Download How does air resistance affect an object in free fall?

F
AIR RESISTANCE
WHAT IS THE EFFECT OF AIR
RESISTANCE ON A FALLING OBJECT?
BY: SAM HATALA
mg
EXPERIMENT BACKGROUND
The experiment I have conducted investigates the application of Newton’s Second Law to a foam
ball dropped through the air from a predetermined height. Newton’s Second Law states that in
the presence of unequal force, an object will accelerate and, therefore, its speed, direction or
both will change. In this case, the opposing forces acting on the ball, gravity and air resistance,
fight to control the behavior of the ball. Gravity works to pull the ball to the ground while air
resistance, commonly called the drag force, works to resist the downward pull of gravity. As the
ball falls through the air, its velocity will increase until the drag force equals the force of gravity.
This state of equilibrium is known as terminal velocity. The purpose of this experiment is to
analyze the relationship between the force of gravity on the foam ball as it falls through the air
and its terminal velocity, which is affected by the presence of air resistance. I will also assess the
relationship between the kinetic energy of the actual ball drop and a theoretical ball drop.
EXPERIMENT PROCEDURE
Using the Verniar Lab Quest 2 System and the Verniar Motion Detector, I was
able to measure the velocity, acceleration, position, and time of descent of a
foam ball. The motion detector was set on top of a desk .83m tall, so that the
end of the sensor stuck out from the end of the desk. The ball was then dropped
from a position .17m under the sensor. The data was collected and then
recorded. I created graphs of my data in Excel, which allowed me to formulate a
better analysis. Next, I solved for the theoretical velocity of the ball, using
conservation of energy, and compared it with the actual velocities recorded.
After that, I found the difference in kinetic energy values for the actual ball drop
and the theoretical ball drop, using the actual velocities and theoretical
velocities I had solved for earlier, and graphed this data.
EXPERIMENT ILLUSTRATION
Sensor
Desk
HYPOTHESIS
Air resistance will have a negligible effect on the
ball’s change in velocity, because the ball’s velocity
will not be great enough to create a significant
resistance force, from the height at which the ball is
released.
RECORDED DATA
Time (s)
Position (m)
Veloc. (m/s)
Theo. Veloc.
Accel. (m/s²)
KE actual*
KE theor.*
0
-0.001
0
0.177
0.05
-0.001
0.004
0.533
0.1
-0.001
0.023
1.768
0.15
0
0.106
0
4.446
0.006
0
0.2
0
0.433
0
7.689
0.094
0
0.25
0.034
0.958
0.816
9.332
0.459
0.333
0.3
0.097
1.452
1.379
9.179
1.054
0.951
0.35
0.182
1.889
1.889
8.294
1.784
1.784
0.4
0.287
2.301
2.372
6.109
2.647
2.813
0.45
0.409
2.65
2.831
0.457
3.511
4.007
0.5
0.563
2.649
-10.133
0.55
0.736
1.514
-17.657
0.6
0.72
0.269
-13.631
0.65
0.709
-0.029
-5.466
0.7
0.706
-0.027
-1.191
*times mass
Velocity vs Time Graph
3
2.5
Velocity (m/s)
2
1.5
1
0.5
0
0
-0.5
0.1
0.2
0.3
0.4
Time (s)
0.5
0.6
0.7
0.8
DATA ANALYSIS
PE = KE
mgh = ½mv²
2gh = v²
v = √(2gh)
Position (m) Veloc. (m/s) Theo. Veloc.
-0.001
0
-0.001
0.004
-0.001
0.023
0
0.106
0
0
0.433
0
0.034
0.958
0.816
0.097
1.452
1.379
0.182
1.889
1.889
0.287
2.301
2.372
0.409
2.65
2.831
0.563
2.649
0.736
1.514
0.72
0.269
0.709
-0.029
0.706
-0.027
KE actual
KE = ½mv²
= (.5v²)m
KE theor.
0.006
0.094
0.459
1.054
1.784
2.647
3.511
0
0
0.333
0.951
1.784
2.813
4.007
Actual vs Theoretical Kinetic Energy over Time
4.5
4
3.5
Time (s)
3
2.5
2
1.5
1
0.5
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Kinetic Energy x mass (J)
Actual
Theoretical
0.35
0.4
0.45
0.5
HYPOTHESIS
Air resistance will have a negligible effect on the
ball’s change in velocity, because the ball’s velocity
will not be great enough to create a significant
resistance force, from the height at which the ball is
released.
CONCLUSION
Through the process of performing my experiment and analyzing my
recorded data, I have demonstrated that my hypothesis is accurate, in
suggesting that the height of the ball drop is insufficient to allow the full
extent of air resistance to be realized. If dropped from a greater height,
the ball would achieve a higher velocity and air resistance would, likewise,
be greater. However, I also proved that even over a relatively small
distance of less than one meter, air resistance does have an effect on the
velocity of the downward fall, forcing it toward a constant value, as
acceleration approaches zero.