Daily Archives: 11th October

Heavier going up, lighter coming down

If you’ve every felt a little bit heavier in a lift going up, or a little bit lighter in a lift coming down, you’re not imagining it.

Imagine standing on a set of scales in a lift. The Earth pulls you down onto the scales and the scales push back on you with an equal force – that’s the force that the scales read.

Einstein’s equivalence principle, part of the framework of general relativity, is that it is impossible to tell the difference between acceleration due to gravity and acceleration due to an external force*. If the lift is accelerating upwards this must be because a force is exerted upon the lift in an upward direction and as this is in addition to the force of the scales pushing upward, you feel heavier.

Some of the world’s fastest elevators, those found in the Taipei 101, go from stationary to 60 km/h in sixteen seconds, which means they accelerate at 1.05 m/s². When this is added to the acceleration due to gravity (9.81 m/s²) it increases the weight of an object by just under 11% – an 80 kg man would feel like he had a mass of 89 kg. When decelerating, the opposite is true – an 80 kg man would feel like he had a mass of 71 kg.

If the lift was accelerating downward quickly enough, at 9.81 m/s², then the person inside would feel completely weightless. This is how weightlessness is simulated in aircraft, accelerating downward in a powered dive at the same rate as gravity.

* Einstein’s equivalence principle is actually about the difference between inertial mass and gravitational mass but the difference isn’t particularly important here.