Question

which diagram best represents the forces acting on the box resting on the small hill? ($f_f$ = frictional force, $f_n$ = normal force, and $f_w$ = weight, $f_a$ = applied force)

a (2)
b (4)
c (1)

Explanation:

To determine the correct force diagram for the box on the incline (small hill):

1. Normal Force (\(F_N\)): Acts perpendicular to the incline's surface (not vertical, as the incline is sloped).
2. Weight (\(F_W\)): Acts vertically downward (gravity).
3. Frictional Force (\(F_f\)): Acts parallel to the incline, opposing the box’s tendency to slide (up or down; here, if there’s an applied force, friction opposes it).
4. Applied Force (\(F_a\)): Acts along the incline (as per the diagram’s context, likely parallel to the slope).

Analyzing the options:

• Option (4): \(F_N\) is perpendicular to the incline, \(F_f\) is parallel (opposing \(F_a\)), \(F_W\) is vertical, and \(F_a\) is along the incline. This matches the force directions: \(F_N\) (perpendicular to surface), \(F_f\) (parallel, opposing \(F_a\)), \(F_W\) (vertical down), and \(F_a\) (along incline).

Other options fail:

• (1): \(F_N\) is not perpendicular to the incline.
• (2): \(F_f\) direction is incorrect (should oppose \(F_a\), not align with it).
• (3): \(F_N\) is vertical (incorrect for an incline).

Answer:

b. (4)