Savchenko Problem 2.2.24
Physics · thermodynamics
Problem
Two bodies of mass m₁ and m₂ are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread. 43Intuitive explanation
The key insight is that the thread constrains both bodies to move together—they must maintain constant separation . When body 2 moves perpendicular to the thread with velocity , the thread must pull it toward body 1, creating centripetal acceleration. Body 1 accelerates away from its initial rest state. Use conservation of momentum (the system has no external horizontal forces) to find how the velocities evolve, then apply Newton's second law to either body to find the tension needed to maintain the circular constraint.
Intuitive explanation
The key insight is that the thread constrains both bodies to move together—they must maintain constant separation . When body 2 moves perpendicular to the thread with velocity , the thread must pull it toward body 1, creating centripetal acceleration. Body 1 accelerates away from its initial rest state. Use conservation of momentum (the system has no external horizontal forces) to find how the velocities evolve, then apply Newton's second law to either body to find the tension needed to maintain the circular constraint.