If I add a downward force in addition to the force of gravity, does this affect my normal force as well?
Example: A book on a table has a mass of 35 kg, and the Force of gravity is 343 N [down]. But then I apply a vertical force of 25 N [down]. What does my normal force become?
The normal force is the mass times the force of gravity, N = mg, which would be 343 Newtons of force the book is generating on the table. The table is generating an upwards force of 343 Newtons as well, supported by the floor which is what the normal force is, the force that keeps the book from going through the table and continuing its acceleration to the floor. If you add 25 Newtons of force to what is already there, it would be simple addition, providing, of course, the table is strong enough to counteract the additional 25 Newtons of force. So 343 Newtons plus 25 additional Newtons would be 368 Newtons of normal force generated by the table, pushing against the 368 Newtons of downward force generated by the book and your additional push. Force is a physics component that is a result of Newtons 2nd law of motion, that the force generated by an object is the result of its mass times its acceleration.