A block with mass m is revolving with linear speed v₁in a circle of radius r₁on a frictionless horizontal surface (see Fig. E10.42). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r₂.D

(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 v₁ and the radius r₁.

(b) Use 

to calculate the work done by 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.

Figure E10.42: 

Transcribed Image Text:

W = SR T(r) · dr