The bar on top of the plank serves as a point of contact for the variable force to act upon. It allows for the force to be applied at a specific location and direction.
The surface is described as frictionless because it eliminates the effects of friction, allowing for a more simplified analysis of the system. This assumption is often used in theoretical physics problems to focus on the main principles without the added complexity of friction.
The variable force acts as an external force on the system, causing both the bar and plank to accelerate in the direction of the force. The magnitude and direction of the acceleration will depend on the strength and direction of the variable force.
The use of a plank allows for a more realistic scenario, as most objects in the real world are not perfectly rigid. The plank will experience some amount of deflection due to the applied force, which can affect the overall motion of the system.
The concept of energy conservation applies to the system because the total energy of the system (kinetic and potential) remains constant as long as no external forces, such as friction, are present. This allows for the prediction of the final velocity of the bar and plank based on the initial conditions and the applied force.