Final answer:
The correct equivalent spring constant for the combined system of two springs in series and three springs in parallel, all with spring constant K, is 3K/7, not 7K/2.
Step-by-step explanation:
To determine the equivalent spring constant Keq for a configuration of springs, you need to consider the arrangement of the springs.
For springs in series, the equivalent spring constant is found using the formula 1/Keq = 1/K1 + 1/K2, and for springs in parallel, it is the sum of their spring constants, Keq = K1 + K2 + K3.
Given that all springs have the same spring constant K, for two springs in series, the equivalent spring constant would be K/2. For three springs in parallel, the equivalent spring constant would be 3K.
When combining these systems, where you have two springs in series (at Keq = K/2) attached to three springs in parallel (at Keq = 3K), you treat the series combination as one spring and add it to the parallel combination.
The overall equivalent spring constant would be 1/Keq_series + 1/Keq_parallel = 2/K + 1/3K, which simplifies to Keq = 3K/7.
Therefore, the answer 7k/2 is not correct; the correct overall equivalent spring constant should be 3K/7.