A uniform solid disk hockey puck of mass and radius slides across horizontal ice…

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A uniform solid disk hockey puck of mass 0.20 kg0.20\,\text{kg} and radius 0.050 m0.050\,\text{m} slides across horizontal ice while spinning. At the instant considered, the puck’s center of mass has speed v0=6.0 m s−1v_0=6.0\,\text{m\,s}^{-1} and the disk has an angular speed of ω0=40 rad s−1\omega_0=40\,\text{rad\,s}^{-1} about its central axis. Kinetic friction between the puck and the ice has coefficient μk=0.15\mu_k=0.15. Throughout the motion the bottom surface of the puck slides continuously on the ice; there is no transition to rolling without slipping. Air resistance is negligible. (a) Write an expression for the total initial kinetic energy of the puck in terms of the given quantities. (b) Determine the magnitude of the kinetic friction force acting on the puck while it is sliding. (c) Using an appropriate energy relation, derive an algebraic expression for the total distance dd the puck travels before coming to rest as a function of m,v0,ω0,μkm, v_0, \omega_0, \mu_k, and gg. (d) Calculate the numerical value of dd for the values provided.

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