Let's solve each part step by step: --- ### **A. Symbolic Equation Relating Mass and Density** **Equation:** The mass (\(m\)) of an object is related to its density (\(\rho\)) and its volume (\(V\)) by: \[ m = \rho V \] **Additional Quantities:** - **Density (\(\rho\))**: The mass per unit volume of a substance. - **Volume (\(V\))**: The amount of space the object occupies. **Assumptions:** - The object is made of a uniform material, so its density is constant throughout. - The object is solid (not hollow or porous in a way that changes its average density). --- ### **B. Mass of Three Objects Made of the Same Wood** Choose three objects (let's call them A, B, and C), each with a different volume \(V_A\), \(V_B\), and \(V_C\). **Equation for Each:** \[ m_A = \rho V_A \\ m_B = \rho V_B \\ m_C = \rho V_C \] Given: \(\rho = 700 \text{ kg/m}^3\) Suppose the volumes are as follows (these are example values, you should use the actual volumes if given in your figure): - \(V_A = 0.001 \, \text{m}^3\) - \(V_B = 0.0015 \, \text{m}^3\) - \(V_C = 0.002 \, \text{m}^3\) **Numerical Values:** \[ m_A = 700 \times 0.001 = 0.7 \text{ kg} \] \[ m_B = 700 \times 0.0015 = 1.05 \text{ kg} \] \[ m_C = 700 \times 0.002 = 1.4 \text{ kg} \] **Make sense?** Yes; more volume means more mass, for the same material. --- ### **C. Total Mass of the System** **Equation for Total Mass:** \[ m_{\text{total}} = m_A + m_B + m_C = \rho V_A + \rho V_B + \rho V_C = \rho (V_A + V_B + V_C) \] **Numerical Value:** \[ m_{\text{total}} = 700 \times (0.001 + 0.0015 + 0.002) = 700 \times 0.0045 = 3.15 \text{ kg} \] --- #### **Why Might the Equation in Part A be Incorrect for the System?** - The equation \(m = \rho V\) assumes **one object** with a **uniform density**. - For a system of objects **with different densities** or materials, you cannot simply use \(m_{\text{total}} = \rho_{\text{system}} V_{\text{system}}\), unless all parts have the same density. - If you have a system with different materials/densities, you must sum the masses of each part: \[ m_{\text{total}} = \sum_i \rho_i V_i \] **Other systems where it's incorrect:** - Mixtures of materials (wood and metal) - Objects with hollow spaces or different densities --- ### **Order of Objects by Increasing Mass** Given the example volumes above, the objects in order of increasing mass: - \(V_A\) (0.001 m³, 0.7 kg) - \(V_B\) (0.0015 m³, 1.05 kg) - \(V_C\) (0.002 m³, 1.4 kg) So, **left to right: A, B, C**. --- ## **Summary Table** | Object | Volume (m³) | Mass (kg) | |--------|-------------|-----------| | A | 0.001 | 0.7 | | B | 0.0015 | 1.05 | | C | 0.002 | 1.4 | --- **Final Answers:** - Symbolic equation: \(m = \rho V\) - Masses: \(m_A = 0.7\) kg, \(m_B = 1.05\) kg, \(m_C = 1.4\) kg - Total mass: \(3.15\) kg - Equation is incorrect for multiple objects with different densities/materials. - Order: A, B, C (increasing mass) Let me know if you have the actual volumes, and I can update the calculations!