Question d= 4.6 ft 26.2 If the rope wraps three full turns plus the basic wrap (1659) around the peg, determine if the 80-kg man can keep the 300-kg crate from moving. The coefficients of static friction between the rope and the peg and between the man's shoes and the ground are u=0.1 and u'= 0.4. respectively. 15° Yes

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Transcribed Image Text: d= 4.6 ft 26.2 If the rope wraps three full turns plus the basic wrap (1659) around the peg, determine if the 80-kg man can keep the 300-kg crate from moving. The coefficients of static friction between the rope and the peg and between the man's shoes and the ground are u=0.1 and u'= 0.4. respectively. 15° Yes

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The tension fore in a rape increases exponentially with no. of turns.Tension of the two ends of the ropeT_{2}=T_{1} e^{\mu \theta}This equation is Euler-Eyteloein equationIt the man is on verge ofslipping, F=\mu_{s}^{\prime} \mathrm{N}=0.4 \mathrm{~N}\begin{array}{l} \pm \sum F_{x}=0 ; 0.4 N-T \sin 15^{\circ}=0 \\+\uparrow F_{y}=0 ; N+T \cos 15^{\circ}-80(9.81)=0\end{array}Solving\begin{array}{l}T=486.55 \mathrm{~N} \\\beta \rightarrow \text { This is } \beta \\N=314.82 \mathrm{~N} \\\stackrel{N}{15 N} \rightarrow=0.4 \mathrm{~N} \\\mathrm{~N} \quad T_{2}=300(9.81) \mathrm{N} \\T_{1}=T=486.55 \mathrm{~N} \\\beta=n(2 \pi)+\left[\left(\frac{90^{\circ}+75^{\circ}}{180^{\circ}}\right) \pi\right]=(2 n+0.9167) \pi \\T_{2}=T_{1} e^{\mu \beta} \\300 \times 9.81=486.55 e^{(2 n+0.9167) \pi} \\\ln 6.049=0.1(2 n+0.9167) \pi \\n=2.406 \\\end{array}But Here n>3, so man can hold itCS Scanned with CamScanner ...