Elevator dynamics — how does the cable tension compare with the weight when a lift (elevator) is moving?

Introduction / Context:
The apparent tension in an elevator cable depends on the elevator’s acceleration. Understanding this relation helps in sizing hoists and in interpreting load-sensor readings and safety-brake triggers.

Given Data / Assumptions:

• Elevator car mass m, weight W = mg.
• Upward acceleration a > 0 when speeding up upward or slowing down downward; downward acceleration a > 0 when speeding up downward or slowing down upward.
• Neglect cable mass and friction for the basic relation.

Concept / Approach:

Apply Newton’s second law along the vertical. For upward acceleration: T − W = ma ⇒ T = W + ma > W. For downward acceleration: W − T = ma ⇒ T = W − m*a < W. Thus, tension increases above weight when accelerating upward and decreases below weight when accelerating downward.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Elevator scale thought experiment: a person’s apparent weight is lower when the car accelerates downward and higher when it accelerates upward, mirroring cable tension behavior.

Why Other Options Are Wrong:

Options claiming constant tension ignore acceleration. Saying “more when moving downwards” reverses the sign. “Less when moving upwards” contradicts Newton’s law for upward acceleration.

Common Pitfalls (misconceptions, mistakes):

Confusing direction of motion with direction of acceleration (e.g., moving up while slowing down implies downward acceleration and reduced tension).

Final Answer:

it is less when the lift is moving downwards