Week 2 – Movement
In the second week, we got introduced to the movement and Newton's laws theorems, laws which can represent a substantial importance regarding this module. For the Movement part, we have received a set of exercises to solve in order to understand better the concepts behind the laws of movement. In the first exercise, a formula which calculates the average speed of a vehicle on a straight road for a mile at a speed of 50 mph then the vehicle turns around and rides back at a speed of 70 mph is needed. The average of the speed is the distance which has been covered over the time, thus representing the only mathematical computation which had to be done. Following this subquestion, I had to find the average velocity which resulted to be 0 because the car turns around so the distance covered had to be subtracted. Als, it does not matter with what speed the car has manoeuvred the velocity will still be 0.
In the second exercise, one of the requirements was to check which of the two weights struck the ground first, one being dropped straight down and one being thrown horizontally. The answer is that both of them have touched the ground at the same time because the force of the gravity affects both of the weights, in the same way, the mode in which they got dropped not representing an important factor. The time required for them to hit the ground was taken from the height formula, as it can be seen in the solution of the exercise. The distance can be seen in the second picture and it was found by performing the multiplication between the velocity with the time.
For the last exercise, which was again about speed, a special formula was needed, which can be seen in the following picture, where v1 represented the ultimate velocity and v2 the initial one. For this exercise to give a correct result the conversion from km/h to m/s had to be done. The answer is a negative one because the vehicle is decelerating (or slowing down).
Week 2 – Newton's Law
The second paper sheet with physics queries was about Newton's laws of motion, the three physics laws which created the foundation for classical mechanics physics. They characterize the relationship between a body and the forces which are acting upon it, and its motion in response to those forces. To be more specific, the first law defines the force qualitatively, the second law showcases a quantitative measure of the force and the third and final law underlines the idea that a single isolated force does not exist. After I have studied the laws of Newton I began working on the exercises, starting with the first one. In order to solve the first query, I have applied the first and the second law of Newton. In order to resolve the second exercise, the second law of Newton needs to be applied, F = m*a because the acceleration can be found from this formula.
In the third exercise, I had to draw the forces by Tarzan hanging from a vine. The forces which I have drawn represent the friction created between Tarzan and the vine, the weight and the tension created in the point where the character hold the vein.
Week 2 – 3D Coordinate Systems
For this specific query, the main idea was to mainly focus ideas of multiplication and/or commutation of the matrices formulas so we received an exercise where we had to check if two matrices perform the commutation or not. Before starting to resolve the problem, I have studied the concepts of 3D Coordinate systems. After I got familiarized with the concepts, I started solving the exercises. The first step was to write the formulas which I needed in order to solve the problem. After that, I introduced some values, gave θ a value of 90 degrees and made the x, y and z values equal with 2 to simplify the calculations. Following the declaration of the variables and finding the angle values, I have started multiplying the two newly formed matrices. The result was a negative one because (as it can be seen in the following pictures), the calculations have shown that the two matrices did not commute with the values which I have declared.
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