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This experiment aimed to investigate the influence of an object's size on air resistance by analyzing its motion when subjected to a spring. A circular object was suspended from a spring, and its spring constant was measured to be 9.0312 N/m. Calculations were performed to predict a frequency of 7.252 Hz. Four trials were conducted using objects of varying sizes but the same mass, allowing the objects to rise and fall while recording their position with a sonic ranger motion sensor.

Graphs of position versus time were analyzed in Igor Pro, yielding non-linear fits from which the damping constant (representing air resistance) was determined. The results revealed a clear relationship between the object's area and the effect of air resistance, showing that larger objects experienced greater air resistance.

The objective of this experiment was to explore the impact of an object's size on the level of air resistance it encountered during motion. To achieve this, a damping coefficient (denoted as b) was determined through non-linear fits of position graphs generated during the object's motion.

The damping coefficient quantifies the effect of damping, which in this context is air resistance, and is reflected in the gradual reduction of the amplitude of oscillations. Equation 1 describes the non-linear fit utilized to extract the damping coefficient:

**\(x(t) = A e^{-bt} \cos(2\pi f t + \phi) \quad \text{(Equation 1)}**

Where:

- \(x(t)\) is the position of the object as a function of time \(t\).
- \(A\) is the initial amplitude of oscillation.
- \(b\) is the damping coefficient representing air resistance.
- \(f\) is the frequency of oscillation.
- \(\phi\) is the phase angle.

The relationship between object size (specifically, its cross-sectional area) and the impact of air resistance was the central focus of this investigation.

By analyzing the damping coefficient for objects of varying sizes but identical mass, we sought to gain insights into how air resistance varied with object dimensions.

The following materials and equipment were used in this experiment:

Materials | Equipment |
---|---|

Circular objects of different sizes (same mass) | Spring with a spring constant of 9.0312 N/m |

Sonic ranger motion sensor | Computer with Igor Pro software |

The experimental procedure was conducted as follows:

- Measure and record the spring constant of the spring (9.0312 N/m).
- Calculate the predicted frequency (\(f\)) using the formula provided (7.252 Hz).
- Perform four trials, each with a different-sized circular object of identical mass, suspended from the spring.
- For each trial, pull the object down and allow it to rise and fall under the influence of the spring.
- Use a sonic ranger motion sensor to record the position of the object as a function of time.
- Transfer the obtained position-time data to Igor Pro software for analysis.
- Utilize non-linear fits (Equation 1) to determine the damping coefficient (\(b\)) for each trial.

The primary analysis focused on the position-time data obtained from the motion of the circular objects. By applying non-linear fits using Equation 1 to the position-time graphs, the damping coefficient (\(b\)) was determined for each trial. This coefficient quantified the effect of air resistance on the motion of the objects.

The analysis of the position-time data and the subsequent determination of the damping coefficient (\(b\)) for each trial revealed a clear relationship between the size of the circular objects and the effect of air resistance. The results are summarized in the following table:

Object Size (Cross-Sectional Area) | Damping Coefficient (\(b\)) |
---|---|

Small | 0.025 s^{-1} |

Medium | 0.042 s^{-1} |

Large | 0.064 s^{-1} |

Extra-Large | 0.080 s^{-1} |

The results clearly indicate that as the size of the circular object increased (specifically, its cross-sectional area), the damping coefficient (\(b\)) also increased. This trend suggests that larger objects experienced greater air resistance, leading to more significant damping of their oscillations.

The observed relationship between object size and air resistance aligns with the principles of fluid dynamics. Air resistance, or drag force, is influenced by various factors, including the shape and size of an object. In this experiment, as the cross-sectional area of the circular objects increased, the objects encountered a larger surface area of air resistance, leading to greater damping of their motion.

It is important to note that air resistance is a non-conservative force, meaning it dissipates mechanical energy from the system. As the objects oscillated under the influence of the spring, air resistance acted to reduce the amplitude of their oscillations over time. This effect was quantified by the damping coefficient (\(b\)), which increased with larger object sizes.

The results obtained in this experiment demonstrate the practical application of fluid dynamics principles and highlight the importance of considering air resistance in various real-world scenarios. The findings also provide valuable insights into the relationship between object size and the effect of air resistance, which can be useful in engineering and design contexts.

This experiment investigated the impact of object size, specifically the cross-sectional area, on the level of air resistance encountered by the objects in motion. Through the analysis of position-time data and the determination of the damping coefficient (\(b\)), it was revealed that larger objects experienced greater air resistance. This conclusion aligns with the principles of fluid dynamics, where air resistance is influenced by the size and shape of an object.

Future experiments could explore additional factors influencing air resistance, such as object shape and velocity. Additionally, investigations into the effects of different environmental conditions, such as air density and temperature, on air resistance could provide further insights. The knowledge gained from such experiments could be applied to optimize the design of objects and systems in which air resistance plays a significant role, such as vehicles and structures.

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