My dissertation for my Astrophysics MPhys degree at the University of Liverpool compiles research, simulations and calculations to come to concise conclusions about the feasibility of a human mission as stated in the project title.
A drawing in TikZ.
The first picture draws an impossible brick, which induces
an optical illusion similar to that triggered by Escher's
The second picture draws a Penrose triangle, another similar
The purpose of this lab was to illustrate the validity of the law of conservation of energy along with the determination of the spring constant of a given spring. For the first part the spring constantk was to be found from a given spring. Through the suspension of various known metal masses on a vertically suspended spring, the spring constant was determined. Two methods were used: the algebraic rearrangement of Hooke's Law and a slope analysis of a linear regression on a Force (N) against Stretch Length (m) scatter plot. The spring constant k was determined to be 26.438 ± 1.063. For the second part of the lab, the aim was to validate the law of conservation of energy through the oscillation of a vertically suspended spring. Data was collected using a Vernier Motion Detector 2 machine and the various energies (kinetic energy, gravitational potential energy and spring potential energy) were collected and summed up. The sum of these energies yielded a fairly constant energy total (2.287 J ± 0.025 J) which supports the authenticity of the law of conservation of energy. While there were some uncertainties due to the lab setup, human error and equipment error it did not affect the validity of the methods during experimentation. Overall, the spring constant k of a given spring was determined and the law of conservation of energy was validated through the calculation of total energy during a suspended mass' oscillation.
A minimal example showing how to choose different options for section and subsection labelling (including upper and lower case Roman numerals) by redefining the appropriate commands.