Final answer:
The spring constant of the relaxed vertical spring is 24.5 N/m.
Step-by-step explanation:
To determine the spring constant, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The equation for Hooke's law is F = kx, where F is the force, k is the spring constant, and x is the displacement.
In this case, the block is dropped onto the relaxed vertical spring, so the displacement is the distance the spring compresses. The weight of the block is given by the equation mg, where m is the mass of the block and g is the acceleration due to gravity. We can equate the weight of the block to the force exerted by the spring to find the spring constant:
mg = kx
Plugging in the given values, we have:
0.3 kg * 9.8 m/s² = k * 0.12 m
Simplifying this equation gives us the spring constant:
k = (0.3 kg * 9.8 m/s²) / 0.12 m = 24.5 N/m