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The same simulation in 3D: press the 3D tab above the picture (same controls, same numbers).
Floor: smooth floor. μ = 0 is frictionless ice; rubber on dry concrete is about 0.7 sliding and 1.0 to start (more than this slider).
Newton’s three laws explain forces and motion: an object keeps its motion unless a net force acts (1st), net force = mass × acceleration, F = ma (2nd), and forces come in equal, opposite pairs (3rd). A 10 N net force on a 2 kg cart gives 5 m/s²; push a wall and it pushes back just as hard.
Five hands-on labs that go with the simulator, two high-school labs (Go deeper) and a sorting game. Each one is checked by the page and gets a ✓ when you finish it (saved in this browser). Using the printable lesson pack? Its “Mission 2–6” are Labs 1–5 here, with the same titles and buttons.
Two teams pull a cart on wheels (mass 60 kg). Press New challenge, add up each team, predict what the cart will do, then run it. Five correct challenge predictions finish the lab (you need at least one balanced round and one where the cart is already rolling). You can also build your own setups with the buttons. Forces in the same direction add; forces in opposite directions subtract. The difference is the net force.
A free-body diagram shows every force acting on one object as an arrow. Turn on the forces that act in each situation and choose the direction of the net force. Solve all 8.
Pull a crate slowly with a spring scale. Watch the reading climb while the crate stays still (static friction matches your pull), then drop as it starts to slide (kinetic friction). Record trials, compare surfaces and masses, then find the friction coefficient of the mystery surface: μs = peak force ÷ normal force. (Teaching values: ice 0.10 / 0.03, wood 0.50 / 0.30, rubber 0.90 / 0.70.)
| # | Surface | Mass (kg) | Normal force (N) | Peak pull = max static friction (N) | Sliding pull = kinetic friction (N) |
|---|
A string pulls a cart with a steady force along a 1.00 m low-friction track. The timer measures how long it takes from rest. Work out the acceleration with a = 2d ÷ t², plot a against F, and use the slope (= 1 ÷ mass) to find the mass of the mystery cart.
| # | Cart | Force F (N) | Time t (s) | a = 2d/t² (m/s²) |
|---|
Skater A and skater B stand on smooth ice and push on each other for 0.5 s. Answer both questions before you press Push. Get 3 rounds right.
High school (HS-PS2-1). Two masses hang on a light string over a frictionless pulley. Treat them as one system: the net force is (m1 − m2) g and the total mass is m1 + m2. Type your prediction for the acceleration first, then press Release. The pink arrows show the tension (up) and the weight (down) on each mass.
High school (HS-PS2-1). Tilt the ramp slowly. The block stays put while static friction can hold it (mg sinθ ≤ μs mg cosθ, so tanθ ≤ μs). Past that angle it slides with a = g (sinθ − μk cosθ). Here static and kinetic friction are different (μs > μk; values from OpenStax table 5.1). Find μs of the mystery surface from the angle where it starts to slip. Then lower the angle slowly: it keeps sliding below the slip angle, down to tanθ = μk. Starting is harder than keeping it going.
Click a card, then click the law it shows best (or its “Place card here” button). Click a placed card to take it back. Get all 12 right with at most 2 mistakes per check: more than 2 mistakes sends every card back to the pile.
| Word | Meaning |
|---|---|
| Force | A push or a pull, measured in newtons (N). |
| Net force | The overall force on an object when all forces are added, taking direction into account. |
| Balanced forces | Forces that add to zero. The motion does not change: at rest stays at rest, moving keeps the same speed and direction. |
| Unbalanced forces | Forces with a net force that is not zero. The object speeds up, slows down or changes direction. |
| Inertia | The tendency of an object to keep its state of motion. More mass means more inertia. |
| Acceleration | How quickly velocity changes, in m/s². |
| Friction | A force between touching surfaces that opposes sliding (or the start of sliding). |
| Static friction | Friction on an object that is not sliding; it matches the push up to a maximum value. |
| Kinetic friction | Friction on a sliding object; usually smaller than the maximum static friction. |
| Normal force | The push of a surface on an object, at right angles to the surface. |
| Mass and weight | Mass is the amount of matter (kg) and is the same everywhere; weight is the pull of gravity on it (N). |
| Action–reaction pair | The two equal and opposite forces two objects exert on each other (third law). |
Vectors and the second law. Force and acceleration are vectors, so the full law is ΣF⃗ = m a⃗. With a constant net force the motion follows v = v0 + a t and x = x0 + v0 t + ½ a t². Written with momentum p = m v, it is Fnet = Δp ÷ Δt, the form Newton used.
Analyze the data (HS-PS2-1). In ② F = ma with a 5 kg crate and μ = 0.10, the readouts give a = 1.02, 3.02, 5.02, 7.02, 9.02 and 11.02 m/s² for pushes of 10 to 60 N. The a–F graph is a straight line with slope 1 ÷ m = 0.20 kg−1 that crosses the force axis at μmg = 4.9 N: the slope gives the mass and the intercept gives the friction. Lab 4 does the same with timed runs (a = 2d ÷ t²).
Momentum is conserved (HS-PS2-2). In ③ Action–reaction the two carts push on each other with 60 N for 0.3 s, so each gets an impulse of F Δt = 18 N·s in opposite directions. A 5 kg cart leaves at −3.60 m/s and a 10 kg cart at 1.80 m/s: pA = −18 and pB = +18 kg·m/s, so the total stays 0. Conservation of momentum follows from the third law.
A block on a rough incline. Gravity has a part mg sinθ down the slope and a part mg cosθ into it, so N = mg cosθ and a sliding block accelerates at a = g (sinθ − μk cosθ). With θ = 30° and μk = 0.20: a = 9.8 × (0.500 − 0.173) ≈ 3.2 m/s². A block at rest starts to slip when tanθ > μs.
Two masses over a pulley (Atwood machine). The net force on the system is (m1 − m2) g and the total mass is m1 + m2, so a = (m1 − m2) g ÷ (m1 + m2) and the string tension is T = 2 m1 m2 g ÷ (m1 + m2). With 3 kg and 2 kg: a = 1.96 m/s² and T ≈ 23.5 N, between the two weights (19.6 N and 29.4 N).
Air resistance and terminal velocity. Drag grows roughly with the square of the speed, FD ≈ ½ ρ CD A v². A falling object speeds up until drag equals its weight; then the net force is zero and it falls at a constant terminal speed. A belly-down skydiver reaches about 55 m/s (about 200 km/h); an open parachute brings it down to about 5 m/s.
Model limits. The simulator uses g = 9.8 m/s² (the standard value is 9.80665 m/s²), one friction coefficient for starting and sliding, no air resistance and no rolling friction for the carts. Friction really depends a little on speed and on the surfaces’ condition; μ values are typical, not exact.
Pick one answer for each question, then press Check my answers to see the explanations. New questions picks another set.
A 45-minute lesson for grades 6–8. Hook on a projector (Full screen button): the page opens in ② F = ma with a 5 kg crate on a floor (μ = 0.10). Ask “At what push will it start to move?”, then drag the Push slider up slowly. Up to 4.9 N friction matches the push and the meter says Balanced; then it breaks free. Pairs then do the six missions (each asks for a prediction first; a certificate prints when all six are done) and one or two of the labs.
The labs below the simulator are the ones from the earlier version of this page: tug of war (Lab 1), free-body diagrams (Lab 2), friction with a spring scale (Lab 3), a timed F = ma track (Lab 4) and skaters (Lab 5), plus a “Which law?” sort. Labs 3 and 4 have a mystery surface / cart for a data challenge. Labs 6 (Atwood machine) and 7 (inclined plane with μs and μk) are high-school “Go deeper” labs with a prediction / mystery-surface check.
All simulator values come from F = ma with g = 9.8 m/s² and are exact for the model. The simulator uses one friction coefficient for starting and sliding (a simplification); the friction-lab surfaces (ice 0.10 / 0.03, wood 0.50 / 0.30, rubber 0.90 / 0.70) are teaching values close to textbook tables. Go deeper covers data analysis (HS-PS2-1), momentum conservation (HS-PS2-2), inclines, pulleys and air resistance for high school and AP Physics 1.
Standards: NGSS MS-PS2-1 (third law, partial), MS-PS2-2 (forces, mass and the change in motion) · Go deeper: HS-PS2-1 (F = ma data), HS-PS2-2 (momentum)
| Time | Step | What students do | Go to |
|---|---|---|---|
| 5 min | Hook | Predict when the crate moves; push it up slowly (② F = ma) | Simulator |
| 10 min | Explore | Missions 1–3: stuck crate, double the push, balanced but moving | Simulator |
| 8 min | Inertia & 3rd law | Missions 4–6: puck on ice, heavy puck, carts push apart | Simulator |
| 12 min | Lab | Lab 1 (tug of war) and Lab 2 (free-body diagrams); grades 8+: Lab 3 or 4 | Labs |
| 10 min | Check | Order game, then the 10-question quiz or worksheet part E as an exit ticket | Quiz |
Worksheet: a print-out for students and a separate answer key page for the teacher (opens the print dialog; choose "Save as PDF" to keep a file).
First law: an object keeps its motion (at rest, or the same speed in a straight line) unless a net force acts on it. Second law: net force = mass × acceleration (F = ma). Third law: when one object pushes on another, the second pushes back with an equal force in the opposite direction.
Key takeaway: motion changes only with a net force; F = ma; forces come in pairs.Forces are balanced when they add up to zero, for example 300 N to the left and 300 N to the right. Balanced forces do not change motion: an object at rest stays at rest and a moving object keeps the same speed and direction. Forces are unbalanced when there is a net force; then the object speeds up, slows down or changes direction, in the direction of the net force.
Key takeaway: balanced = no change in motion; unbalanced = acceleration.Add the forces as arrows. Forces in the same direction add (50 N + 100 N to the right = 150 N right). Forces in opposite directions subtract, and the net force points toward the bigger one (150 N right and 100 N left give 50 N right). Up–down and left–right forces are added separately. If the result is zero, the forces are balanced.
Key takeaway: same direction: add; opposite directions: subtract.Mass is the amount of matter in an object and its inertia, measured in kilograms; it is the same everywhere. Weight is the pull of gravity on that mass, W = m × g, measured in newtons. On the Moon (g = 1.62 m/s²) your mass is the same but your weight is about one sixth of your weight on Earth.
Key takeaway: mass in kg stays the same; weight in N depends on gravity.Static friction acts on an object that is not sliding. It matches your push exactly, up to a maximum of μs × N, which is why a heavy box can stay still while you push it. Kinetic friction acts once the object slides and is about μk × N, usually a bit smaller. That is why the spring-scale reading in Lab 3 peaks just before the crate moves and then drops.
Key takeaway: starting a slide takes more force than keeping it going.Draw the object as a box or a dot. Then draw one arrow for each force that acts ON the object, pointing the way the force acts: weight down, normal force away from the surface, friction along the surface against the sliding, tension along a rope, air resistance against the motion, and any push or pull. Make bigger forces longer. Never add a “force of motion”: if the speed is constant, the arrows balance.
Key takeaway: one arrow per force on the object; no “force of motion”.No. The two forces of a third-law pair are always equal in size (yes, always, even when a truck hits a small car) and opposite in direction, but they act on different objects, so they cannot cancel. When you push a wall, the wall pushes you back: one force acts on the wall, the other on you. Forces cancel only when they act on the same object.
Key takeaway: equal and opposite, but on different objects.Gravity pulls a heavier object harder, but the heavier object also has more inertia. The two effects cancel exactly: a = F ÷ m = m g ÷ m = g. Without air resistance all objects fall with the same acceleration, about 9.8 m/s² on Earth.
Key takeaway: more weight, but also more mass to move.Seatbelts work because of the first law: in a crash your body keeps moving forward. Rockets use the third law: they push gas backward and the gas pushes them forward. Engineers use the second law to find the forces needed to speed up cars, elevators and planes, and spacecraft paths are computed with Newton’s laws.
Key takeaway: seatbelts, rockets, cars and spacecraft all follow them.They are very accurate at everyday speeds and sizes. They fail at speeds close to the speed of light (special relativity), for atoms and smaller (quantum mechanics) and in very strong gravity (general relativity). For cars, balls, bridges and most spacecraft they are accurate enough to use without corrections.
Key takeaway: everyday motion: yes; near light speed, atoms or black holes: no.