A solid disk of mass and radius rests on a horizontal rough table
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A solid disk of mass 4.0kg and radius 0.10m rests on a horizontal rough table. A light, inextensible string is wrapped around the rim of the disk, passes over a small frictionless pulley fixed at the table’s edge, and supports a hanging block of mass 1.5kg, as shown in the verbal description. When the system is released from rest, the string unwinds without slipping and the disk rolls without slipping on the table. The moment of inertia of a solid disk about its central axis is 21MR2.
(a) Draw separate free-body diagrams for (i) the disk and (ii) the hanging block. Clearly label all forces.
(b) Write the appropriate equations of motion for the two objects and derive an expression for the magnitude of the acceleration of the system in terms of the given masses, g, and any necessary geometric quantities.
(c) Using your expression, calculate (i) the magnitude of the acceleration, (ii) the tension in the string, and (iii) the magnitude and sense (direction) of the static friction force acting on the disk.
(d) Determine the minimum coefficient of static friction required between the disk and the table so that the disk continues to roll without slipping for the entire motion.