Question
Using the concept of torque, explain why a traffic cone placed on its base is in stable equilibrium, while a traffic cone placed on its tip is in unstable equilibrium.
Final Answer
see the solution video for an explanation of stable equilibrium.
Solution video
OpenStax College Physics for AP® Courses, Chapter 9, Problem 3 (Test Prep for AP® Courses)
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Video Transcript
This is College Physics Answers with Shaun Dychko. A traffic cone placed on its base like this is in stable equilibrium, because if its moved away from its equilibrium position it will naturally left on its own, fall back to its equilibrium position. So what I mean by that is consider the center of mass being position here say. If it was tilted over, so that it was pointing like this say, and it was resting on its edge here, this would be the pivot point and then the center of mass would be here say. The center of mass has a lever arm this much, perpendicular to the pivot point and gravity is straight down here, and this green arrow I'm trying to represent the perpendicular lever arm. Well, that is a torque that is clockwise and so it would tend to make the traffic cone go back to where it started. It would tend to make the base go flat again against the ground. So because a small perturbation from equilibrium causes the thing to go back to its equilibrium position, this is said to be a stable equilibrium. However, if the traffic cone is upside down, you can still have equilibrium and the center of mass is here, and left just like this, it is possible for the center of gravity to be directly above this pivot point here and therefore have no torque. It would not cause the cone to fall. But if the cone was tilted over a little bit, and you had a pivot point here, now you have the center of gravity here and forces straight down. It would have a perpendicular lever arm like this, and so it would have some torque now because the lever arm is non-zero. But this torque is going to be counter-clockwise and it will result in the cone falling over and not returning to its equilibrium position, it won't make it stand up any more. Whereas before when you had the base on the ground, it did make it stand up. But now with the tip on the ground, the torque due to gravity is going to cause it to fall. This is an unstable equilibrium when small perturbations from the equilibrium position cause it to get even further away from the equilibrium position.