Final answer:
The formula when an additional downward force is applied to an object at rest on a flat surface is N = w + F, where N represents the normal force, w is the weight (mass times gravity), and F is the additional force.
Step-by-step explanation:
When an object with mass m is sitting on a flat surface, the normal force N is equal and opposite to the gravitational force, often referred to as the object's weight w, which is calculated as m × g, where g is the acceleration due to gravity. If an additional force is applied downward on the object, this force F adds to the weight to increase the normal force exerted by the surface: N = w + F.
When considering the forces acting on an object at rest or moving at a constant velocity on a flat surface, you use Newton's second law Fnet = m × a, where Fnet is the net force, m is the mass of the object, and a is the acceleration, which in this case of no motion, is zero.
Therefore, the formula that applies when an additional force is being applied down on an object at rest on a flat surface is N = w + F, where N is the normal force, w is the weight of the object, and F is the additional downward force.