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Concept module

Drag and Terminal Velocity

Drop one body through a fluid and use mass, area, and drag strength to see drag grow with speed until force balance settles into terminal velocity.

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Starter track

Step 5 of 50 / 5 complete

Fluid and Pressure

Earlier steps still set up Drag and Terminal Velocity.

1. Pressure and Hydrostatic Pressure2. Continuity Equation3. Bernoulli's Principle4. Buoyancy and Archimedes' Principle+1 more steps

Previous step: Buoyancy and Archimedes' Principle.

Start from track beginning

Why it behaves this way

Explanation

This page keeps drag bounded and honest by following one object released from rest through one fluid. Weight stays constant at $m g$ , while the upward resistive force grows with speed according to the compact rule $F_{d} = k A v^{2}$ . That makes the motion neither constant-acceleration free fall nor a full fluid-dynamics sandbox.

Terminal velocity is the balance point, not a mystery cap on motion. As the object speeds up, the drag arrow grows until it nearly matches the weight arrow. At that stage the net force shrinks toward zero, so the acceleration collapses and the speed levels off even though the object keeps moving downward.

Mass, area, and drag strength matter in different ways. More mass raises the weight that drag must match, so the terminal speed is higher. More area or stronger drag makes the same speed produce a larger resistive force, so the balance happens sooner and at a lower speed. This bounded model keeps gravity fixed, folds fluid-and-shape details into one drag-strength constant $k$ , and ignores buoyancy so the force story stays compact and readable.

Key ideas

01Drag depends on speed in this bench, so it starts small right after release and grows rapidly as the object speeds up.

02Weight stays constant while drag changes, which is why the net force is largest early and much smaller later in the fall.

03Terminal velocity means drag and weight are balancing so the net force is near zero. It does not mean the object has stopped moving.

04A larger mass raises terminal speed, while a larger area or stronger drag lowers terminal speed because those settings change how quickly drag catches up to weight.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the live bench directly. The current controls set the terminal-speed prediction, and the current time on the rail sets the live force-balance example.

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View plans

Frozen valuesUsing frozen parameters

For the current setup with $m = 2$ , $A = 0.05$ , and $k = 12$ , what terminal speed does the bounded drag model predict?

m

Mass

2 kg

A

Area

0.05 m^2

k

Drag strength

W

Weight

19.6 N

1. Turn mass into the constant downward weight

With gravity fixed on this page, the current setup gives

W = m g = 19.6 N

2. Use the terminal-speed balance condition

Terminal speed is where drag catches the weight, so

k A v_{t}^{2} = m g

with

k = 12

and

A = 0.05 m^{2}

3. Solve for the resulting balance speed

That gives

v_{t} = m g / (k A) = 5.72 m/s

for the current controls.

Current terminal speed

W = 19.6 N, v_{t} = 5.72 m/s

This setup sits in the middle, so the balance speed is neither especially low nor especially high.

Terminal-speed checkpoint

Two objects use the same drag strength and the same frontal area, but one has twice the mass. Which one has the higher terminal speed?

Make a prediction before you reveal the next step.

Decide whether the heavier object balances drag sooner or later.

Check your reasoning against the live bench.

The heavier object has the higher terminal speed.

The heavier object has a larger constant weight. Drag has to grow to a larger value before it can balance that weight, so the speed at balance is higher.

Common misconception

Terminal velocity happens because gravity turns off once the object has been falling for a while.

Gravity does not disappear. The weight force stays essentially constant throughout this page.

What changes is the drag force. It grows with speed until it almost matches the weight, so the net downward force becomes very small.

Quick test

Variable effect

Question 1 of 5

Use the force story, not just the formula. Each question checks whether the drag-balance picture is stable enough to explain the graphs.

At the same mass and drag strength, what does a larger area do to terminal speed?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows one object dropping through one fluid column with a distance ruler on the left and a readout card on the right. The object changes width with area, while mass is represented through the force readouts rather than by resizing the object itself. Optional overlays show a constant downward weight arrow, an upward drag arrow that grows with speed, a net-force arrow, a terminal-speed cue, and a distance guide.

The time rail controls one bounded fall from rest over four seconds. Compare mode can ghost a second setup behind the current one so two force-balance stories stay on the same scale.

The readout card reports mass, area, drag strength, distance fallen, current speed, terminal speed, drag force, and net downward force.

Graph summary

The speed-history graph is the main motion graph. The speed curve rises and then flattens toward the constant terminal-speed line.

The force-balance graph keeps the forces honest: weight stays flat, drag rises, and the net downward force shrinks toward zero.

The three response graphs isolate mass, area, and drag strength. The mass sweep rises, while the area and drag-strength sweeps fall because larger drag-side factors lower terminal speed.

Bridge mechanics and fluids next

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Compare free-flight and drag-limited motionMechanics

Drag and Terminal Velocity

Fluid and Pressure

Explanation

Step through the frozen example

For the current setup with m=2, A=0.05, and k=12, what terminal speed does the bounded drag model predict?

At the same mass and drag strength, what does a larger area do to terminal speed?

Keep this idea moving

Projectile Motion

Continuity Equation

Bernoulli's Principle

For the current setup with $m = 2$ , $A = 0.05$ , and $k = 12$ , what terminal speed does the bounded drag model predict?