Question

analyze the forces acting on the crate shown in the diagram. explain why the crate will not move in the direction of the applied force ($f_{app}$).

Explanation:

1. Forces on the crate:

• Vertical forces: Gravitational force (\(F_{\text{grav}}\)) acts downward, normal force (\(F_{\text{norm}}\)) acts upward. These two are equal in magnitude and opposite in direction, so they balance (net vertical force = 0).
• Horizontal forces: Applied force (\(F_{\text{app}}\)) acts to the right, frictional force (\(F_{\text{fric}}\)) acts to the left.

1. Why no movement in \(F_{\text{app}}\) direction:

The magnitude of the frictional force (\(F_{\text{fric}}\)) is equal to the magnitude of the applied force (\(F_{\text{app}}\)) (since the crate is not moving, it’s in static equilibrium). In horizontal direction, net force \(F_{\text{net, horizontal}} = F_{\text{app}} - F_{\text{fric}} = 0\) (because \(F_{\text{app}} = F_{\text{fric}}\)). According to Newton’s first law, if net force on an object is zero, it remains at rest (or in uniform motion if already moving). Since the crate was initially at rest and net force is zero, it does not move in the direction of \(F_{\text{app}}\).

Answer:

The forces acting on the crate are: gravitational force (\(F_{\text{grav}}\), downward), normal force (\(F_{\text{norm}}\), upward), applied force (\(F_{\text{app}}\), rightward), and frictional force (\(F_{\text{fric}}\), leftward). Vertically, \(F_{\text{grav}}\) and \(F_{\text{norm}}\) balance. Horizontally, \(F_{\text{app}}\) and \(F_{\text{fric}}\) have equal magnitudes (static friction balances \(F_{\text{app}}\)), so net horizontal force is zero. By Newton’s first law, a net force of zero means the crate (initially at rest) remains at rest, so it does not move in the direction of \(F_{\text{app}}\).