The final answers should be [Force on AB is 175lbs] and the [Length is 2.34ft.]
ID: 1919973 • Letter: T
Question
The final answers should be [Force on AB is 175lbs] and the [Length is 2.34ft.] Please show me how you have got these answers and I will awards points respectively. Thank You.
The ring of negligible size is subjected to a vertical force of 200 lb. Determine the longest length l of cord AC such that the tension acting in AC is 160 lb. Also, what is the force acting in cord AB? Hint: Use the equilibrium condition to determine the required angle 9 for attachment, then determine l using trigonometry applied to Delta ABC.Explanation / Answer
Let, F = force acting on AB
Z = angle theta, ie. angle ACB
The forces should be equal in X-axis and in Y-axisas well.
In the X-axis,
160Cos(Z) = FCos(40) ----- [1]
In the Y-axis,
FCos(50) + 160Sin(Z) = 200 ------[2]
Calculating the values of Cos(50) and Cos(40), and solving the equations [1] and [2],
134.26Cos(Z) + 160Sin(Z) = 200
Let, A = 134.26, B = 160, C = 200
Cos(Z) = {(C/A) - (B/A)Sin(Z)}
On squaring both sides and making (Cos(Z))^2 = {1 - (Sin(Z))^2}, the equation becomes as
(Sin(Z))^2 *{1 + (B/A)^2} - 2*(B*C/A^2)*Sin(Z) + (C/A)^2 - 1 = 0
Putting the values of A, B and C, we get,
2.42(Sin(Z)^2) - 3.55Sin(Z) + 1.22 = 0
Solving this quadratic, we get,
Sin(z) = - 0.55
Cos(Z) = 0.835
So, Z = 33.38
Putting the value on equation [1],
F = 174.45
From Trigonometry,
2Sin(40) = LSin(33.38)
So, L = 2.34
Finally,
F = 174.5 lb
L = 2.34 ft
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