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

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Question Number 147147 by nadovic last updated on 18/Jul/21

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

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