Modelling Terminal Speeds PDF

Preview

Summary

Download Modelling Terminal Speeds PDF

Description

1 Modelling Terminal Velocity SPH 4U1 Friday, September 8, 2017 Terminal Velocity Terminal velocity is achieved when an object in free fall no longer accelerates or decelerates and moves at a constant speed. This happens when the force of air resistance acting on the object becomes proportional to the force of gravity pulling it down. Hence, an accelerating object has an increasing force of air resistance until it matches in magnitude the weight of the falling object. At this point, there are two proportional forces acting on the object in opposite directions, resulting in a net force of zero. Thus the object reaches terminal velocity and starts moving at a constant velocity (Encyclopaedia Britannica, 2016). Preliminary Questions 1. When comparing the speed between one filter and two filters falling towards the ground, two filters fell faster than the single filter. The more filters there are, the faster they fall. This observation makes it clear that there is a relationship between the velocity of fall and the number of filters. A reasonable prediction about this relationship would be that the velocity of fall increases as a multiple of the number of filters. For example, assume a single filter fell down at a terminal velocity of 0.5 m/s. Then, three filters would fall down three times faster at 1.5 m/s. Likewise, four filters would fall down four times faster at 2 m/s and so on. However, this pattern would most likely not apply to a very high number of coffee filters due to different limitations and real-world discrepancies. 2. If there were no air resistance, the coffee filter and the baseball would both be able to experience the same acceleration due to gravity. However, the coffee filter’s rate of fall would still be slower than the baseball as it is much lighter. As the coffee filter will not reach a terminal velocity, a higher number of coffee filters will bring the rate of fall closer to that of the baseball. 3. For one falling coffee filter, below is a prediction of the graph Velocity vs Time.

2

The coffee filter will first accelerate due to gravity, and its rate of fall will increase. However, due to air resistance, the coffee filter will quickly reach a terminal velocity and will continue to fall at a fixed rate. This terminal velocity will be a low speed as a single coffee filter is very light. 4. When the filter reaches a terminal velocity, the net force acting upon it is zero. This is because the air resistance acting on the coffee filter is equal to the acceleration due to gravity that is pulling the coffee filter down. Hence, the coffee filter is able to reach a constant velocity or terminal velocity while it falls down. Observations # of filters in the stack

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Time (s)

1

1.56

1.79

1.81

1.72

2

1.08

1.39

1.23

1.23

3

0.85

0.85

1.10

0.93

4

0.73

0.92

0.89

0.85

5

0.65

0.62

0.71

0.66

3 Calculations of Terminal Velocity Number of Filters

Total Mass (g)

Terminal Velocity, vT, (m/s)

1

0.866

0.890

2

1.73

1.24

3

2.60

1.65

4

3.46

1.80

5

4.33

2.32

Analysis Terminal Velocity vs Mass Graph

3. Based on the resultant graph from the data collected, the terminal velocity of an object and its mass have a quadratic relationship. This conclusion is due to the line of best fit being curved, not straight which would make it linear. Hence, if an object increases in mass four times, its terminal speed would only become twice as fast. This can also be seen in the graph as the terminal speed of the object is about 1 m/s when it weighs near 1g. However, the terminal speed doubles and reaches 2 m/s when the mass becomes 4g. Likewise, drag force also depends on the velocity of

4 the object. It is commonly recognized that an object moving at a faster velocity experiences a larger amount of drag. This relationship is largely connected to the mass and velocity of the object as explored before. As the object starts to fall, it experiences an increasing amount of drag until a balance is reached resulting in a terminal velocity. As the mass of an object increases, the drag force must also increase to the same value to reach its terminal velocity. The higher magnitude of drag that must be achieved, the more time it takes to reach its terminal velocity, resulting in longer periods of acceleration and thus higher values of speed. Hence, objects with a larger mass that require a larger force of drag experience faster velocities. 4. As drag force and the mass of the object are proportional, drag force also experiences a quadratic relationship with velocity. Terminal Velocity vs. Mass During freefall, different masses have different values of terminal velocity. For example, a human’s terminal velocity is far higher than a feather’s terminal velocity. In the beginning, both objects start to fall down due to the force of gravity. As they accelerate, they start to feel air resistance which opposes the force of gravity. Both objects must experience a magnitude of air resistance proportional to their mass to reach a terminal velocity. In this situation, the feather needs a far lower amount of air resistance than the human as it is much lighter. As they both fall, the feather reaches its desired amount of drag first and thus continues to fall at a fixed velocity. However, the human still continues to accelerate until they reach their desired amount of air resistance. At this point, the human has accelerated for a far longer period of time and experiences a faster fixed velocity. Thus, the human has a far higher terminal velocity compared to the feather (The Physics Classroom, 2017). Conclusion In conclusion, the objective of exploring the effects of air resistance and its relationships with mass and terminal velocity of a falling object were met and completed. As an object falls, it experiences an increasing magnitude of air resistance until it becomes proportional to the force of gravity acting on it, resulting in a terminal velocity. Depending on the mass of the object and the amount of air resistance needed for a net force of zero, the period of acceleration may vary. Heavier objects have longer periods of acceleration, thus having higher values of terminal

5 velocities. For this experiment, the different factors had a quadratic relationship as the terminal velocity only doubled when the mass increased by a factor of four. The nature of these relationships was not expected when compared to the preliminary answers. However, this result is also very reasonable as the data has been organized and thoroughly analyzed.

6 References Elephant and Feather - Air Resistance. (2017). Retrieved September 07, 2017, from http://www.physicsclassroom.com/mmedia/newtlaws/efar.cfm The Editors of Encyclopaedia Britannica. (2016, October 24). Terminal Velocity. Retrieved September 06, 2017, from h ttps://www.britannica.com/science/terminal-velocity...