Irodov Problem 1.219

Problem Statement

A body of mass m moves in a circle of radius R on a smooth horizontal surface. It is connected to the center by a string. Find the tension if the kinetic energy is T.

Given

m, R, KE = T. Circular motion.

Concepts & Formulas

KE = ½mv² → v² = 2T/m. Tension (centripetal force) = mv²/R = m·(2T/m)/R = 2T/R.

Step-by-Step Solution

Step 1: v² = 2T/m.
Step 2: F_c = mv²/R = 2T/R.
Step 3: This equals the string tension.

Worked Calculation

Tension = 2T/R.

Boxed Answer

Tension = 2T/R (where T is kinetic energy)

Physical Interpretation

Tension equals twice the kinetic energy divided by the radius — a clean relationship between the string force and the energy stored in circular motion.