Short Answer 
The solution outlines three steps to determine the minimum force needed to move a board from under a box on a frictionless surface. First, it defines the masses involved, then establishes the forces with equations related to friction, and finally calculates the minimum force using the total mass and derived acceleration.
Step 1: Define the Parameters
Begin by clearly defining the parameters important to the problem. Here, we have two masses:
- Mass of the box: denoted as m‚ÄöCA
- Mass of the board: denoted as m‚ÄöCC
Next, establish that the situation is on a frictionless surface where a frictional force (Fr) exists between the box and the board.
Step 2: Establish the Forces
From our understanding of forces, we need to set up equations based on the frictional force acting on the box:
- First, we describe Fr as m‚ÄöCAa (Equation 1).
- Then, considering the force between the box and the board, we express Fr as Œºsm‚CAg (Equation 2).
By equating these two expressions, we derive the acceleration of the system as a = μsg.
Step 3: Calculate the Minimum Force
To find the minimum force (Fmin) that must be applied to the board, we use the total mass of the box and the board multiplied by the acceleration:
- Using the formula, we find Fmin = (m‚ÄöCA + m‚ÄöCC)a.
- Substituting the acceleration (a = Œºsg) into the equation gives Fmin = (m‚CA + m‚CC)Œºsg.
This result provides the force required to pull the board out from under the box. Cheers, I hope this helps!