co A puck of mass m=1.50 kg slides in a circle of radius r=20.0 cm on a frictionless table whi

step 1 For this problem on the topic of force and motion, as we can see in the figure, we have a puck o

Co A puck of mass m=1.50 kg slides in a circle of radius...

co A puck of mass $m=1.50 \mathrm{~kg}$ slides in a circle of radius $r=20.0 \mathrm{~cm}$ on a frictionless table while attached to a hanging cylinder of mass $M=2.50 \mathrm{~kg}$ by means of a cord that extends through a hole in the table (Fig. 6-43). What speed keeps the cylinder at rest?

Key Concepts

Uniform Circular Motion

This concept describes the motion of an object traveling at constant speed along a circular path. Even though the object's speed remains constant, its velocity changes direction continuously, resulting in an inward (centripetal) acceleration. This acceleration is given by the formula a = v²/r, where v is the speed and r is the radius of the circle.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circle, always directed toward the center of the circle. It is calculated using F = m * v²/r, where m is the mass of the object, v is its speed, and r is the radius. This force is provided by other interactions in a system, such as tension in a string or gravitational force.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a). In circular motion problems, this principle is used to relate the net inward force (centripetal force) to the mass and the centripetal acceleration, connecting dynamic quantities with the forces involved.

Tension in a Cord and Equilibrium

In systems involving cords or strings, the tension transmits force from one part of the system to another. When a component, such as a hanging mass, is at rest, the tension in the cord must balance other forces acting on it (such as gravity). This equilibrium condition allows one to equate the gravitational force on the hanging mass to the centripetal force required for the object in circular motion.

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