PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
An elevator car of mass 800kg is connected by a light, inextensible cable over a frictionless pulley to a counterweight of mass 600kg. A motor can pull on the cable so that the tension in the cable is held constant at 7.0×103N. Kinetic friction between the elevator car and its guide rails exerts a constant 500N downward force on the car; friction on the counterweight and in the pulley bearings is negligible. At the instant shown, the system is released from rest.
(a) Taking the elevator car and counterweight together as a single system, derive an expression for the magnitude of the acceleration a of the system in terms of the masses, the cable tension T, and the friction force f. Clearly indicate the direction you take as positive.
(b) Use your expression to calculate the numerical value of the acceleration and state which object (the elevator car or the counterweight) moves downward.
(c) The motor maintains the stated cable tension for 3.0s. Determine the speed of the elevator car at the end of this time interval.
(d) Calculate the total work done by the motor on the system during the 3.0s period.