Reference no: EM133681763
Engineering Mathematics
Description
Select one of Workshops 1-5 to write a report on.
Formatting requirements:
• Use a simplistic style, without decorative text/borders etc.
• All mathematics is to be formatted either in Microsoft Word equation editor, or a non- Microsoft Word equivalent such as LaTeX.
• Write in a self-contained manner.
Content requirements:
The report should be succinct and minimal, that is, only include highly relevant material. Include exactly the following headings
Introduction - Describe the problem, including any relevant background information.
Analysis - Provide the derivation of the mathematical formulation of the problem. In the process of doing so, describe any assumptions you are making, introduce the variables you have chosen, and provide any known constants that you are using.
Solutions - Solve the mathematical formulation, showing each step.
Interpretation - Interpret the solution of the mathematical formulation in the context of the original problem. Make sure to include relevant units.
Discussion - Explore and discuss the extension problems described in the workshop document. Other extensions may be acceptable, but discuss with your tutor beforehand.
References - Include any references you have used, such as sources for your known constants, or for interesting features of your problem.
Workshop
A projectile is fired away from the Earth so that it escapes the Earth's gravitational pull. The projectile has no acceleration, it only moves via the initial velocity (i.e. it is not a rocket). The minimum initial velocity required to escape is known as the ‘escape velocity'.
Problem 1
Find the escape velocity for a projectile. You may ignore air resistance.
Extension Problems
For the assignment, attempt any two of the following:
Plot the escape velocity as a function of gravity. Indicate any notable values for gravity, for example, on different planets.
Explore the possibility of actually reaching the escape velocity in practice, what kind of energy would be required to give an object that kind of speed?
Model the effect of air resistance. This will involve defining air density at a given altitude and selecting a drag coefficient and mass for the projectile. Plot the height of the object as a function of time.
Length requirements:
A maximum length is needed on these reports to not overburden our markers. Please adhere to the below maximum lengths, anything significantly different will attract penalty.
• Introduction and Analysis sections combined are under 1.5 pages
• Solutions and Interpretation sections combined are under 1.5 pages
• Discussion section is under 1.5 pages
• References are unrestricted