Exifessignent 18 of 24 Concepts completed Multiple Choice Question A particie moves from point \( A_{1} \) to \( A_{2} \). Identify the correct equation for the principle of conservation of energy. The kinetic energy is given by the symbol \( T \), the gravitational potential energy is given by the symbol \( V_{g} \) and the elastic potential energy is given by the symbol \( V_{e} \) \( T_{1}+V_{\mathrm{g} 1}+V_{e f}=T_{2}+V_{g 2}+V_{e 2} \) \( \frac{T V_{i n}}{V_{21}}=\frac{T_{i} v_{i z}}{V_{2}} \) \( T_{1}-V_{g_{1}}-V_{e t}=T_{2}-V_{g_{2}}-V_{e 2} \) \( T_{1} V_{51} V_{e t}=T_{2} V_{s 2} V_{e 2} \)

To identify the correct equation for the principle of conservation of energy, we need to understand the concept itself. The principle of conservation of energy states that the total energy in a closed system remains constant. This means that the sum of kinetic energy, gravitational potential energy, and elastic potential energy at one point must equal the sum of these energies at another point. Let's analyze the given options: 1. **Option 1:** \[ T_{1} + V_{g1} + V_{e f} = T_{2} + V_{g2} + V_{e2} \] This equation states that the total energy (kinetic + gravitational potential + elastic potential) at point \( A_1 \) is equal to the total energy at point \( A_2 \). This aligns with the principle of conservation of energy. 2. **Option 2:** \[ \frac{T V_{in}}{V_{21}} = \frac{T_{i} v_{iz}}{V_{2}} \] This equation does not represent the conservation of energy. It seems to involve ratios that do not correspond to energy conservation. 3. **Option 3:** \[ T_{1} - V_{g1} - V_{et} = T_{2} - V_{g2} - V_{e2} \] This equation suggests a difference rather than a conservation. It does not correctly represent the total energy conservation. 4. **Option 4:** \[ T_{1} V_{51} V_{et} = T_{2} V_{s2} V_{e2} \] This equation also does not represent the conservation of energy. It seems to imply a product of energies rather than a sum. Based on this analysis, the correct equation for the principle of conservation of energy is: **Option 1:** \[ T_{1} + V_{g1} + V_{e f} = T_{2} + V_{g2} + V_{e2} \]