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Question Number 114223 by mathdave last updated on 17/Sep/20

Answered by mr W last updated on 18/Sep/20

a=g(sin θ−μ cos θ)  v_2 ^2 −v_1 ^2 =2as  v_2 ^2 −v_1 ^2 =2g(sin θ−μ cos θ)s  ⇒μ=tan θ−((v_2 ^2 −v_1 ^2 )/(2gs cos θ))  ⇒μ=tan 30°−((30^2 −10^2 )/(2×10×100×cos 30°))=0.115

$${a}={g}\left(\mathrm{sin}\:\theta−\mu\:\mathrm{cos}\:\theta\right) \\ $$$${v}_{\mathrm{2}} ^{\mathrm{2}} −{v}_{\mathrm{1}} ^{\mathrm{2}} =\mathrm{2}{as} \\ $$$${v}_{\mathrm{2}} ^{\mathrm{2}} −{v}_{\mathrm{1}} ^{\mathrm{2}} =\mathrm{2}{g}\left(\mathrm{sin}\:\theta−\mu\:\mathrm{cos}\:\theta\right){s} \\ $$$$\Rightarrow\mu=\mathrm{tan}\:\theta−\frac{{v}_{\mathrm{2}} ^{\mathrm{2}} −{v}_{\mathrm{1}} ^{\mathrm{2}} }{\mathrm{2}{gs}\:\mathrm{cos}\:\theta} \\ $$$$\Rightarrow\mu=\mathrm{tan}\:\mathrm{30}°−\frac{\mathrm{30}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} }{\mathrm{2}×\mathrm{10}×\mathrm{100}×\mathrm{cos}\:\mathrm{30}°}=\mathrm{0}.\mathrm{115} \\ $$

Commented by mathdave last updated on 18/Sep/20

thank ,great work

$${thank}\:,{great}\:{work} \\ $$

Commented by Tawa11 last updated on 06/Sep/21

great sir

$$\mathrm{great}\:\mathrm{sir} \\ $$

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