Your weight in a lift
Stand on a bathroom scale in a lift. See what it reads as the lift starts going up, moves steadily, starts going down, and, if the cable snapped, falls freely.
Core concept
A scale shows how hard it pushes up on you: N = m(g + a), so you seem heavier when the lift speeds up upward, lighter when it speeds up downward, and weightless in free fall
Topic: Science around us
A bathroom scale does not measure your mass: How much matter something has, measured in grams or kilograms. It is the same everywhere. All key words directly: it measures how hard it has to push up on you, then divides by 9.8 to show kilograms. Standing still, it pushes with your weight: The pull of gravity on something, measured in newtons. It is less on the Moon. All key words, mg. In a lift that is speeding up upward, the scale must push harder than your weight to speed: How far something travels in a certain time, like kilometres per hour. All key words you up too: N = m(g + a). When the lift speeds up downward, a is negative, so it pushes less and you seem lighter. Moving steadily, up or down, there is no acceleration, so the reading is normal. If the lift fell freely, a = −g and the scale would read zero: you would be weightless, just as astronauts are in orbit.
What you will learn
- Use F = ma to find the push of a scale in an accelerating lift.
- Explain why you feel heavier or lighter in a lift.
- Explain weightlessness in free fall.
Before you start
- Know Newton's second law, F = ma, and weight = mg.
Materials
- A bathroom scale (only in a lift with an adult; or just watch how you feel in a lift)
Equipment
- None
Procedure
- Record a 45 kg student as the lift starts going up.
- Record the lift moving steadily, then starting down.
- Record free fall.
How this simulation is simplified
- The lift speeds up or slows at 2 m/s²; g = 9.8 m/s².
- The scale shows its push divided by 9.8, as kilograms.