9.A raft of wood of mass  120kg floats in water. The weight that can be put on the raft to make it just sink should be  (ρraft   =  600kg/m3)

To solve this problem, we need to use the principle of buoyancy, which states that the buoyant force (the force that keeps the raft afloat) is equal to the weight of the water displaced by the raft.

Step 1: Calculate the volume of the raft We know the mass (m) of the raft is 120 kg and the density (ρ) of the raft is 600 kg/m^3. We can use the formula for density, which is ρ = m/V, where V is the volume. Rearranging for V gives us V = m/ρ. Substituting the given values gives us V = 120 kg / 600 kg/m^3 = 0.2 m^3. So, the volume of the raft is 0.2 cubic meters.

Step 2: Calculate the weight of the water displaced by the raft The weight of the water displaced by the raft is equal to the buoyant force, which is also equal to the weight of the raft plus the additional weight that can be put on it before it sinks. The weight of an object is its mass times the acceleration due to gravity (g), which is approximately 9.8 m/s^2. The density of water (ρ_water) is 1000 kg/m^3. So, the mass of the water displaced by the raft is its volume times the density of water, or m_water = V * ρ_water = 0.2 m^3 * 1000 kg/m^3 = 200 kg. Therefore, the weight of the water displaced by the raft is m_water * g = 200 kg * 9.8 m/s^2 = 1960 N.

Step 3: Calculate the additional weight that can be put on the raft The weight of the raft is m_raft * g = 120 kg * 9.8 m/s^2 = 1176 N. Therefore, the additional weight that can be put on the raft before it sinks is the weight of the water displaced by the raft minus the weight of the raft, or 1960 N - 1176 N = 784 N.

So, the additional weight that can be put on the raft to make it just sink is 784 N.