Friction at contacts — ladder on rough ground and smooth wall A ladder rests on rough ground and leans against a perfectly smooth vertical wall. How does the frictional force act at the upper contact with the wall?

Introduction / Context:
Contact friction depends on the nature of the surfaces. A smooth wall implies no tangential resistance, which is a standard assumption in ladder equilibrium problems in engineering statics.

Given Data / Assumptions:

• Ground is rough (can provide friction).
• Wall is perfectly smooth (frictionless).
• Ladder is in static equilibrium.

Concept / Approach:
At a smooth contact, only the normal reaction can act; there is no frictional component along the surface. Therefore, at the upper end (ladder–wall contact), friction is zero and the reaction is purely normal, i.e., horizontal, directed from the wall to the ladder.

Step-by-Step Solution:

Verification / Alternative check:
Consider a limiting case: if both wall and ground were smooth, the ladder could not be in equilibrium unless special geometry or external support existed, highlighting the role of ground friction alone in the given setup.

Why Other Options Are Wrong:

• Downward/Upward at the upper end: These imply nonzero wall friction, contradicting the smooth-wall assumption.
• Perpendicular to the wall at the upper end: That describes the wall’s normal reaction, not friction.
• Horizontal toward the wall: Again, this is the normal reaction direction, not friction.

Common Pitfalls:
Confusing normal reaction with friction; forgetting that a smooth surface cannot transmit tangential force.

Final Answer:
Zero at the upper end