A 2kg box sits at rest on a level floor. Two children push on the box at the same time. Eli pushes horizontally to the right on the box with a force of 4N. Jamie pushes straight downward on the box with a force of 3N. The box does not move (there is friction between the box and the floor). What is the magnitude of the upward force of the floor on the box?

If needed, g=10ms2

To find the magnitude of the upward force of the floor on the box, we need to consider the forces acting on the box.

First, let's determine the net horizontal force acting on the box. Eli pushes horizontally to the right with a force of 4N. Since the box does not move horizontally, there must be an equal and opposite force acting in the opposite direction. This force is the force of static friction, which prevents the box from sliding. So, the force of static friction must also be 4N.

Next, let's consider the vertical forces acting on the box. Jamie pushes straight downward with a force of 3N. Since the box is at rest and not accelerating vertically, the sum of the vertical forces must be zero. The weight of the box, given by its mass (2kg) multiplied by the acceleration due to gravity (g=10m/s²), is given by:

Weight = mass × acceleration due to gravity
Weight = 2kg × 10m/s²
Weight = 20N

Since the sum of the vertical forces is zero, the normal force exerted by the floor upward must be equal in magnitude and opposite in direction to the weight of the box. Therefore, the magnitude of the upward force of the floor on the box is 20N.