Minimum mass to break loose: Atwood machine with static friction and kinetic friction, acceleration.

New videos every week! Subscribe to Zak's Lab    / @zakslab   Questions or requests? Post your comments below, and I will respond within 24 hours. Minimum mass to break loose: Atwood machine with static friction, then it breaks loose and we use kinetic friction to find the acceleration. In this problem, we start with an Atwood machine where one mass is on a level surface and that mass has static and kinetic friction coefficients given. The other mass hangs off a light frictionless pulley. The first part of the problem is to find the minimum mass to break loose. For the analysis of this problem, the system is static, so we quickly get the tension in the string by applying Newton's second law to the hanging mass (the acceleration is zero). Then we apply Newton's second law to the mass on the level surface, and we assume the static friction force is maximum for the chosen hanging mass. We are able to solve for the size of the hanging mass that maxes out the static friction force, and this is the mass required to break loose. Once the Atwood machine is moving, we switch to using the coefficient of kinetic friction, acceleration is no longer zero, so that the tension is not equal to mg anymore! We set up Newton's second law for each mass, and this gives us a system of equations where the unknowns are tension and acceleration. We eliminate tension from the system of equations by adding them, then we solve for the acceleration of the Atwood machine.