Answer :
Final answer:
To find the elongation change of the spring, the gravitational force on the wooden block is calculated and then the buoyant force is subtracted to find the net force. Hooke's Law is then used to solve for the elongation change, resulting in an answer of 0.095 cm. So, the best option is c, 0.095 cm.
Explanation:
The student is asking about the elongation change (ΔL) in a light spring when a wooden block is attached and the system reaches static equilibrium in the water.
To solve this, we'll use Hooke's Law and the buoyant force concept.
The spring constant (k) is given as 176 N/m, and the block's weight in the water is the difference between the gravitational force and the buoyant force acting on the block.
The gravitational force (Fg) is mass (m) times the acceleration due to gravity (g), Fg = m * g = 4.73 kg * 9.81 m/s².
The buoyant force (Fb) is the weight of the displaced water, which can be found using the block's density (ρ) and volume (V), as Fb = ρ * V * g.
To find the volume of the wood block, we use its mass and density, V = m / ρ. Once we have the volume, we can find the buoyant force. The net force (Fnet) on the spring is then Fg - Fb, which equals the spring force (Fs) at equilibrium. According to Hooke's Law, Fs = k * ΔL. We can now set Fnet to Fs and solve for ΔL.
When we calculate these values and solve for ΔL, we find that the correct elongation change in the spring is option c) 0.095 cm.
So, the best option is c, 0.095 cm.
