Problem 1: A uniform sphere of mass m and radius r is projected along arough horizontal surface with a linear velocity vo. The coefficient of kineticfriction between the sphere and the surface is µ. Determine(a) the work done by friction force on the sphere until the time t, atwhich the sphere will start rolling without sliding, and(b) calculate the total kinetic energy of the sphere at instants t=0 andt=t:{T = Translation +Trotation =mv3 +÷low²}.(c) Is the change in total kinetic energy equal to the work done by thefriction force in the time interval [0, t,]?(d) Will there be friction between the sphere and the horizontal surface after the instant t=t,? Explain why.Note: Do NOT use D'Alembert's Principle.

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