Ladder Equilibrium — Direction of Friction at the Wall A ladder rests on smooth ground and leans against a rough vertical wall. At the upper end (wall contact), the direction of the frictional force will be:

Introduction / Context: Ladder problems test understanding of friction directions. When one contact is smooth (no friction) and the other is rough (with friction), the frictional force must oppose the impending motion at the rough contact surface.

Given Data / Assumptions:

• Ground is smooth ⇒ no friction at the foot; reaction at ground is normal (vertical).
• Wall is rough ⇒ friction is available along the wall at the top contact.
• Ladder tends to slip due to its weight acting through its center of gravity.

Concept / Approach: With no horizontal reaction at the smooth ground, the wall must supply the horizontal reaction. The ladder’s upper end tends to slide downward along the wall under weight and geometry. Friction acts opposite to the direction of relative motion (or impending motion) along the surface of contact; hence it must act upward along the wall at the upper end to resist sliding down.

Step-by-Step Reasoning:

Verification / Alternative check: Remove friction at wall hypothetically: the upper end would certainly slide downward. Thus actual friction must be upward to prevent that motion.

Why Other Options Are Wrong: “Towards/away from the wall” describe horizontal directions, but friction acts tangential to the wall (vertical). “Downward” would aid the slip, not oppose it.

Common Pitfalls: Reversing friction direction; assuming friction acts at the smooth contact, which it does not.

Final Answer: Upward at the upper end.