Friction and inclined planes – naming the critical angle The angle of the plane (with horizontal) at which a body just begins to slide down the rough incline is called:

Introduction / Context:On a rough inclined plane, a stationary block will begin to move down only when the component of its weight parallel to the plane exceeds the limiting friction. The inclination that just triggers motion has a standard name in engineering mechanics.

Given Data / Assumptions:

• Rigid block on a homogeneous rough plane.
• Static friction characterized by coefficient μ_s; limiting friction F_max = μ_s N.
• Angle θ measured from horizontal (conventional). The identity is independent of mass.

Concept / Approach:At impending motion: W sin θ = μ_s W cos θ. Rearranging gives tan θ = μ_s. The angle θ at this onset is called the angle of repose. The angle of friction φ is related by tan φ = μ_s and satisfies φ = θ at limiting equilibrium; terminology differs depending on whether we speak about the plane or the friction pair.

Step-by-Step Solution:

Verification / Alternative check:Experimentally, measure μ_s on a horizontal plane by pulling until slip; convert to φ via tan φ = μ_s. Tilting the plane to the same φ reproduces impending motion—confirming θ = angle of repose.

Why Other Options Are Wrong:

• angle of friction: refers to friction pair property; while numerically equal at onset, the conventional name for plane inclination is “angle of repose”.
• angle of projection: belongs to projectile motion, unrelated.
• angle of drawbar pull: not a standard mechanics term here.

Common Pitfalls:Using the two terms interchangeably without context; examiners often expect “angle of repose” for the plane’s inclination.

Final Answer:angle of repose