Final answer:
To find the spring constant, we can use Hooke's Law, which states that the force exerted by the spring is directly proportional to the displacement of the object attached to it. In this case, the object is a wooden cube. When the wooden cube is completely submerged in water, the buoyant force is equal to the weight of the cube. The spring constant can be calculated using the formula (ρ * g * V) / x.
Step-by-step explanation:
To find the spring constant, we can use Hooke's Law, which states that the force exerted by the spring is directly proportional to the displacement of the object attached to it. In this case, the object is a wooden cube. We can use the equation:
F = kx
where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the object. When the wooden cube is completely submerged in water, the buoyant force is equal to the weight of the cube. The buoyant force can be calculated using the formula:
FB = ρ1 * g * V
where ρ1 is the density of water, g is acceleration due to gravity, and V is the volume of the cube. Since the cube is floating motionlessly, the buoyant force is equal to the force exerted by the spring:
FB = k * x
We can rearrange the equation to solve for the spring constant:
k = FB / x
Substituting the given values:
k = (ρ1 * g * V) / x
Similarly, we can find the spring constant when the cube is submerged in olive oil:
k = (ρ2 * g * V) / x
Now we can calculate the spring constant:
ρ1 = 1000 kg/m³
ρ2 = 895 kg/m³
l = 12.5 cm = 0.125 m
h1 = 25.0 cm = 0.25 m
h2 = 23.7 cm = 0.237 m
g = 9.8 m/s²
k = (ρ1 * g * V) / x = (1000 kg/m³ * 9.8 m/s² * (0.125 m)³) / (0.25 m - 0.125 m) = 2450 N/m
k = (ρ2 * g * V) / x = (895 kg/m³ * 9.8 m/s² * (0.125 m)³) / (0.25 m - 0.237 m) = 16541.5 N/m
So the spring constant is approximately 2450 N/m when the cube is submerged in water and 16541.5 N/m when the cube is submerged in olive oil.