Friction on an incline — the angle an inclined plane makes with the horizontal when a body placed on it is just about to move down the plane is called the:

Introduction / Context:At impending motion on a rough inclined plane, the balance between gravitational component down the slope and limiting friction defines a characteristic angle. This angle is central to heap stability, conveying, and slope design problems in mechanical and geotechnical engineering.

Given Data / Assumptions:

• Static friction model with coefficient μ between block and plane.
• Impending motion downward (limiting equilibrium).
• Plane angle θ with the horizontal.

Concept / Approach:

At the verge of sliding down, the component of weight along the plane balances the limiting friction: mgsin θ = μmgcos θ ⇒ tan θ = μ. The angle θ_r at which this occurs is the angle of repose. The angle of friction φ is defined by tan φ = μ; therefore θ_r = φ at impending motion.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Plot friction cone or use friction circle; impending motion occurs when resultant reaction makes an angle φ with the normal such that tan φ = μ, again implying θ_r = φ.

Why Other Options Are Wrong:

Angle of inclination is a generic geometric term. Angle of friction is a material property equal to the angle of repose only at impending motion, but the named condition asked is specifically the angle of repose.

Common Pitfalls (misconceptions, mistakes):

Confusing steady sliding (kinetic friction) with impending motion (static friction); mixing degrees and radians when computing θ from μ.

Final Answer:

angle of repose