Answer to Question #208052 in Mechanics | Relativity for Harshal Ahire

Question #208052

A body of weight 50N is hauled along a tough horizontal plane by a pull of 18N acting at an angle of 14° with the horizontal. Find the coefficient of friction


1
Expert's answer
2021-06-17T15:08:10-0400

F1=18NF_1= 18N

let F resultant force\text{let }\vec F \text{ resultant force}

F=ma\vec F= m \vec a

a=0 since the body is hauled\vec a = 0 \text{ since the body is hauled}

F=0\vec F=0

F=F1+Ffr+N\vec F = \vec F_1+\vec F_{fr}+\vec N

for vertical axis Y:\text{for vertical axis Y:}

Nmg+F1sin14°=0\vec N-mg+\vec F_1\sin14\degree= 0

N=mgF1sin14°=5018sin14°=45.66\vec N =mg - \vec F_1\sin14\degree= 50-18*\sin14\degree=45.66

for horizontal axis X:\text{for horizontal axis X:}

F1cos14°Ffr=0\vec F_1 \cos14\degree-F_{fr}=0

Ffr=F1cos14°=18cos14°=17.47F_{fr}=\vec F_1 \cos14\degree=18*\cos14\degree=17.47


μ=FfrN=17.4745.66=0.383\mu= \frac{F_{fr}}{N}=\frac{17.47}{45.66}=0.383

Answer: μ=0.383\text{Answer: } \mu= 0.383


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