Part A
A person holds up a 10 kg box by applying a perfectly horizontal force of 300 N to press it against a rough wall. What is the magnitude of the normal force exerted on the box by the wall?
System: Box as point particle subject to external influences from the earth (gravity), the wall (normal force and friction) and the person (applied force).
Model: Point Particle Dynamics.
Approach: We begin with a free body diagram for the box:
It is important to note that any surface has the potential to exert a normal force and that the normal is always perpendicular to the plane of the surface. If the wall did not exert a normal force, the box would simply pass through it.
From the free body diagram, we can write the equations of Newton's 2nd Law.
\begin
[\sum F_
= F_
- N = ma_
]
[ \sum F_
= F_
- mg = ma_
]\end
Because the box is held at rest, it has no acceleration at all (ax = ay = 0). Setting ax = 0 in the x direction equation gives:
\begin
[ N = F_
= \mbox
]\end