A bullet with the same density as water is shot straight down into a very deep
water tank. What happens after sufficient time?
The bullet eventually comes to a halt at an intermediate depth.
The bullet eventually falls to the bottom of the tank
The bullet initially moves down but eventually floats to the surface.
The bullet eventually oscillates between two depths.
A bullet with the same density as water, shot straight down into a very deep water tank, eventually falls to the bottom of the tank after sufficient time. This occurs because its density matches water’s (1 g/cm³), so the buoyant force equals its weight, yielding neutral buoyancy in theory—but real-world drag and motion ensure it settles at the bottom. High initial velocity causes rapid deceleration due to water’s drag force, which scales with velocity squared and water’s high density (800 times air’s), slowing it profoundly unlike in air.
Physics of Neutral Buoyancy
For an object at rest, Archimedes’ principle states buoyant force \( F_b = \rho V g \), where \( \rho \) is water density, \( V \) is displaced volume, and \( g \) is gravity. Since the bullet’s density equals \( \rho \), \( F_b \) matches its weight \( mg \), producing zero net force for neutral buoyancy. However, shot downward with high speed (~300-1000 m/s), viscous drag \( F_d \approx \frac{1}{2} C_d \rho A v^2 \) (where \( C_d \) is drag coefficient, \( A \) area, \( v \) velocity) dominates initially, converting kinetic energy to heat and slowing it.
Once velocity drops near zero, no significant drag remains, but any residual downward momentum carries it to the tank bottom in a deep tank. It lacks upward propulsion to rise, unlike lighter objects, and assumes no air pockets or tumbling that could alter effective density. Real bullets sink post-deceleration due to these dynamics, not hovering mid-water.
Why Other Options Fail
- Halts at intermediate depth: Incorrect; neutral buoyancy halts vertical acceleration at rest, but initial kinetics propel it fully downward without equilibrium mid-depth. Drag dissipates energy en route, but no force arrests it short of bottom.
- Floats to surface: Wrong; density parity prevents positive buoyancy needed to rise. Lighter bullets (\( \rho < 1 \) g/cm³) float, but this one neither sinks nor rises indefinitely at rest.
- Oscillates between depths: Implausible; no periodic restoring force like springs or undamped harmonics exists. Drag overdamps motion, preventing sustained oscillation in viscous water.
This scenario highlights fluid dynamics in ballistics, where water’s resistance trumps neutral buoyancy for moving objects, ensuring the bullet reaches bottom.
