Question

A block of mass M = 2kg is placed inside a rigid tube with length L= 2m connected to two springs of resisting lengths L1= 80cm and L2 =100cm, with spring constant k1= 200 N/M and k2= 300 N/M respectively connected at the ends A and B of the tube. Determine the elongations of the two springs when the tube AB is positioned Vertically.

Finally consider one configuration in which the tube rotates in a horizontal plane centered at B, and determine for which value of the rotation period the spring k1 is no longer elongated.

Answer 1

$l_1'=l_2-\frac{\frac{l_1}{k_1}+\frac{l_2}{k_2}}{\frac{1}{k_1}+\frac{1}{k_2}}=100-\frac{\frac{80}{200}+\frac{100}{300}}{\frac{1}{200}+\frac{1}{300}}=12~cm,$

$l_2'=\frac{\frac{l_1}{k_1}+\frac{l_2}{k_2}}{\frac{1}{k_1}+\frac{1}{k_2}}-l_1=\frac{\frac{80}{200}+\frac{100}{300}}{\frac{1}{200}+\frac{1}{300}}-80=8~cm.$