EXSC 662 - Mechanical Analysis of Activity

Brigham Young University

These projects will be due one week after the assigned date

**#1: Projectile Motion (work alone on this project)**

**This project is designed to help you learn to derive characteristics of projectiles to determine the trajectory a projectile will follow**

- Look at the projectile motion equations from the Online Book.
- Write out the derivation of maximum height, horizontal displacement, and flight time (the long and short equations).
- These will be shown in class

- Use the golf ball simulator to see what the optimal velocity is to get the ball in the cup for the following situations:
- Angle of 20 deg with a range from 1.204 kg/m
^{3}to 0.77 kg/m^{3} - Angle of 20 deg and wind from -8 to +8 m/s

- Angle of 20 deg with a range from 1.204 kg/m
- Answer the following questions:
- What happens to the optimal velocity as air density is decreased (Be descriptive, is the slope linear)?
- What happens to the optimal velocity as wind goes from -8 to +8 m/s (Be descriptive, is the slope linear)?
- What happens to the optimal angle when going for maximum distance when using a velocity of 70 m/s as air dentisty goes down and gravity goes up (try air density of 1.0 kg/m
^{3}and g = -9.797 m/s^{2}when compared with a starting air density of 1.2 kg/m^{3}and g = -9.806 m/s^{2})?

**Turn in your derivations of the characteristics of projectile equations (probably handwritten). Turn in your responses to the questions related to the golf ball simulator (preferably typed).**

**#2: Velocity & Acceleration (work with one partner on this project)**

**This project is designed to help you learn to calculate velocity and acceleration from position and time data.**

- Save the horizontal and vertical position data from the ball we will drop in class and track with the Vicon system
- Bring the horizontal and vertical position data into a spreadsheet.
- Calculate the velocity and acceleration horizontally and vertically and create graphs of each (six graphs total).
- Answer the following questions
- What is the vertical velocity of the ball at the highest point of the flight?
- In theory, what should the horizontal acceleration of the ball be?
- In theory, what should the vertical acceleration of the ball be?
- Explain the discrepancies between the measured and theoretical accelerations.

**Turn in the spreadsheet and responses to the questions with you and your partners name on it (one copy for the pair of you is all that is needed).**

**#3: Angular Kinematics (work with one partner on this project)**

**You will learn in this project how angular momentum, angular velocity, and linear velocity all relate to each other in a tetherball game.**

- We will measure the position of a ball attached to a string attached to a post as it spins around. The string will wrap around the pole leading to a shortening radius.
- You will have a spreadsheet showing the radius and the position.
- Calculate the angular inertia, angular momentum, and angular and linear velocities.
- Create graphs of the above variables versus time.

**Turn in the spreadsheet (we will discuss the results as a group in class)**

**#4: DLT (work with one partner on this project)**

**This project will provide you practice with using Vicon Motus to perform a DLT and check the accuracy of it.**

- Setup a survey pole calibration (This file will help you obtain coordinates).
- Follow the steps you learned in class for filming and digitizing a calibration in Vicon Motus (make sure you sign up for the computer through http://calendar.google.com)
- Film and digitize an object of known length within and without the calibrated area.
- Answer the following questions:
- How much did the actual length compare with the digitized coordinates?
- What methods will you use to obtain the most accurate data when using Motus?

**Turn in the responses to the questions and be prepared to discuss the answers in class.**

**#5: Running Mechanics (work alone on this project)**

**This project will provide you the opportunity to practice using the Vicon system and pull information related to the mechanics of running as velocity is increased.**

- Take any data you are interested in from Vicon after the data collection is performed in class.
- Create a graph of some characteristic you measure and write up about 150 words discussing what you found.

**Turn in the responses to the questions and be prepared to discuss your project in class.**