A large gate weighing 175 N is supported by hinges at the top and bottom of the

Question

A large gate weighing 175 N is supported by hinges at the top and bottom of the wooden frame, and is further supported by a wire. (Assume the positive x-direction is to the right and the y-direction is upward.) (a) What must the tension in the wire be for the force on the upper hinge to have no horizontal component? In Newtons (b) What is the horizontal force on the lower hinge? (Take the direction of pushing the gate away from the hinges to be positive and the direction of pulling the gate towards the hinges to be negative.) IN Newtons (c) What is the sum of the vertical forces on the hinges? In Newtons

Explanation / Answer

let the langth of wooden frame=3m and height=1.5 m,string is attached in the middle with 45 degree angle take moment about the lowest point 220*1.5=(T/sqrt(2))*1.5+(T/sqrt(2))*1.5 T=123.74 N b)F2x=T*(1/sqrt(2)) F2x=87.5 N c)F2y+F1y=175-T*[1/sqrt(2)] F2y+F1y=87.5 N

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