Question: Why does a person feel heavier in an accelerating lift?

Step 1 — What is weight? True weight = gravitational force = mg (always acting downward, independent of motion).

Step 2 — What do we actually "feel"? We feel the normal force N that the floor exerts on us. This is apparent weight. A weighing scale reads N, not mg.

Step 3 — Apply Newton's Second Law to the person in the lift. Let upward be positive. Forces on person: N (up), mg (down). Net force = ma (upward, if lift accelerates up). $N - mg = ma$ $N = m(g + a) = W'$

Step 4 — Interpret the result. When a > 0 (upward), N > mg → person feels heavier than actual weight. When a < 0 (downward), N < mg → person feels lighter. When a = g (free fall), N = 0 → no floor force → weightlessness.

Step 5 — Why is this not "real" weight change? True weight mg never changes (gravitational force depends only on mass and g). Only the normal force — what the floor pushes on you — changes with acceleration. A scale in the lift measures N, not mg, which is why the reading changes.

Step 6 — Connection to spaceflight. Astronauts in orbit are NOT outside Earth's gravity (g at 400 km altitude is still ~8.7 m/$s^{2}$). They feel weightless because their spacecraft is in free fall around Earth. The "fall" and the "forward motion" combine to create an orbit — continuous free fall that never hits the ground.

Conclusion: Apparent weight = normal force = what you "feel." It changes with acceleration because Newton's Second Law requires a net force to produce acceleration. That net force is the difference between N and mg.