The Lennard-Jones equation is given as U = (A/r^12) - (B/r^6) The box is placed

Question

The Lennard-Jones equation is given as U = (A/r^12) - (B/r^6)

The box is placed on a cement floor and that the molecules from the cement have a Lennard-Jones potential energy with A = 7.8125e12 and B = 1e9. (Here, the units are such that the r is given in Angstroms. For example, to find the potential energy for a separation of 6 Angstroms, plug in 6, not 6e-10). When the box is placed on the floor, the atoms squeeze together such that the equilibrium separation is reduced by 0.1%. Using this fact, calculate the mass of the box in kilograms.

Note that even such a tiny, tiny change from the equilibrium causes a force enough to support a reasonably heavy box.

Explanation / Answer

This looks like fun. OK, you know the relationship between potential energy and force

F = - dU/dr = - [ -12 A / r^13 + 6 B / r^7 ] = 12 A / r^13 - 6 B / r^7

The force is zero at the equilibrium position

0 = 12 A / r^13 - 6 B / r^7

6 B / r^7 = 12 A / r^13

r^6 = 2 A / B = 2 (7.8125e12) / (1e9) = 1.5325 E+4

r = 5.000

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