WHAT IS THE EFFECT OF AIR RESISTANCE ON A FALLING

OBJECT? BY: SAM HATALA

F AIR RESISTANCE

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

Desk

Sensor

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 DATATime (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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.5

0

0.5

1

1.5

2

2.5

3

Velocity vs Time Graph

Time (s)

Velo

city

(m/s

)

DATA ANALYSIS

PE = KE KE = ½mv²

mgh = ½mv² = (.5v²)m

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 00 0.433 0

0.034 0.958 0.8160.097 1.452 1.3790.182 1.889 1.8890.287 2.301 2.3720.409 2.65 2.8310.563 2.649 0.736 1.514

0.72 0.269 0.709 -0.029 0.706 -0.027

KE actual KE theor.

0.006 00.094 00.459 0.3331.054 0.9511.784 1.7842.647 2.8133.511 4.007

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Actual vs Theoretical Kinetic Energy over Time

Series1 Series3

Kinetic Energy x mass (J)

Tim

e (s

)

Actual Theoretical

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.