Final answer:
The force constant of the spring is calculated using Hooke's Law, and after converting displacement to meters and calculating the weight of the mass, it is determined to be approximately 2074 N/m, with the closest given option being 2200 N/m.
Step-by-step explanation:
To calculate the force constant of the spring when a 9.09 kg mass compresses it by 4.30 cm, we can use Hooke's Law, which states that the force exerted by a spring is equal to the negative product of the displacement and the spring's force constant (F = -kx). The negative sign indicates that the force exerted by the spring is opposite in direction to the displacement.
First, we convert the displacement from centimeters to meters: 4.30 cm = 0.0430 m. We know that the force exerted by the spring must balance the weight of the mass. The weight of the mass (W) can be found by multiplying the mass (m) by the acceleration due to gravity (g): W = m * g. Assuming g = 9.81 m/s2, the weight of the mass is W = 9.09 kg * 9.81 m/s2 = 89.2 N.
Thus, F = kx becomes 89.2 N = k * 0.0430 m, solving for k gives us k = 89.2 N / 0.0430 m, which results in a spring force constant k ≈ 2074 N/m.
The closest answer from the given options is (b) 2200 N/m.