Apparent Weight: Elevators and Rides

Lesson 10 of 11 · 7 min · Free, no account needed

What you will learn

A scale measures the support force that pushes you up, not your mass. In a lift it reads N = m (g + a).
Accelerating upward makes you feel heavier; accelerating downward makes you feel lighter. Steady speed feels normal.
In free fall (a = -g) the scale reads zero: you feel weightless, but your mass and the pull of gravity are still there.

Why do you feel heavy when a lift starts up, and floaty at the top of a drop ride?
First a bet: what do the scales show as the lift starts going up?
Turn the lift's acceleration. Watch the scale.
Try speeding up upward (+) and downward (-). Try -9.8 too.
Drop tower: up 56 m, a pause, then free fall. Press Play.
The kid on the seat still stands on scales.
What a scale really measures has a name.
Apparent weight: what a scale reads. It is the support force N of the floor or seat, not your mass.
Newton's second law with up as +: N - mg = m a, so N = m (g + a). Moving up or down does not matter, only the acceleration.
g-force = N ÷ mg. Standing still: 1 g. Starting up: more than 1 g. Free fall: 0 g, you float. Simplified model: g = 9.8 m/s² and no air.
A scale in a lift recorded this. Draw how fast the lift moved.
The lift starts at rest and goes up.
Game: comfort ride. Take a lift up 20 floors in 14 s or less.
Passengers feel bad above 1.2 g and below 0.8 g. The motor tops out at 6 m/s.
Math: the scale reading is a straight line in a. Where does it hit zero?
N = 50 a + 490: slope m, shifted up by mg.
A 50 kg kid stands on scales in a lift accelerating upward at 2 m/s². What does it read, in newtons?
Your comfort ride against the express. Press Play.

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