Let's focus on **step 6**: *Determine the required torque to be applied on link #2*. We'll do this in **2 steps** as requested, with explanations at each step. --- ## **Step 1: Calculate the Required Force and Acceleration Quantities** ### **Given Data** - \( r_{O_2B} = 6.\, \text{cm} = .06\, \text{m} \) - \( \dot{\theta}_2 = 12.\, \text{rad/s} \) (CW, constant) - \( m_5 = 50.\, \text{g} = .05\, \text{kg} \) - \( I_{G_5} = 6.5 \times 10^{-5}\, \text{kg} \cdot \text{m}^2 \) - \( \vec{a}_{G_5} = 690\, \text{cm/s}^2 = 6.9\, \text{m/s}^2 \) at \( 318^\circ \) - \( \ddot{\theta}_5 = 108\, \text{rad/s}^2 \) (CW) ### **Explanation:** We need to find the torque required on link #2 to drive the system, taking into account the dynamic forces on link #5 (the slider). #### **Dynamic Equation for Link 5:** \[ \sum M_{O_2} = I_{G_5} \ddot{\theta}_5 + m_5 \cdot r_{G_5} \cdot a_{G_5} \] But since link #5 is a slider, the term for angular acceleration applies only if there's rotation, otherwise focus on linear force required to accelerate the slider. --- ## **Step 2: Compute the Torque on Link #2** ### **A. Compute Force Required to Accelerate the Slider (Link 5)** \[ F = m_5 \cdot a_{G_5} = .05\, \text{kg} \times 6.9\, \text{m/s}^2 = .345\, \text{N} \] This force must be generated by the mechanism, originating from the torque applied to link #2. ### **B. Determine the Torque about \( O_2 \)** Assume the force acts at a distance (moment arm) equal to \( r_{O_2B} \): \[ \tau_{O_2} = F \times r_{O_2B} = .345\, \text{N} \times .06\, \text{m} = .0207\, \text{N}\cdot\text{m} \] ### **Explanation:** - The required torque is the product of the force needed to accelerate the slider and the radius (moment arm) of link #2. - This is a simplified calculation; for more accuracy, you'd need to consider the direction of the force, the exact mechanism geometry, and possibly the effect of angular acceleration if the slider rotates. --- ## **Final Answer** \[ \boxed{\tau_{O_2} = .021\, \text{N}\cdot\text{m}} \] (Rounded to three decimal places) --- ### **Summary of Steps:** 1. **Calculated the required force for the slider using mass and acceleration.** 2. **Multiplied this force by the radius of link #2 to get the required torque.** Let me know if you want to see the detailed force polygon construction or further dynamic analysis!