A Theoretical Study on the Perception of Weight in a Moving Elevator

Abstract

The present study shows the time dependence of the weight, perceived of a man, inside an elevator in motion. The sensation of this weight is caused by the upward force exerted by the elevator upon the man. A function has been empirically chosen to express the time dependence of velocity. Using this function, the upward force, acting on the man, has been calculated to determine thereby his apparent weight. Fractional change of weight, perceived by the man, has been estimated. The ratio of the apparent weight to the actual weight has been determined. For the upward and downward motions of the elevator, the present article graphically shows the time dependence of its speed, acceleration, ratio of the apparent to actual weight and the fractional change of weight, for different values of a parameter that controls the sharpness of the velocity-versus-time curve. To quantify the degree of comfort that one gets, while riding in an elevator, a parameter called comfort factor has been defined. It has been defined in two different ways, showing clearly the factors that reduce or enhance the level of comfort in such a journey. A major purpose of this study is to show the science students, the time evolution of what we perceive as our weight inside an elevator, using very simple mathematics, going far beyond the qualitative or semi-quantitative discussions of the school-level textbooks for senior students.