Newton's Three Laws — One Idea at a Time

Source

Lecture: Introductory classical mechanics — Newtonian dynamics (Newton's three laws of motion).
Simulation: "Newton's Three Laws — One Idea at a Time": three tabbed 1-D scenes (① inertia · ② F = ma · ③ action–reaction), with a labeled ⚠ counterfactual model per scene.
Concept: Force changes motion — it does not sustain it: F_net = 0 ⇒ constant velocity; a = F_net/m; interaction forces come as equal-magnitude opposite pairs acting on two different bodies.
Serves: ① zero net force ⇒ constant v (not rest), with balanced mg/N arrows drawn; ② live a = F_net/m readout — same force, double mass ⇒ half acceleration; ③ equal & opposite pair on different bodies, recoil |a_A|/|a_B| = m_B/m_A with Σp = 0.
Inquiry: Does v change while F_net = 0? What speed does the puck keep after F returns to 0? Same 4 N on 1 kg vs 2 kg — what happens to a? During contact, do the two force readouts differ?
Misconception: "If an object is moving there must be a net force pushing it along" — zero net force means constant velocity, not rest. (Scene ③ adds: "the heavier body pushes harder.")

Pedagogy principles applied

ID	Principle	How it shows up here
CF	Counterfactual mode	⚠/✓ buttons implement both models exactly: Aristotle v = F/k (k = 2 N·s/m) in ①–②; an unequal-pair "heavier pushes harder" model in ③ whose Σp violation is visible as the ⊕ centre-of-mass drifting off its start line.
RV	Real values, honest labels	SI units throughout, g = 9.81 m/s²; over-long force arrows are capped with a visible break glyph but always carry the true numeric label; counterfactuals are always tagged ⚠ on-canvas.
RD	Readout discipline	Exactly two readouts per scene, each targeted by the current prediction/steps; t, x, v_A, v_B, Σp live in the collapsed 📊 Data panel and are referenced only when a step asks.
HERO	One hero scene	A single canvas owns the viewport; the Predict panel is visually senior; Data/Model panels start collapsed and the formal layer starts hidden.
L1–L3	Scene fidelity	①: balanced mg/N drawn, v-vector unchanged at F_net = 0; ②: exact constant-force kinematics (4 N on 1 kg for 2 s ⇒ v = 8 m/s, x = 8 m) with live a = F_net/m; ③: equal-opposite arrows anchored on the two different bodies, never one.
PRED	Prediction first, optional	Each scene loads paused with Play prominent; verdict and rebuttal appear only after the watch window; the sim is fully playable without ever predicting — nothing is gated.
MIS	Structural misconception targeting	"Moving needs a pusher" lives inside prediction choices and the ⚠ mode; rebuttals appear only when that choice is selected — no standing misconception card.
LOAD	Playable from load	No control is ever disabled; sliders preview their effect live even while paused (a = F/m, body sizes, arrows); Reset replays from the start.
EXACT	Exact claims + audit hook	All feedback numbers are computed from the sim's own formulas (a = F/m, ratio = m_A/m_B); window.__audit.at() returns accel = F_net/m for scene ② — matching the kernel row (6−2) N on 2 kg ⇒ 2 m/s².

Newton's Three Laws

Teach me

Speed

Guided Inquiry

1 · The apparatus

Let’s meet the setup. A body rests on a horizontal, frictionless surface. Its weight mg (red, down) and the normal force N (blue, up) cancel, so the only force that can change its motion is the horizontal applied force F.

And the green arrow shows the body's velocity — keep an eye on it.

2 · A puck already moving

Let’s start with a puck that’s already moving. It’s sliding at 2 m/s, and the horizontal net force on it is zero. Once time runs, what do you think happens to its velocity?

3 · A steady push

Now let’s add a push. A steady 4 N force acts on a 1 kg body starting from rest on the same frictionless surface. What do you think — while that force stays on, its velocity will:

4 · Two bodies pushing apart

Now for two bodies at once. Heavy A (4 kg) and light B (1 kg) are pressed together at rest, then push each other apart. During the contact, how do you think the forces on the two bodies compare?

5 · A heavier partner

Let’s change just one thing. The two bodies stay in contact for a fixed 0.8 s and push with 5 N each way. If A's mass were raised from 4 kg to 8 kg, what do you predict for B's final speed?

6 · Vary the masses

Now it’s your turn to experiment. The pair is running, so set m_A and m_B to different values and compare the two speeds once the bodies separate.

Which body ends up faster, and by what factor? See if the numbers match what you’d predict.

Listen

Scene & Controls

▾

Scene

F (applied)+0.0 N

m (mass)1.0 kg

v = 2.00 m/s

📊 Data (live)

▾

① Law of inertia

F_net = 0 ⇔ dv/dt = 0

Zero net force means velocity is constant — any constant, not necessarily zero. Rest (v = 0) is just one special case. On the puck, mg and N cancel: balanced forces ⇒ no change of motion.

② F = ma

a = F_net/m ; x = x₀ + v₀t + ½at²

Kernel-verified checks: forces +6 N and −2 N on m = 2 kg ⇒ F_net = 4 N and a = 2 m/s². From rest, 4 N on 1 kg for 2 s ⇒ v = 8 m/s and x = 8 m. Same F on double m ⇒ half a.

③ Action–reaction

F on A = −(F on B) ⇒ |a_A|/|a_B| = m_B/m_A

+5 N on B ⇒ −5 N on A, always — on the two different bodies. From rest, m_Av_A + m_Bv_B = 0 (total momentum stays zero).

⚠ The counterfactuals (for contrast)

v = F/k (k = 2 N·s/m) ; F_X ∝ m_X

⚠ Aristotle (scenes ①–②): force sustains velocity — F = 0 ⇒ instant rest. ⚠ "Heavier pushes harder" (scene ③): body X pushes with 5 N·m_X/m̄ — an unequal pair, so Σp is not conserved. Both are implemented exactly so you can watch them fail.

The Physics

Newton's three laws · what this sim shows, the physics behind it, and every control

At a glance

This sim takes Newton's three laws one at a time, in three frictionless scenes: a sliding puck, a car under a steady push, and two crates that push each other apart. Every force is drawn as a labelled arrow, so you can see what forces do to motion.

What you'll learn

What happens to a moving body when the net force on it is zero.
How a steady force changes a body's velocity over time.
How the acceleration depends on the force and on the mass.
How the forces two bodies exert on each other compare, and how each body responds.

Left: the body in scenes ① and ②, with its four arrows. Right: the two crates of scene ③, pressed together at rest.

What's on screen

mg (red, down): the body's weight.
N (blue, up): the surface pushing up.
F (amber): the applied force in scenes ① and ②; in scene ③, the force each crate feels while they touch.
v (green, above): the velocity; longer means faster.
x = 8 m flag (pink, scene ②): a mark on the road. The ruler below counts distance.
Readouts and the 📊 Data panel in the sidebar; in scene ③, a phase tag (Pre-launch, Contact, Separated).

See itOpen scene ①: a puck sliding on ice. Watch for: the red mg and blue N arrows on the puck, the green v arrow above it, and the ruler sliding past underneath.

The controls

Press ⌖ on a row to see where that control sits in the sim.

Control	What it changes	Range
Scene	Picks ① Inertia, ② F = ma or ③ Pairs. Each scene opens at its own starting values, paused.	① ② ③ Free Exploration opens on ③
F (applied) (① ②)	The horizontal push on the puck or car. A negative value pushes left. Moving it restarts the run.	−10 to +10 N opens at 0 N in ①, 4 N in ②
m (mass) (① ②)	The body's mass. The body grows with it, and so do mg and N.	0.5–8 kg opens at 1 kg
m_A (③)	The mass of crate A, on the left.	0.5–8 kg opens at 4 kg
m_B (③)	The mass of crate B, on the right.	0.5–8 kg opens at 1 kg
Readouts	Two lines: v and F_net in ①; a and v in ②; the force on A and on B in ③.	panel
📊 Data (live)	t, x, v (and a) in ① and ②; v_A, v_B, their ratio, m_A/m_B and total momentum Σp in ③.	panel
▶ Play / ⏸ Pause	Runs or freezes the motion.	top bar
Speed	Plays the motion faster or slower on screen. The physics stays the same.	0.25×–4× opens at 0.5×
↻ Reset	Puts the current scene back to its starting values and runs it again.	top bar

Fixed: g = 9.81 m/s², no friction or air drag. Each run starts over after 10 s of sim time.

What zero net force does

On the puck, the weight mg and the normal force N cancel, and nothing acts along the ice. The net force is zero, so the velocity does not change: the puck keeps its 2 m/s, in the same direction. This is Newton's first law.

Zero net force means constant velocity, and constant velocity means zero net force.

Constant velocity, not only rest. Rest is just the case v = 0.
Friction hides this in everyday life. A book pushed across a table stops because friction acts on it, not because the push ended. On the ice there is no friction, and nothing needs to push.
Zero net force is not zero forces. mg and N act all the time; they balance.

Scene ① at its starting values: F_net = 0 and v stays at 2 m/s. The dashed red line is the old idea (Aristotle's) that motion stops when the push stops; the sim does not show it.

See itThe puck slides at 2 m/s with no applied force. Watch for: the v readout staying at 2.00 m/s, and the green arrow never changing length.

What a steady push does

A net force does not set a speed. It sets how fast the velocity changes: the acceleration. This is Newton's second law.

Only the net force counts, and the acceleration points along it.

4 N on the 1 kg car gives a = 4 m/s². From rest, v grows by 4 m/s every second for as long as the force acts.
Nothing here opposes the push, so there is no top speed. A steady speed under a steady push needs a backward force, such as friction or drag, that grows until it cancels the push.
After 2 s: v = at = 8 m/s, and x = ½at² = 8 m, the pink flag.

Scene ② at its starting values: v rises in a straight line, and the area under it is the distance covered.

See itA steady 4 N push on the 1 kg car, from rest. Watch for: the green v arrow growing longer every second, and v reading about 8 m/s as the car passes the pink x = 8 m flag.

What the mass changes

From a = F_net/m: double the force and the acceleration doubles; double the mass and it halves. Only the ratio F/m matters, so 8 N on 2 kg moves exactly like 4 N on 1 kg. Mass measures how hard it is to change a body's velocity.

F m

These are scene ②'s F and m.

A negative F accelerates the car to the left. From rest it simply drives off leftward.

See itThe same 4 N on 1 kg, then on 2 kg, each stopped at t = 2 s. Watch for: the card showing both speeds side by side.

See itRun the F and m from the panel above, from rest. Watch for: the a readout matching the panel, and v changing by that much every second.

Forces come in pairs

A force is always an interaction between two bodies. When B pushes on A, A pushes on B with a force of the same size in the opposite direction. This is Newton's third law.

Equal, whatever the masses. During contact in scene ③, both readouts show 5.0 N. The heavier crate does not push harder.
The pair never cancels. The two forces act on different bodies, and each body moves under its own force. Forces cancel only when they act on the same body, like mg and N on the puck.

Key idea. To find a force's partner, swap the two bodies: "B pushes A" pairs with "A pushes B".

See itA (4 kg) and B (1 kg) push apart, paused mid-contact. Watch for: the force on A and the force on B both reading 5.0 N, in opposite directions.

See itNow A is 8 kg and B is 0.5 kg, sixteen times lighter. Watch for: the two forces still reading 5.0 N each.

How each body responds

In scene ③ each crate feels 5 N for 0.8 s, so each gets the same push, or impulse: FΔt = 4 N·s, in opposite directions. Each body answers with a = F/m, so, starting from rest, it leaves at v = FΔt/m.

Scene ③ at its starting values: one 5 N pair for 0.8 s.

A (4 kg) leaves at 1 m/s to the left; B (1 kg) at 4 m/s to the right. The lighter body is faster, by the mass ratio m_A/m_B.
The total momentum stays zero: 4 × (−1) + 1 × (+4) = 0. Equal and opposite forces inside a system always leave its total momentum unchanged.

The sim fixes the pair at 5 N for 0.8 s. With a real spring between the crates, a heavier A would also change how long the push lasts, and so B's speed. The third law holds either way.

See itRun the pair with A = 4 kg, then A = 8 kg, each until they separate. Watch for: the card showing both runs' exit speeds and Σp side by side.

Where it matters

Walking and driving. A foot or a tyre pushes the ground backward; the ground's equal push forward is the force that moves you. Without grip, as on scene ①'s ice, there is no forward force.
Rockets. A rocket pushes its exhaust gas backward, and the gas pushes the rocket forward. It needs no ground to push on, so it works in empty space.
Seatbelts. When a car stops suddenly, your body keeps moving forward until a force (the belt) stops it. That is the first law.

Go deeper: you pull the Earth up

The Earth's acceleration under your weight, for a 70 kg person.

The Earth pulls a 70 kg person down with about 687 N, and the person pulls the Earth up with the same 687 N.
Same force, but the Earth's mass is about 6 × 10²⁴ kg, so its acceleration is about 10⁻²² m/s², far too small to notice.

Summary

In one line. A net force changes a body's velocity at the rate F/m, and every force comes paired with an equal and opposite force on another body.

Key points

Zero net force: the velocity stays constant, at any value (first law).
A net force sets the acceleration, a = F_net/m, not the speed (second law).
Forces come in pairs, acting on two different bodies (third law).
How each body responds: the lighter body changes its velocity more.

Common mix-ups

"If it's moving, something must be pushing it." Only a change in motion needs a force.
"A steady force gives a steady speed." It gives a steady acceleration. A steady speed needs the forces to balance.
"Action and reaction cancel, so nothing can move." They act on different bodies, so they never cancel each other.

Things to try on your own

In scene ①, set F to −2 N and watch the puck slow down, stop and come back.
In scene ②, set F = 8 N and m = 2 kg, and check that the car still reaches the pink flag at t = 2 s.
In scene ③, swap the masses (A = 1 kg, B = 4 kg) and compare the exit speeds in the Data panel.