Speaker
Description
Two bodies of the same mass attached to opposite ends of a massless spring of natural length l₀ move on a smooth semi-plane (x<0) of a horizontal plane with the same velocity v₀, and the spring is not deformed. Assume that at the initial instant of time, the second body crosses the line x=0 and starts to slide on the rough semi-plane (x>0) while the first body continues to move on a smooth semi-plane. According to the Amontons-Coulomb law, the second body is acted on by the dry friction force F_fr=μN that is proportional to the normal reaction force N=mg, where μ is a coefficient of friction, and g is a gravity acceleration. As the friction force is directed opposite the second body velocity v₂>0 the string is compressed and the bodies are acted on by the elastic force F₂=−k(x₂−x₁−l₀) =−F₁, where k is a stiffness of the spring, and x₁, x₂ are the x-coordinates of the bodies. The system starts to oscillate while the velocity of its center of mass decreases and may become zero. Depending on the initial velocity v₀ of the bodies, different kinds of motion of the system can arise as a result. In particular, if the spring is asymmetric and its stiffness k for extension is greater than its stiffness for compression it may happen that the first body moving to the left (v₁<0) starts to pull the second body and the system moves to the left. Therefore, the center of mass of the system starts to move to the left and this phenomenon may be interpreted as reflection of the bodies by friction. In this talk, we analyze and classify possible motions of the system depending on the initial conditions.
