# Calculate retarding force from free fall object

## Group 27
* 黃彥彰, Department of Physics, National Taiwan University
* 梁仁謙, Department of Physics, National Taiwan University
* 黃柏程, Department of Physics, National Taiwan University
* 張育昕, Department of Life Science, National Taiwan University

## Abstract
Using objects with different shape and texture to find the coefficient $k$ proportinal to air resistance and the $n^{th}$ power of $v$ in that formula $F=-kv^n$.

## Background and Objectives

We want to find the relationship between k, n and terminal velocity of a free fall. In textbook we often derive theorems by simplifying objects as a point-like particle.[^textbk] However, things don't work like that in real life. We are interested to find the air resistance of a realistic object applying on the theorem. We expect k will have something related to cross-sectional area.[^exp]

<figcaption>Fig. 1: Gravitational force and air resistant force. </figcaption>

## Methods, Steps and Progress

### Methods
Material:
1. Student card
2. Paper
3. Badminton
4. Basketball
5. (打點計時器)

Step:
1. Measure the temperature and moisture at the experimental environment.
2. Let objects start a free fall from a fixed height.
3. Calculate the time they fall and their terminal velocity.
4. Measure the surface area of the object
5. Find $k$ and $n$.

### Timetable

|Week|Task |
|----|------|
|1 |Preparation |
|2|Designing poster layout.|
|3|Do the experiment|
|4|Do the experiment again|
|5|Calculate the result and analyze|

### Responsibilities
Preparation-黃彥彰\
Do experiment-張育昕\
Do calculations-梁仁謙\
Do poster-黃柏程

## Expected Difficulties and Solutions
1. Collect materials
2. Hard to have a precise result
3. There might be a problem to set a scale that we can apply on the whole proce

## Results and Evaluation
The retarding force has a relationship between $k$ and $n$. And $k$ may also depend on other property of the meterial such as cross section area, shape, structure, and moisture.

## References
[^textbk]:J.B. Marion and S.T. Thornton, "Classical Dynamics for Particles and Systems", 5th ed., Harcourt Brace & Co., Philadelphia, 2003.
[^exp]:When Does the Air Resistance Force Make a Difference?https://www.wired.com/2015/01/air-resistance-force-make-difference/