The $8$ lb block rests on a surface for which ${}_k=0\mathrm{.}5.$ It is acted upon by a radial force of $2$ lb and a horizontal force of $7$ lb $,$ always directed at $30$ from the tangent to the path as shown $($Figure $1)$

Part A

If the block is initially moving in a circular path with a speed $v_1=3f\frac{t}{s}$ at the instant the forces are applied, determine the tim required before the tension in cord $AB$ becomes $25$ lb $.$ Neglect the size of the block for the calculation.

Express your answer with the appropriate units.

Figure

$1$ of $1$

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