Chapter 10, Problem 10.91CP

CALC A block with mass m is revolving with linear speed υ₁ in a circle of radius r₁ on a frictionless horizontal surface (see Fig. E10.40). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r₂. (a) Calculate the tension T in the string as a function of r, the distance of the block from the hole. Your answer will be in terms of the initial velocity υ₁ and the radius r₁. (b) Use $W={\displaystyle {\int }_{r_1}^{r_2}\stackrel{\to }{T}(r)•d\stackrel{\to }{r}}$ to calculate the work done by $\stackrel{\to }{T}$ when r changes from r₁ to r₂. (c) Compare the results of part (b) to the change in the kinetic energy of the block.