Let's solve **Question 4** (Atwood Machine): Given: - \( m_1 = .240\, \text{kg} \) - \( m_2 = .352\, \text{kg} \) We are to find the **acceleration** of the blocks (\( a \)). --- ## **Step 1: Write the Equation for Acceleration** The acceleration for an Atwood machine is given by: \[ a = \frac{(m_2 - m_1)g}{m_1 + m_2} \] where \( g = 9.8\, \text{m/s}^2 \). **Explanation:** We subtract \( m_1 \) from \( m_2 \) because the heavier mass will accelerate downward, and the lighter mass will accelerate upward. The total mass in the denominator accounts for the inertia of both blocks. --- ## **Step 2: Plug in the Values and Solve** \[ a = \frac{(.352\, \text{kg} - .240\, \text{kg}) \times 9.8\, \text{m/s}^2}{.240\, \text{kg} + .352\, \text{kg}} \] \[ a = \frac{(.112)\times 9.8}{.592} \] \[ a = \frac{1.0976}{.592} \] \[ a \approx 1.85\, \text{m/s}^2 \] **Explanation:** Substitute the values for each mass and gravitational acceleration, do the arithmetic, and simplify to get the acceleration. --- ## **Final Answer** \[ \boxed{1.85 \, \text{m/s}^2} \]

# Atwood Machine Problem Solution ## **Question 4** Given: - \( m_1 = 0.240\, \text{kg} \) - \( m_2 = 0.352\, \text{kg} \) We need to determine the **acceleration** of the blocks (\( a \)). --- ## **Step 1: Write the Equation for Acceleration** The formula for acceleration in an Atwood machine is: \[ a = \frac{(m_2 - m_1)g}{m_1 + m_2} \] where \( g = 9.8\, \text{m/s}^2 \). ### **Explanation:** We use this formula because it accounts for the difference in mass between the two blocks. The heavier block (\( m_2 \)) will accelerate downward, while the lighter block (\( m_1 \)) will accelerate upward. The denominator represents the total mass that contributes to the acceleration. --- ## **Step 2: Plug in the Values and Solve** Substituting the values into the equation: \[ a = \frac{(0.352\, \text{kg} - 0.240\, \text{kg}) \times 9.8\, \text{m/s}^2}{0.240\, \text{kg} + 0.352\, \text{kg}} \] \[ a = \frac{(0.112\, \text{kg}) \times 9.8\, \text{m/s}^2}{0.592\, \text{kg}} \] \[ a = \frac{1.0976\, \text{kg m/s}^2}{0.592\, \text{kg}} \] \[ a \approx 1.85\, \text{m/s}^2 \] ### **Explanation:** We first compute the difference in mass, multiply by gravitational acceleration, and then divide by the total mass. The result gives us the magnitude of acceleration of the system. --- ## **Final Answer** \[ \boxed{1.85\, \text{m/s}^2} \]