Why did the normal force not enter into your solution?

Have you ever played a prank on someone, where they stand on a scale and you are behind them, and stealthily putting your foot on the scale to make them seem heavier? You're adding an extra force, in addition to the person's weight to the scale, and the scale responds by pushing back with the same force. This pushing back force is called the normal force, or contact force. Normal forces don't exist unless objects are touching and are always perpendicular to the surface(s). There is no general equation to calculate the normal force but there is a method to calculate the normal force.