OpenStax College Physics for AP® Courses, Chapter 7, Problem 18 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. This is a graph of the force parallel to displacement of this motorcycle versus its distance along the loop-the-loop and it's gonna start here at position number one at which point its displacement is to the right and gravity is straight down and so there's no gravity parallel to the displacement at this position one and so we have zero here on our graph. This label for this vertical axis is F with a vector symbol over it to remind us that positive and negative indicates a direction whereas the horizontal axis does not have the vector symbol on it because this is a distance, this is not displacement so we have force parallel to displacement versus distance. Now as this motorcycle goes to position two, at this point we have gravity downwards— let's make this green— the force of gravity it's down whereas the displacement is upwards so this is the change in position and so the gravity is anti-parallel to the displacement at position two and so that means... and gravity is down and I want to indicate opposite direction with a negative sign. So the positive and negative here does not actually indicate the direction of the force of gravity because the direction of the force of gravity is always negative— if we take up to be positive, gravity is always down— so this graph is not a graph of gravity, it's a graph of to what extent is gravity parallel or anti-parallel to the displacement. So at position two, it is maximally anti-parallel so it's at a maximum negative amount at this position. And then at position three, when this motorcycle gets over here— position three— now we have gravity still straight down as it will always be so I can just move this arrow over here but the displacement is to the left now and there is no gravity parallel or anti-parallel to the displacement and so at position three, we are back to zero again as we were at position one. And then carrying on to position four here, we have gravity down and the displacement also is down so gravity and displacement are parallel to each other and we are gonna indicate that with a positive. So the amount of force parallel to the displacement is at a maximum positive amount at this position and so we have that indicated here at position four. And then returning back to position one again, we have displacement to the right and gravity down and so there's no gravity parallel to displacement of that position one again. And there we go!