Short Answer 
The concept of torque involves calculating the product of force and distance from a pivot point to ensure balance. To achieve equilibrium, the sum of torques from both students reveals that the heavier student must move 0.2 L closer to the center, balancing the system effectively.
Step 1: Understand the Concept of Torque
Torque is defined as the product of force and distance from the pivot point. To keep an object balanced, we need to evaluate the sum of torques acting around a certain point, usually the center. The formula for calculating torque is:
- Torque (œN) = Force (F) x Distance (d)
Step 2: Calculate the Net Torque
To determine if a system is in equilibrium, we need to find the sum of torques acting on the system. Here, we compute the torques for both students, which gives us:
- Torque of heavier student: (2.5 M‚ÄöCA g)(L/2)
- Torque of lighter student: (M‚ÄöCC g)(L/2)
The sum of these torques results in 0.75 M‚ÄöCA g L, indicating the need for adjustments to achieve balance.
Step 3: Adjust Student Positions for Balance
To achieve a state of balance where the net torque equals zero, the heavier student must move closer to the center. By setting up the equation for torque balance:
- 0 = (2.5 M‚ÄöCA g)(x) – (M‚ÄöCC g)(L/2)
Solving for the distance (x) reveals that the heavier student should move 0.2 L towards the center to maintain balance. This ensures that the board remains stable and does not accelerate.