Newton's second law states that the resultant of the forces acting on a body is equal to the product between the object mass and its acceleration:
[tex]\sum F = ma[/tex]
The cart in our problem does not move, so its accelerazion is zero, and this means that the resultant of the forces acting on it is zero.
What are these forces? We can identify 4 forces acting on the cart:
- The weight of the cart (mg), directed downward
- The force F exerted by the student to push the cart against the wall: this force is directed horizontally, toward the wall
- The normal reaction of the wall R, directed horizontally, in the opposite direction of F
- The normal reaction of the floor, Rf, that equilibrates the weight of the cart
As we said, the object does not move, so the resultant of these forces is zero. This means that the two forces on the vertical axis are equal in magnitude, as well the two forces on the horizontal axis:
[tex]mg=Rf[/tex]
[tex]F=R[/tex]
