Math Puzzle for April 19, 2024

Alameda Post - A diagram, of three circles of different sizes distributed horizontally, labeled M1, M2, and M3. Below, are two labeled vectors: x is the length from the center of M1 to M2, and L is the length from the center of M1 to M3

Above is simplified schematic of Cavendish’s Gravity Experiment, conducted in 1798 c.e.

  • M1 has a mass of 500 kilograms.
  • M2 has a mass of 200 kilograms.
  • M3 has a mass of 300 kilograms.

The masses are arranged such that M2 experiences equal tugs of gravity from M1 and M3.
Like many phenomena in nature, gravitational attraction obeys an inverse square law.
The attraction of two objects is inversely proportional to the square of their distance apart.
Above, the attraction between M1 and M2 is equal to the attraction between M2 and M3.
The centers of gravity of the three spherical masses are collinear and L = 8.8729833 meters.

Find the appropriate value for x.

x = __________ meters

First correct answer sent to [email protected] wins a gift card worth plenty of ice cream at Tucker’s Ice Cream of Alameda.

Last week’s winner was Madeleine Canavese with x = 22.496026691647103 cm.

Jeff Smith is a former Math teacher and a retired US Navy Lieutenant Commander. Reach him at [email protected].

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