OpenStax College Physics for AP® Courses, Chapter 4, Problem 19 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. Let’s consider what’s happening before and after the rope breaks in this tug-of-war. Before the rope breaks, we have the player exerting a force on the ground is due to the player and then the Newton’s Third Law counterpart to this is a force on the player due to the ground pointing to the left. This is balanced when there is a fair competition here where the teams are not moving one way or the other. This will be balanced by a force of tension to the right due to the other team that’s over here pulling the other way. When the rope breaks, what happens is that there is no longer this force of tension and there still will be this force because the player is still exerting a force on the ground which is in turn exerting a force on the player and so this is why the player is going to accelerate because there is no longer a force of tension on the rope balancing the force exerted by the player on the ground which is then in turn exerting a force on the player due to the ground. So b is the answer, the teams will accelerate in opposite directions as a result. c is definitely not our answer because the force of gravity does not balance the forces exerted by the teams since these forces are in perpendicular directions. Here’s the force due to gravity and so it has no bearing, no effect on the force due to the players except indirectly in that it affects the normal force upwards on the player and then the force due to friction between the player’s shoes and the ground is the coefficient of static friction times the normal force. So indirectly I guess gravity kind of has an effect but not directly in the way that this option c suggests. Option d has a confusion about how forces work, they don’t, force does not jump from one thing to another so that’s not the answer. And force exerted by the two teams are no longer equal; the teams will accelerate in opposite directions as a result. Well they never were equal to begin in, I mean they might have been equal in magnitude but they were not in equal directions and it’s not the reason that they are accelerating. They are accelerating because there’s an unbalanced net force in one direction that’s no longer being balanced by tension in the other. So b is the answer.