This is all the information that's given: A link arm (see figure below) has the mass m and center of gravity / center of mass at point G. The arm is freely articulated at point O. At points A, B and C, respectively, there are attachments for a spring and a rope that runs over a stationary pulley at point D. (neglect the dimensions of the pulley). The spring is untensioned when the angle θ = 2.0 m and then gives a force F = k s, where s is the elongation of the spring. If the arm is in equilibrium, the sum of all moments of force on the arm must be zero, ie.
Sum(Mi) = Sum(ri) × Fi = 0
Data: m = 150 kg, k = 2.0 kNm^−1, OG = 1.4m, OB = 2.1m, OC = 4.2m, D = (6.5, 2.0) m, g = 9.8ms^−2
a) Identify all the forces that give a moment (m.a.p. 0) and express both the forces and position vectors for the forces' points of attack in component form. Help: Write all vectorial quantities as an amount multiplied by a unit vector
b) Set up and solve (moment) the equilibrium equation with respect to the amount of clamping/tension force in the line. Express this as a function of the angle, ie T(∅).
c) Determine the smallest possible value for the angle ∅min.
d) Assume that the line can withstand a maximum load T = 15.0 kN and determine the corresponding angle ∅max
e) Show T(∅) graphically for ∅min <= ∅ <= ∅max
f) What will be the maximum value for ∅ if we do not have to consider the limitations of the line?
I'm not completely sure that I understand what is asked from the first question, but I've found the angle, the positions vectors OC, OB and OG but I'm unsure as what to do with them? From these I've also calculated CD. I think I'm supposed to find the moment for T but nt sure?
A teacher suggested that I take the cross product of CD and OC but as they are in the plane (2D) that's not possible so I might have misunderstood him.
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