1. **Stating the problem:** We have a hanging mass $m_2$ with forces acting on it: gravity downward and tension upward. The equation given is $$m_2 g - T = m_2 a$$. The question is why the terms $m_2 g$ and $m_2 a$ appear in this equation and what tension $T$ represents. 2. **Understanding the forces:** Gravity exerts a downward force on the mass equal to its weight, which is $$m_2 g$$ where $g=9.8$ m/s$^2$ is acceleration due to gravity. 3. **Newton's Second Law:** The net force on the mass causes it to accelerate. According to Newton's second law, $$F_{net} = m a$$, where $F_{net}$ is the net force, $m$ is the mass, and $a$ is the acceleration. 4. **Writing the forces:** The forces acting on $m_2$ are: - Downward force: gravity $m_2 g$ - Upward force: tension $T$ 5. **Net force direction:** Taking downward as positive (since gravity acts downward), the net force is: $$F_{net} = m_2 g - T$$ 6. **Applying Newton's second law:** The net force equals mass times acceleration: $$m_2 g - T = m_2 a$$ 7. **Why $m_2 g$ and $m_2 a$ appear:** - $m_2 g$ is the weight (force due to gravity) pulling the mass down. - $m_2 a$ is the product of mass and acceleration, representing the net force causing the mass to accelerate. 8. **What is tension $T$?:** Tension is the upward force exerted by the string or rope holding the mass, opposing gravity. **Summary:** The equation balances the downward gravitational force and the upward tension to produce the net force that accelerates the mass. Final answer: The terms $m_2 g$ and $m_2 a$ represent the weight and the net force (mass times acceleration) respectively, while $T$ is the tension force opposing gravity.