A.2 · IB Physics
Terminal velocity
Drop a ball into a fluid. Drag grows with speed until it balances the weight, then the acceleration falls to zero and the velocity levels off. Compare with free fall and see how mass and drag change the final speed.
Predict first
Start from the defaults (mass 1.0 kg, drag coefficient 0.012 kg m⁻¹). If you raise the mass to 4.0 kg and leave k alone, what happens to the terminal velocity?
At terminal velocity mg = kv², so vt = √(mg ÷ k). Quadrupling m multiplies vt by √4 = 2.
Check it in the model: Move the Mass, m slider from 1.0 to 4.0 kg and compare the Terminal velocity v_t readout (28.6 then 57.2 m s⁻¹).
weight mg drag kv² v–t curve no drag (v = gt)
a = g − (k ÷ m)v²
terminal: mg = kv², so v_t = √(mg ÷ k)
g = 9.8 m s⁻²
Try this
- Keep k = 0.012 kg m⁻¹ and raise the mass from 1.0 to 4.0 kg. How does v_t change, and does the curve take longer to flatten?
- Choose 'Ball in honey' and watch the 'Drag' readout. At what percentage of v_t is the net force already below 10% of the weight?
- Tick the free-fall comparison. At what time does the real curve first depart noticeably from the straight line v = gt?
Exam tip: at terminal velocity the ball is still moving but no longer accelerating, because drag equals weight and the net force is zero; on a v–t graph the gradient tends to zero while the speed stays constant.