Drei Gesetze, die alle Bewegung im Universum erklären.
Schau dir das zuerst an — Lehrerschmidt erklärt alle drei Newtonschen Gesetze und F = m · a.
Lehrerschmidt — "Newtonsche Gesetze (3 Axiome) | F = m · a | Physik – einfach erklärt" (~9 min)
🔎 Was fällt dir auf?
Mia is at the stables. She observes three things and writes them down:
Bella (480 kg) stands perfectly still in the field, even though gravity is pulling her down. She doesn't sink into the ground, and she doesn't fly up. She just… stays.
When Mia pushes a heavy bale of hay with the same force as a small bag of feed, the bag shoots forward but the bale barely moves.
When Bella jumps over a fence and lands, the ground pushes back up against her hooves — hard enough that Mia can feel it through the saddle.
Before reading on: what is different about each of these three situations? Can you guess the pattern?
💡 Deine Vermutung
Write one sentence each: why does Bella stay still? Why does the light bag accelerate more? What is "pushing back" against Bella's hooves when she lands?
📋 Die drei Newtonschen Gesetze
1. Gesetz — Trägheitssatz (Law of Inertia)
An object stays at rest or in uniform motion unless a net force acts on it.
Bella stands still → the forces on her are balanced (gravity down, ground pushing up). The net force is zero. She stays still. On a horse going around a bend at speed, Mia feels herself wanting to go straight — that's inertia resisting the change in direction.
2. Gesetz — Aktionsprinzip (F = ma)
Force equals mass times acceleration: F = m · a
$$F = m \cdot a \qquad a = \frac{F}{m} \qquad m = \frac{F}{a}$$
The same push (force) gives a big acceleration to the light bag and a tiny acceleration to the heavy bale. Double the mass → half the acceleration. Unit: 1 Newton (N) = 1 kg·m/s²
3. Gesetz — Reaktionsprinzip (Action & Reaction)
Every force has an equal and opposite reaction force.
When Bella's hooves push the ground downward, the ground pushes her hooves upward with exactly the same force. She doesn't fall through the ground because the ground pushes back. Rockets work the same way: the engine pushes exhaust gases downward, and the gases push the rocket upward.
⚖️ Balanced vs. Unbalanced Forces
Balanced forces (net force = 0): object stays still or moves at constant speed (Law 1)
Unbalanced forces (net force ≠ 0): object accelerates — speeds up, slows down, or changes direction (Law 2)
Weight is a force: W = m · g, where g = 9.81 m/s² on Earth. Bella's weight: 480 × 9.81 = 4 709 N downward. The ground pushes up with exactly 4 709 N. Net force = 0. She doesn't move.
📐 Maths connection: F = ma is the same rearrangeable three-variable formula as v = s/t and I = Prt. Cover the variable you want to find: a = F/m means the same thing as using the formula triangle. You already know how to do this from maths lessons 01–05.
🧪 Ausprobieren — Feel Newton's Third Law
Push a wall. Push your hand against a solid wall. Feel your hand being pushed back — that's the wall's reaction force. You never push on anything without it pushing back equally.
Blow up a balloon and let it go without tying. The air rushes out one way (your "exhaust"), the balloon shoots the other way. This is exactly how a rocket engine works.
Sit on a rolling chair (if you have one) and throw a heavy book forward. You roll backward — because the book pushes back on you as you push it forward.
For each experiment: identify which object pushes, which is pushed, and in which direction. The forces are always equal in size, opposite in direction.
Worked Examples
Example 1 — F = ma calculation
Mia pushes a hay cart (mass 60 kg) and it accelerates at 1.5 m/s². What force is she applying? (Ignore friction for now.)
F = m · a: F = 60 × 1.5 = 90 N
90 N is roughly the weight of a 9 kg object — about the weight of a large bag of potatoes.
Example 2 — Finding mass from force and acceleration
A net force of 2 400 N gives a car an acceleration of 3.2 m/s². What is the car's mass?
m = F ÷ a: m = 2 400 ÷ 3.2 = 750 kg
Example 3 — Weight and the normal force
Mia (55 kg) stands on a bathroom scale in an elevator. The elevator accelerates upward at 2 m/s². What does the scale read in newtons?
Normal weight: W = 55 × 9.81 = 539.55 N
Net force needed for upward acceleration: F = 55 × 2 = 110 N upward
Scale must provide: 539.55 + 110 = 649.55 N ≈ 650 N
She feels heavier when the elevator accelerates upward. Astronauts feel this at rocket launch (many times their body weight).
Problems
Problem 1
Which Newton's law explains each situation? Write 1st, 2nd, or 3rd.
Situation
Law
A parked car stays still until someone pushes it.
___
A swimmer pushes the pool wall and glides forward.
___
A truck needs a bigger engine than a car to reach the same speed.
___
A passenger lurches forward when the bus brakes suddenly.
___
A gun recoils backward when a bullet is fired forward.
___
A heavier ball takes more force to roll at the same acceleration.
___
— work on paper —
Problem 2
Calculate the missing value in each row. Use F = m · a.
Force (N)
Mass (kg)
Acceleration (m/s²)
?
12
4.5
300
?
6
840
120
?
?
0.5
22
— work on paper —
Problem 3
Bella (480 kg) stands still. Calculate: (a) her weight in newtons (use g = 9.81 m/s²), (b) the size of the normal force the ground exerts on her, and (c) the net force on her. Explain your answers using Newton's laws.
— work on paper —
Problem 4
Two teams play tug-of-war. Team A pulls with 1 200 N to the left. Team B pulls with 1 200 N to the right. (a) What is the net force? (b) What happens to the rope? Now Team A adds a player and pulls with 1 350 N. (c) What is the net force now? (d) In which direction does the rope accelerate?
— work on paper —
Problem 5
A 1 200 kg car brakes from 90 km/h to a stop in 6 seconds. (a) Convert 90 km/h to m/s. (b) Calculate the deceleration (negative acceleration). (c) Calculate the braking force. (d) In which direction does this force act relative to the car's motion?
— work on paper —
Problem 6
On the Moon, g = 1.62 m/s². Mia weighs 539.55 N on Earth (55 kg). (a) What does she weigh on the Moon in newtons? (b) Does her mass change on the Moon? Explain the difference between mass and weight.
— work on paper —
Problem 7 Challenge
A rocket at launch has a mass of 500 000 kg. Its engines produce a thrust of 7 600 000 N. (a) Calculate the weight of the rocket on the launch pad (g = 9.81 m/s²). (b) Calculate the net upward force at the moment of launch. (c) Calculate the initial acceleration upward. (d) As fuel burns off, the mass decreases. If the mass drops to 300 000 kg but thrust stays the same, what is the new acceleration? Why does a rocket accelerate faster as it burns fuel?
— work on paper —
Problem 8 Open
Pick one sport (horse riding, skateboarding, swimming, skiing — anything you've done or seen). Identify one example of each of Newton's three laws in that sport. Draw a simple diagram for at least one of them showing the forces with arrows.
— your answer —
Science check ✔ — Newton published these three laws in 1687 in his Principia Mathematica. They held as the complete description of all motion for over 200 years — until Einstein showed they break down at very high speeds (close to the speed of light) and at very small scales. But for everyday objects — horses, cars, rockets, planets — Newton's laws are so accurate that NASA still uses them to navigate spacecraft. For anything you'll ever directly experience, they are effectively perfect.
Show Answer Key
1.1st · 3rd · 2nd · 1st · 3rd · 2nd2.54 N · 50 kg · 7 m/s² · 11 N3.(a) 480 × 9.81 = 4 708.8 N · (b) 4 708.8 N upward (equal and opposite to weight) · (c) 0 N — balanced forces, she is stationary (Newton's 1st law)4.(a) 0 N · (b) it doesn't move / stays still · (c) 1 350 − 1 200 = 150 N to the left · (d) accelerates toward Team A (left)5.(a) 90 × 1000/3600 = 25 m/s · (b) a = Δv/t = (0 − 25)/6 = −4.17 m/s² · (c) F = 1 200 × 4.17 = 5 000 N · (d) opposite to the direction of motion (backward relative to travel)6.(a) 55 × 1.62 = 89.1 N · (b) No — mass is the amount of matter (always 55 kg). Weight is the gravitational force, which depends on g. Mass is a property of the object; weight depends on where you are.7.(a) 500 000 × 9.81 = 4 905 000 N · (b) 7 600 000 − 4 905 000 = 2 695 000 N · (c) a = 2 695 000 / 500 000 = 5.39 m/s² · (d) Net force upward = 7 600 000 − (300 000 × 9.81) = 7 600 000 − 2 943 000 = 4 657 000 N · a = 4 657 000 / 300 000 = 15.52 m/s². Less mass means more acceleration for the same thrust — the rocket gets lighter as it burns fuel, so it accelerates harder and harder.8.Open — any three correct examples with Newton's law named. Look for: 1st law = something staying still or continuing at constant speed without force; 2nd law = force causing acceleration or heavier = slower; 3rd law = two objects exerting equal and opposite forces on each other.
Next up → s05: Cells — The Building Blocks of Life
Switching from physics to biology. Every living thing — from Bella the horse to the bacteria in Mia's yogurt — is made of cells. We'll look at what's inside them and why they matter.