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In this project, we were assigned to test and improve a model car, each time perfecting its speed and efficiency. Initially, we started with a binder with no propulsion or external forces acting upon it and measured the forces acting upon it when pulled across a surface. Afterwards, we prototyped a car that used a mouse trap to move itself. For every single iteration of the prototype, we measured and analyzed data collected from trials. After 3 iterations of prototyping the car, we compiled all of our information in a single slideshow, presenting our findings about the data gathered on our car.
Content
Content
Velocity
Velocity is the amount of distance changed with respect to change of time. In algebraic physics, it is represented as delta x/delta t. In calculus physics, it is represented as dx/dt. In my calculation, the relationship, between velocity and position in the spring vs kinetic energy conversion equation, was essential to converting the acceleration function in respect to distance, into a function with respect to time.
Distance
The definition of distance is the amount traveled through spacial dimensions. In physics, distance is traditionally represented as either x or d. In our project, our goal was to theoretically calculate how far our car travels in distance.
Displacement
Displacement is the total difference in distance traveled through space. For example, the total amount of distance traveled in a curved path may be 5 meters, but the total displacement could be only 2. Displacement is represented by delta x in physics or as dx in calculus physics.
Acceleration
Acceleration is the amount of velocity changed with respect to change of time. In algebraic physics, it is represented as delta v/delta t. In calculus physics, it is represented as dv/dt. In my calculation, the relationship, between velocity and position in the spring vs kinetic energy conversion equation, was essential to converting the acceleration function with respect to distance, into a function with respect to time.
Kinematics
Kinematics is the study of mechanics concerned with the motion of objects without reference to the forces that cause the motion. Some popular kinematics equations are included below (both variants of algebraic and calculus). These kinematic equations were essential in converting our a(v) function into an x(t) one.
Energy
Energy is the sum of forces exerted over some displacement. Energy and work are both synonyms, with work
Spring Force
The spring force is is a force caused by object that behaves as a spring (aka an object whose distance that is stretched corresponds linearly to the amount of tension force it stores within). THe spring force is given the equation F=kx, where k represents the spring constant and x represents the amount of distance the spring is stretched. In our project, the spring in the mousetrap powered the car, and as such was essential for figuring out in order to complete our calculations.
Forces on Slopes
Forces on slopes rely on the trigonometric rules of mathematics. On slopes, the normal force is represented by mgcos(theta), whereas the force of the object going down the slope is mgsin(theta), where theta is the degree of the slope. In addition, the static mu-coefficient of an object is tan(theta), at the exact degree at whic hthe object starts moving. In our proejct, we calculated the forces exerted on our car when it rolls down a slope, and used it to predict the behavior of our car.
Elliptic Integrals
Elliptic integrals were originally founded as a result of trying to find the perimeter of ellipses. Over time, they became a generalized approach to solve for integrals of composite rational and trigonometric functions. In our case, elliptic integrals were used to describe the distance of our car as a function.
Mechanical Advantage (Ideal and Real)
Mechanical advantage is the amount of advantage acquired from a tool used. Real mechanical advantage refers to how much less force is required to complete a task, whereas Ideal mechanical advantage is how much distance is traveled using a tool. The real mechanical advantage equation is F_load/F_effort, and the ideal mechanical advantage equation is x_effort/x_load.
Gravitational Force
Gravitational force is the amount of force exerted in gravity. Theoretically speaking, the force of gravity is entirely dependent on the mass of two objects, as it is assumed that the acceleration due to gravity is always constant. The gravitational force only mattered in our project when we were dealing with slopes, as otherwise the normal force and gravitational forces cancel out.
Normal Force
The Normal force is the force exerted on an object by the intermolecular forces of another object. If the surface on which objcts lies upon is flat, Fn=Fg. However if the object lies on a slope, Fn=mgcos(theta). In our project, we used the normal force exstentively in our calculations, when figuring out the behavior of the car going doing a slope.
Frictional Force
The frictional force is caused by the interaction being two objects in a parallel motion. The equation used to calculate the frictional force is Ff=mu*N, where N is the normal force is mu is the frictional-coefficient. There are three main types of frictional forces: Static friction is the amount of resistance an object shows to moving as a cause of the frictional force, kinetic friction is the force exerted on the object once it is already moving, and rolling friction is the friction exerted on a rolling object.
Mu-Coefficient
The mu-coefficient is a dimensionless quantity that describes the characteristics between the two surfaces of the objects that are creating the friction force. In our project, we had to calculate out the mu-coefficient in order to figure out our frictional forces.
Reflection
Reflection
The amount of time I spent on this project was absolutely ridiculous. When we first started this project, I initially hoped I would not invest all my time into a singular project, a mistake I previously made in the kinematics lab. However, as we went deeper and deeper into the project, I eventually dug myself into a hole of complicating the project to no end.
To be fair, delving far into subjects greatly satisfied my own personal learning. Through all this practice I learnt so much about advanced calculus, continuous physics, spring mechanics and general problem solving. It was also fulfilling when I finally solved and figured out the equations for the project, albeit months after the due date.
However, I need to learn when enough is enough for completing projects. My issue I have always had is finishing anything, and knowing when to stop. In the future, I need to spread my workflow out and target the essential topics before going above and beyond. In addition, I should focus on helping my group out with the other aspects of projects. Because I was so obsessed with my endeavors in it, my partners were left to finish the essential parts of the project on their own. In the end, I should be a good project partner, as opposed to blindly following my own fascinations.
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