Double gravity

Problem

Imagine that Earth’s gravity doubles tomorrow. Explain in five lines how the following would change: weight, mass, the tensions in ropes and beams, and your reaction times.

Solution

This is a science-fiction-physics conceptual problem: it requires carefully distinguishing which quantities depend on $g$ and which do not.

Weight doubles. Weight is the gravitational force $P = mg$. If $g$ goes from $g$ to $2g$ while the mass stays unchanged, the weight of every object doubles: $P' = m\,(2g) = 2\,mg = 2P$ We would feel crushed, every object lifted would “weigh” twice as much.

Mass does not change. Mass measures the amount of matter and the inertia of the body: it is an intrinsic property, independent of the gravitational field. A body of $70\ \text{kg}$ remains $70\ \text{kg}$; what changes is the force with which the Earth attracts it.

The tensions in ropes and beams double. Every structure supporting a weight (a rope holding a chandelier, a beam supporting a roof) must balance a doubled force. Tensions and internal stresses double: many structures designed for normal gravity would fail, because the load would exceed the safety margins.

Reaction times stay unchanged. Reaction time depends on the speed of signal transmission in the nervous system, an electrochemical process that has nothing to do with gravity. So our reflex readiness would not change, even though moving limbs that have become “heavier” would require greater muscular effort.

$\ev{\text{Weight} \to \times 2, \quad \text{mass unchanged}, \quad \text{tensions} \to \times 2, \quad \text{reaction times unchanged}}$

Links

Concepts: Weight force · Newton’s second law Skills: Analysis of limiting cases and science-fiction physics