This project aims to show how the work performed on an object can be calculated using the dot product of the vectors of the object’s displacement and the net force acting on the object. In physics, work is defined as the energy that is transferred to an object by the forces acting on it as it moves along a certain distance. In order to demonstrate how the dot product can be used to calculate work, we performed an experiment to obtain data to be used in our calculations. We rolled seven different balls down a straight slide and measured the time it took for each ball to roll down the slide. We also measured the mass of each ball and the relevant dimensions of the slide (its height, y, and base, x). These measurements, along with basic physics formulas and concepts, were used to determine the net force and displacement vectors for our objects. The dot product between these two is then calculated to determine work. A more complicated process is explained in the bottom right component of our poster. This process applies for slides where the path is not straight, but rather curved. In this situation, line integrals are used, where the curve is integrated over the vector field that is the net force acting on the balls.
Multiple errors were possible and likely occurred. Our measurements likely have small inaccuracies, such as in our measurements of time and our measurements of the height and base of the slide. As shown in the poster, we were unable to find information for the coefficients of rolling friction, nor were we able to calculate it with our available materials in order to determine the net force vector. Thus, we had to go about an alternate method of determining the net force vector. While we tried to account for the curves in the slide at its start and finish, we did not clearly mark these positions, and thus they likely varied in our multiple measurements and trials.
