ing and a rope that runs over a stationary pulley at point D (neglect the dimensions of the pulley). The spring is 2.0 m long in the untensioned position and gives a force F = k s on the arm, where s is the extension / compression 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 = 2.8m, OC = 4.2m, D = (6.5, 2.0) m, g = 9.8ms^−2 a) Identify all the forces that give a moment (with regards to 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 equ
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 2.0 m long in the untensioned position and gives a force F = k s on the arm, where s is the extension / compression 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 = 2.8m, OC = 4.2m, D = (6.5, 2.0) m, g = 9.8ms^−2
a) Identify all the forces that give a moment (with regards to 0) and express both the forces and position
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?
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