This graph shows how the acceleration is gradually decreasing but I have circled the anomalous results. The line of best fit is a curve because when the gradient reaches 0 the object will be travelling at its terminal velocity and there will be no acceleration.
Conclusion: This data shows that air resistance greatly affects an object in free fall on earth. The acceleration on earth is 9.81 m/s^2 when ignoring air resistance so the results clearly show its presence. The acceleration decreases gradually which proves my prediction that the force of air resistance increases as the object falls. To improve the experiment results could be taken at larger distances until the acceleration-time graph shows a gradient of zero, this will show us the time taken for the specific object to reach its terminal velocity. The experiment also showed anomalous results, even though averages were used, so to improve the data anomalous results should be removed and the test repeated.