Spatial-numeric method application to the movable wedge problem for Physics First pedagogy

Abstract

The objective is to solve the college physics problem of a block sliding down a movable smooth wedge without friction anywhere using a spatial-numeric perspective.  The drawing method used the sum of the normal force and weight of the block to find the wedge acceleration.  The drawing method results are equivalent to the algebra method results within drawing accuracy.  The result of a geometric construction with regular drawing uncertainly was shown for the case without any horizontal applied force.  For the case of a given horizontal applied force, an additional numeric graphing method was shown with additional drawing uncertainty in the result.  The geometric construction without graphing resuted in solving the horizontal applied force case via scaling in the concept of modified gravity experienced by the block on the wedge’s slant edge, assuming a pre-requisite knowledge of algebra and trigonometry.  The presented spatial numeric method and results imply a Physics First pedagogy of using the spatial numeric abilities,  with the inclusion of the pre-projectile problem, pre-traffic-light problem, and post-collision problem in a one-semester syllabus.