- mylabmastering.pearson.com /?courseld=13243292#/ A cubical block of wood, 10.0 cm on a side, floats at the interface between oil and water with its lower surface 1.80 cm below the interface (Figure 1). The density of the oil is 790kg/m^3 For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Buoyancy. p=p_(interf) p-p_(a)= p-p_(a)= p-p_(a)=9 Part C What is the mass o Express your ans

Here's how to solve this buoyancy problem:<br /><br />**1. Forces Acting on the Block:**<br /><br />The block is in equilibrium, meaning the forces acting on it are balanced. These forces are:<br /><br />* **Weight (W):** Downward force due to gravity.<br />* **Buoyant Force from Oil (B_oil):** Upward force due to the displaced oil.<br />* **Buoyant Force from Water (B_water):** Upward force due to the displaced water.<br /><br />**2. Expressing the Forces:**<br /><br />* **Weight (W):** W = m * g = ρ_wood * V * g (where m is the mass of the wood, ρ_wood is the density of the wood, V is the volume of the wood, and g is the acceleration due to gravity).<br />* **Buoyant Force from Oil (B_oil):** B_oil = ρ_oil * V_oil * g (where ρ_oil is the density of the oil, and V_oil is the volume of oil displaced).<br />* **Buoyant Force from Water (B_water):** B_water = ρ_water * V_water * g (where ρ_water is the density of water (1000 kg/m³), and V_water is the volume of water displaced).<br /><br />**3. Calculating the Volumes:**<br /><br />* **Total Volume (V):** V = (0.10 m)³ = 0.001 m³ (convert cm to m)<br />* **Volume of oil displaced (V_oil):** V_oil = (0.10 m)² * (0.082 m) = 0.00082 m³ (The block is 10cm high, and 8.2cm is submerged in oil)<br />* **Volume of water displaced (V_water):** V_water = (0.10 m)² * (0.018 m) = 0.00018 m³<br /><br />**4. Setting up the Equilibrium Equation:**<br /><br />Since the block is floating, the upward buoyant forces equal the downward weight:<br /><br />W = B_oil + B_water<br /><br />ρ_wood * V * g = ρ_oil * V_oil * g + ρ_water * V_water * g<br /><br />**5. Solving for the mass of the wood (m):**<br /><br />We know W = m * g, so we can rewrite the equation and solve for m:<br /><br />m = (ρ_oil * V_oil + ρ_water * V_water)<br /><br />m = (790 kg/m³ * 0.00082 m³ + 1000 kg/m³ * 0.00018 m³)<br /><br />m = 0.6478 kg + 0.18 kg<br /><br />m = 0.8278 kg<br /><br />**Answer:**<br /><br />The mass of the wood block is approximately 0.828 kg. You should round to the appropriate number of significant figures as required by your instructor.<br />