Engineering 100-980

Lab 8: Terminal Velocity and Drop Tests

Contents

Materials

Introduction

Galileo Galilei, a 16th century astronomer, philosopher, mathematician, and central figure in the Scientific Revolution of the 17th Century, once wrote that, in the absence of resistance caused by air, a hammer and a feather would fall at the same rate. His claim was verified centuries later on the moon by the crew of Apollo 15, which is also known as the all-UMich Apollo astronaut crew. You can watch the demonstration in the video Hammer vs Feather - Physics on the moon.

This phenomena is not random, and is instead due to drag forces. While we know that the acceleration due to gravity is constant for all objects, we also know that not all objects fall at the same rate, even if it seems they should. This is because of drag force, which is related to properties of the object as well as the cross-sectional area of the object. Terminal velocity is the maximum speed an object can reach while in free-fall. Historically, we have used this to our advantage with the use of parachutes to lead to safe fall speeds for things like payloads, or even humans.

The Drag Equation

Reference Area

In the case of an object attached to a parachute, we can consider the object as a projectile with no thrust that starts from a y-position of greater than 0. We also need to incorporate drag force into our standard projectile equations to help us determine when the object will reach its terminal velocity.

Terminal velocity is when the drag force is equal to the weight of the object, as noted below:

Terminal Velocity

Procedure

Setup

  1. Measure each parachute’s area and record the values in the spreadsheet given below.

  2. Measure the mass of the payload you are carrying for each iteration. (1, 2, 4-5 figurines).

  3. Measure the mass of each parachute with the payload bucket attached.

Parachute Trials

Note: The distance from the floor to the ceiling of the second floor is: 10’ 6”. Imagine you are on the ground. If you walk up one set of stairs the ceiling above your head is this height^.

We are going to measure the terminal velocity of your different sized parachutes with three mass configurations, and create plots of terminal velocity vs mass for different parachutes. We have created a spreadsheet for you to record your values in.

Computations

Submission

On Canvas, you will submit ONE PDF that will include all of the following:

To put said content into a PDF, it is suggested you create a new Google Doc (docs.new) and paste your images and write any text in the document. Export/Download this document as a PDF and upload it. DO NOT SUBMIT A GOOGLE DOC FILE OR SPREADSHEET FILES.

Submitting anything other than a single PDF may result in your work not being graded or your scores being heavily delayed.

Separately: