<p>The spring loaded supporting rods AB and AC in the figure below aer used as s

Question

<p>The spring loaded supporting rods AB and AC in the figure below aer used as shock absorbers for transporting fragile loads. Knowing that the elastic spring constants for the rods AB and AC are kab = 1.2 kN/m and kac = 1.5 k N/m, respectively determine the unstretched length of each rod after the 30 kg block is removed. Neglect the weight of the rods.</p>
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Explanation / Answer

balancing the forces in the horizontal and vertical directions on the 30kg black we have

30*9.81=k1*X1*5/61+k2*X2*5/51.--------(1)

where k1 = kac, k2= kbc.

and in the vertical direction k1*X1*6/61 = k2*X2*4/51.

=> x1=.5832*x2.

substituting the value of x1 in eq.(1) and solving for x2 we have x2= 0.28 m.

substituting in eq.(2) we have x1= 0.163 m.

where x1 and x2 are the extensions produced in the rods due to the given loading.

now the actual lengths of the rods are lac = .781 -.163 = 0.618m

similary lbc = 0.64 - 0.28 = 0.36m

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