On the diagram, two blocks of equal mass are connected by an ideal string. The values of m = 1 kg and k 2 = 100 N / m are given. Initially, both springs are relaxed. Then the left block is slowly pu

Question

On the diagram, two blocks of equal mass are connected by an ideal string. The values of m = 1 kg and k 2 ​ = 100 N / m are given. Initially, both springs are relaxed. Then the left block is slowly pulled down a distance 0.1 m and released. Find maximum possible value of k 1 ​ (in N/m) for which both the blocks will have same magnitude of acceleration just after releasing. Both spring have natural length of 2 m.

TestHub · Accepted Answer

Just after release, for the left block (moving up): $T + k_{1} x - m g = ma$

For the right block (moving down): $k_{2} x + m g - T = ma$

Subtracting: $T = m g - \frac{( k _{1} - k _{2} ) x}{2}$

The string stays taut only while $T \geq 0$ ; at the maximum $k_{1}$ , $T = 0$

$m g = \frac{( k _{1} - k _{2} ) x}{2}$ gives $10 = \frac{( k _{1} - 100 ) \times 0.1}{2}$

$k_{1} = 300$ N/m

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