Tension and Acceleration: Objects Connected By Cables | Symbolic Physics (AP, College 1)
Part of series of physics problems at the AP and undergraduate level, where the emphasis is on the algebraic solutions to problems. The goal is to help students who are less comfortable with symbolic solutions than they are with numerical ones, by bridging the gap between conceptual understanding and algebra techniques. This problem, solved in terms of given variables and universal constants only, is based on this AP Free Response question from 1982:
1982B2. A crane is used to hoist a load of mass m1 = 500 kilograms. The load is suspended by a cable from a hook of mass m2 = 50 kilograms, as shown in the diagram above. The load is lifted upward at a constant acceleration of 2 m/s2.
a. On the diagrams below draw and label the forces acting on the hook and the forces acting on the load as they accelerate upward.
b. Determine the tension T1 in the lower cable and the tension T2 in the upper cable as the hook and load are accelerated upward at 2 m/s2. Use g = 10 m/s2.
The version we see in the video is here:
A crane is used to hoist a load of mass M1. The load is suspended by a cable from a hook of mass M2, as shown in the diagram. The load is lifted upward at a constant acceleration, a m/s^2. Determine the Tension T1 in the lower cable and T2 in the upper cable as the system is accelerated upwards. Answer terms of defined variables and universal constants.