A 6 kg box placed on a flat surface. what is the weight of the box in newtons? what is the normal force acting on the box?

The weight of an object is equal to its mass times the acceleration due to gravity (abbreviated as 'g'). So:


W = mg


Since 1 Newton = 1 Kg-m/s^2, it's straight-forward multiplication of the mass in units of kilograms times 'g' in units of meters per second squared.

The normal force acting on the box must be precisley equal to the force of gravity. That way the sum of all forces acting on the box (gravity plus the table's normal force) cancel out. From F = ma you know that if the sum of forces is zero then the acceleration of the box is zero, and it remains stationary still on the table.