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One-end-of-an-inextensible-string-is-fixed-to-a-ceiling-and-the-other-end-is-tied-to-a-wooden-block-The-block-is-pulled-aside-by-a-horizontal-force-P-such-that-the-string-now-makes-an-angle-of




Question Number 147147 by nadovic last updated on 18/Jul/21
 One end of an inextensible string is   fixed to a ceiling and the other end is   tied to a wooden block. The block is   pulled aside by a horizontal force P,   such that the string now makes an   angle of 45° with the downward    vertical. When the force P  is raised   through an angle of 30°, it decreases by   8N to keep the system in equilibrium   without shifting the string. Find the           (a) value of P.           (b) mass of the block.
$$\:\mathrm{One}\:\mathrm{end}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inextensible}\:\mathrm{string}\:\mathrm{is} \\ $$$$\:\mathrm{fixed}\:\mathrm{to}\:\mathrm{a}\:\mathrm{ceiling}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is} \\ $$$$\:\mathrm{tied}\:\mathrm{to}\:\mathrm{a}\:\mathrm{wooden}\:\mathrm{block}.\:\mathrm{The}\:\mathrm{block}\:\mathrm{is} \\ $$$$\:\mathrm{pulled}\:\mathrm{aside}\:\mathrm{by}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{force}\:\boldsymbol{{P}}, \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{string}\:\mathrm{now}\:\mathrm{makes}\:\mathrm{an} \\ $$$$\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{downward}\: \\ $$$$\:\mathrm{vertical}.\:\mathrm{When}\:\mathrm{the}\:\mathrm{force}\:\boldsymbol{{P}}\:\:\mathrm{is}\:\mathrm{raised} \\ $$$$\:\mathrm{through}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°,\:\mathrm{it}\:\mathrm{decreases}\:\mathrm{by} \\ $$$$\:\mathrm{8N}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{the}\:\mathrm{system}\:\mathrm{in}\:\mathrm{equilibrium} \\ $$$$\:\mathrm{without}\:\mathrm{shifting}\:\mathrm{the}\:\mathrm{string}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\left({a}\right)\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{{P}}. \\ $$$$\:\:\:\:\:\:\:\:\:\left({b}\right)\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{block}. \\ $$

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