Forces in interactions: Newton's third law
Section: Dynamics | Syllabus: Cambridge AS Level Physics (9702)
Newton's Third Law of Motion
Newton's Third Law When an object exerts a force on a second object, the second object simultaneously exerts a force of equal magnitude and opposite direction on the first object. Insight: Interaction PairsAll forces are the result of interactions between objects. If you push a heavy desk, you may move backwards even if the desk only moves a little. This is because the desk pushes back on you with exactly the same force magnitude, but your inertia (resistance to motion) is much less than the desk's.
Criteria for Third Law Force Pairs
For two forces to be a Newton's Third Law pair, they must meet these criteria:
- They are equal in magnitude.
- They act in opposite directions along the same line.
- They are of the same type (e.g., both gravitational).
- They act on different bodies.
Identify the Newton's Third Law pair for the following:
- Book on table: The book pushes the table down; the table pushes the book up (Contact forces).
- Gravity: The Earth pulls a ball down; the ball pulls the Earth up (Gravitational forces).
- Bird flying: The wings push air downwards; the air pushes the wings upwards.
- Magnets: Magnet A repels Magnet B; Magnet B repels Magnet A (Magnetic forces).
Propulsion and Interactions
Jet engines and rockets operate on the principle of Newton's Third Law. By forcing exhaust gases out at high speed, the gases exert an equal and opposite force on the engine, propelling it forward.
Worked Example: Jet Engine ThrustQuestion: A jet engine releases 17 kg of exhaust gas every second at 85 m s^-1. Calculate the propelling force.
SolutionFrom Newton's Second Law, the force on the gas is its rate of change of momentum:
F_gas = (Δ p/Δ t) = (Δ m × v/Δ t) = 17 × 85 = 1445 NBy Newton's Third Law, the gas exerts an equal and opposite force on the engine.
Resultant Propelling Force = 1445 N
The Boat Example: Safety and Forces
When you step off a small boat onto a river bank, you push the boat backwards with your feet. Simultaneously, the boat pushes you forwards.
If the boat is not tied to the bank, it will accelerate backwards easily due to its mass. This increases the distance you must "jump," making it dangerous. If the boat is tied, the entire Earth effectively absorbs that backward force, making the surface stable.
Thought Experiment: Ice SkatersScenario: Skater A and Skater B (equal mass) stand opposite. A pushes B. B does not push. Describe the motion.
AnalysisEven though only B was "pushed," both skaters will move apart with equal speeds. A exerts a force on B, and B simultaneously exerts an equal and opposite force on A. Since their masses are equal (a = F/m), their accelerations are identical.
Diagram: Newton's Third Law (Skaters)Illustrate Skater A pushing Skater B. Show two identical force arrows acting on different bodies: F_A on B (pointing right) and F_B on A (pointing left).
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