FREE ESSAY ON TERMINAL VELOCITY

TERMINAL VELOCITY

SC1: Investigating Terminal Velocity
Introduction
When an object falls through a fluid it accelerates until it reaches its terminal
velocity. At this speed the forces acting on it are balanced.
My task is to investigate the factors that affect the terminal velocity of a falling
object.
Key Factors
? Mass of ball bearing
? Viscosity/density of the fluid
? Surface area of ball bearing
? Texture of the balls surface
? Temperature
I am going to investigate how mass affects the terminal velocity.
Prediction
I think that as the mass of the ball bearing increases so does the weight of the ball
bearing, which requires more friction to balance the ball bearing's weight thus making
the terminal velocity increase.
Mathematical Prediction
I think that the mass of a ball bearing is directly proportional to the terminal
velocity. This is because if the mass of ball bearing doubles so does the weight of the
ball bearing, which requires twice as much friction to balance the ball bearing's weight,
which then doubles the terminal velocity.
Scientific Knowledge
The scientific knowledge to prove my prediction is that as the mass of the ball bearing
increases the weight of the ball bearing is increased that requires more friction to
balance the ball bearings weight which increases the terminal velocity.
As the ball bearing accelerates the friction acting against the falling ball bearing
increases which in turn balances out the forces applied to the ball bearing which reaches
the terminal velocity.
Method
The apparatus was set up as shown (in the diagram on the next page)
Two elastic bands were placed on the tube 60 cm (600 mm) apart measured to the nearest
0.1 cm. The first band placed low enough so that the terminal velocity of the ball
bearing was reached before the ball bearing reached the band and the second band placed
far enough apart so that there would have been a smaller percentage of error. The elastic
bands were placed on the tube so that there are markers for the timing to be started and
stopped on a fixed point.
A group of ball bearings were massed with an electric balance and an average of the ball
bearings were taken. These ball bearings were massed so that an average mass could be
calculated for each size of the ball bearings, by dividing the total mass of the ball
bearings by the number of ball bearings.
The ball bearing was placed on the fluids surface and let to fall through the fluid.
A stop clock was started when the ball bearing reached the first elastic band and stopped
when it reached the second elastic band.
The results were repeated three times for an accurate average time and any "strange
results" were repeated to improve accuracy.
The results are shown in a table on the next page.
Diagram
Results
Average mass results
Ball Number of Balls Mass (g) (2dp) Average mass of one ball (g) (2dp)
A 60 1.80 0.03
B 30 3.37 0.11
C 50 22.07 0.44
D 50 44.20 0.88
E 30 61.54 2.05
Terminal Velocity Results
Average mass (g) (2dp) Distance Fallen (cm) (1dp) Time of Fall (s) (1dp) Terminal
Velocity (cm/s) (1dp)
Trial 1 Trial 2 Trial 3 Average 
0.03 60.0 50.4 48.6 48.9 49.3 1.2
0.11 60.0 22.9 20.6 20.8 21.4 2.8
0.44 60.0 10.3 10.2 10.3 10.3 5.8
0.88 60.0 7.1 7.0 6.5 6.9 8.7
2.05 60 4.8 4.6 4.7 4.7 12.8
Graph
See graph paper.
Conclusion
I have found that my prediction is correct with the fact that as the mass of the ball
bearing increases so does the weight of the ball bearing, which requires more friction to
balance the ball bearing's weight thus making the terminal velocity increase.
Therefore the velocity of the ball bearing would increase which is a greater force than
the friction required to balance the ball bearing, which accelerates the ball bearing. As
the ball bearing accelerates the friction acting against the falling ball bearing
increases which in turn balances out the forces applied to the ball bearing thus reaching
the terminal velocity of the ball bearing.
My mathematical prediction, which I have found to be incorrect because the terminal
velocity can change not only by the change in the mass of the ball bearing but the change
of the viscosity of the fluid or the change of the temperature of the fluid and ball
bearing. Also the fact that the mass of the ball bearing is not proportional to the
terminal velocity because m1 (1.0 g) a value of average mass and its double m2 (2.0 g)
have terminal velocity equivalents p1 (9.4 cm/s) and p2 (13.5 cm/s) (p1 for m1 and p2 for
m2). P2 not being the double of p1, which means that, the relationship between average
mass of a ball bearing and terminal velocity are not directly proportional.
The relationship between mass of the ball bearing and terminal velocity is that the
terminal velocity increases in ever decreasing steps, this is because the larger the
average mass the greater the friction required to balance out the forces acting on the
ball bearing which in turn increases the drag acting on the ball bearing which lowers the
terminal velocity.
Evaluation
I did have some anomalous results. This is because the tube was not exactly upright when
I took these results the ball bearings drifted exactly downwards and went into the side
of the tube apart from getting drag from being near the side of the tube it gained
friction from the solid side of the tube. I repeated this result and removed my incorrect
result. The ball bearing with the greatest mass had a volume so great that it had drag
from the side of the tube because the tube was too narrow for the ball bearing not to get
drag off the side of the tube.
All results that are more than 10% out from any group of results would be considered
inaccurate and would be repeated. The uncertainties in my results after any repeated
results were sufficiently small enough to keep my results reliable.
My results are not accurate enough to get a full curve of best fit because of the drag on
the larger ball bearing as mentioned above.
I have found from my graph that another result could have been taken with the mass of the
ball bearing between 0.88g and 2.05g.
I propose these improvements: -
? Wider tube for the ball bearing with an average mass of 2.05g
? A longer tube for a smaller percentage of error
? More results taken to increase accuracy
I suggest that more ball bearings with different masses should have had results taken to
increase this investigation. Also all the improvements shown above should be taken into
account to extend the experiment.
Bibliography
all mine