A raft is constructed of wood having a density of 6.00x102 kg/m3. Its surface area is 5.40 m2 and its volume is 0.45 m3. When the raft is placed in fresh water, to what depth h is the raft submerged by its weight? The density of fresh water is 1000 kg/m3.

Hint: Use Newton’s second to sum the forces (Buoyancy and weight) that are in equilibrium.

To determine the depth to which the raft is submerged, we need to calculate the buoyant force acting on the raft and then equate it to the weight of the raft.

First, let's calculate the weight of the raft. The weight (W) of an object is given by the formula: W = m*g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).

The mass (m) of the raft can be found using its volume (V) and density (ρ), using the formula: m = V*ρ. In this case, the volume is given as 0.45 m^3 and the density is given as 6.00x10^2 kg/m^3. Therefore, the mass of the raft is: m = (0.45 m^3)*(6.00x10^2 kg/m^3) = 270 kg.

Next, let's calculate the buoyant force (FB) acting on the raft. The buoyant force is equal to the weight of the fluid displaced by the object, and can be calculated using the formula: FB = ρw*g*V, where ρw is the density of the fluid and V is the volume of the displaced fluid.

In this case, the density of fresh water is given as 1000 kg/m^3 and the volume of the raft is given as 0.45 m^3. Therefore, the buoyant force acting on the raft is: FB = (1000 kg/m^3)*(9.8 m/s^2)*(0.45 m^3) = 4410 N.

Since the raft is in equilibrium, the weight of the raft (W) is equal to the buoyant force (FB). Therefore, equating the two forces, we have: W = FB. Substituting the values we calculated, we get: 270 kg * 9.8 m/s^2 = 4410 N.

Now, let's solve for the depth (h) to which the raft is submerged. The pressure exerted by the fluid is given by the equation: P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.

We can rearrange the equation to solve for h: h = (W / (A*ρw*g)), where W is the weight of the raft, A is the surface area of the raft, and ρw and g are the density of the fluid and acceleration due to gravity, respectively.

Substituting the values we calculated, we have: h = (4410 N / (5.40 m^2 * 1000 kg/m^3 * 9.8 m/s^2)). Simplifying this expression, we find that the depth (h) to which the raft is submerged is approximately 0.079 m or 7.9 cm.

Therefore, the raft is submerged to a depth of approximately 7.9 cm when placed in fresh water.