STUCK IN PHYSICSFalling. Faster. Then steady.
Release a fully submerged sphere. Watch drag grow until it nearly balances the effective weight.
Change the viscosity, size and densities to find what changes terminal velocity.
The sphere
The fluid
Illustrative properties, not temperature-controlled measurements. Changing settings resets the release.
Release and inspect
Schematic, not to scale. Travel is enlarged to show the approach to terminal velocity. No surface or bottom collision is modelled.
Velocity against time
Acceleration against time
Displacement against time
Speed against time
Distance travelled against time
Velocity and displacement are signed, with downward positive. Speed and distance travelled are non-negative. Once near terminal speed, acceleration approaches zero and distance continues increasing almost linearly. The observation continues to 12 time constants; it does not stop at the 99% threshold.
The model: weight, upthrust and drag
Positive velocity is downward. Weight acts downward, upthrust acts upward, and drag opposes motion. This is an idealised Stokes’ law model for a small sphere moving slowly through a still fluid.
Terminal velocity is approached asymptotically. “Near terminal” here means at least 99% of the predicted terminal speed; it does not mean exact equality at a finite time.
Predict, then check
Double the radius while keeping densities and viscosity fixed. What happens to the predicted terminal speed?
Increase viscosity. Does the sphere settle faster or slower?
Make the sphere less dense than the fluid. Which way does it move, and which way does drag act?
When densities match, a sphere released from rest remains at rest. Use the force arrows to explain why the sphere accelerates at first, then moves at nearly constant speed.