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Solved: CP CALC A block with mass m is revolving with
Chapter 10, Problem 103CP(choose chapter or problem)
A block with mass m is revolving with linear speed \(v_1\) in a circle of radius \(r_1\) on 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 \(r_2\).
(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 \(v_1\) and the radius \(r_1\).
(b) Use \(W=\int_{r_{1}}^{r_{2}} \overrightarrow{\boldsymbol{T}}(r) \cdot d \overrightarrow{\boldsymbol{r}}\) to calculate the work done by \(\vec{T}\) when r changes from \(r_1\) to \(r_2\).
(c) Compare the results of part (b) to the change in the kinetic energy of the block.
Questions & Answers
QUESTION:
A block with mass m is revolving with linear speed \(v_1\) in a circle of radius \(r_1\) on 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 \(r_2\).
(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 \(v_1\) and the radius \(r_1\).
(b) Use \(W=\int_{r_{1}}^{r_{2}} \overrightarrow{\boldsymbol{T}}(r) \cdot d \overrightarrow{\boldsymbol{r}}\) to calculate the work done by \(\vec{T}\) when r changes from \(r_1\) to \(r_2\).
(c) Compare the results of part (b) to the change in the kinetic energy of the block.
ANSWER:Solution 103CP