Elevator physics – apparent pressure while accelerating upward When a lift (elevator) moves upward with constant upward acceleration a, the pressure/normal force a person exerts on the floor is _____ proportional to a.

Introduction / Context:
The “heavier” feeling in an accelerating elevator is a classic application of Newton’s second law. The scale reading (or floor reaction) is often called the apparent weight or pressure. This item asks how that reaction varies with upward acceleration.

Given Data / Assumptions:

• Person of mass m standing on the elevator floor.
• Elevator accelerates upward with acceleration a (constant).
• g is gravitational acceleration; neglect air drag and other forces.

Concept / Approach:
Apply Newton’s second law in the vertical direction. Take upward as positive. The floor exerts a normal force N on the person; weight acts downward.

Step-by-Step Solution:

Verification / Alternative check:
A spring scale between the feet and the floor would read N; as a increases, the spring compresses more, confirming the direct proportionality.

Why Other Options Are Wrong:

• inversely: would imply N decreases when a increases, contrary to N = m(g + a).
• independent of a: true only for a = 0 (constant velocity).
• quadratically: there is no a^2 term in the linear relation.

Common Pitfalls:
Mixing up the sign convention or interpreting “pressure” as atmospheric pressure rather than the normal reaction per unit area. Here “pressure” corresponds to the contact force effect.

Final Answer:
directly