This video shows us how to solve a one-dimensional hybrid “forces” and “kinematic” problem. We are pulling a person out from a well over 10 seconds with an initial velocity of zero, but our rope has a threshold that can handle it. We want to see if we put this rope under too much tension force or not. We will mix a time-dependent equation of motion from kinematic physics with a free-body diagram and Newton’s second law to predict the applied tension force on the rope. 

A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Cable 1 carries the tension force 1 and, with some angle, is mounted to the ceiling. The same is true for cable 2; this cable carries the tension force 2 and is mounted with some angle to the ceiling. We are asked to find an expression for the tension force 1, the tension in cable 1, which does not depend on the tension force on cable 2. Our answer needs to be expressed in terms of some or all of the variables mass, the angle of cable one and two with respect to the ceiling, and the magnitude of the acceleration due to gravity or g. Then, we will check our final answer under a “Special Case” of having cable one vertical and cable two almost horizontal.