4.4 Newton's Third Law of Motion

Newton's Third Law of Motion

Newton's Third Law describes how forces always come in pairs: whenever one object pushes or pulls on a second object, the second object pushes or pulls back with equal force in the opposite direction. This law is essential for understanding how objects interact, from walking across a room to launching a rocket into orbit.

more resources to help you study

practice questions

Applications of Newton's Third Law

The formal statement: for every action force, there is an equal and opposite reaction force. If object A exerts a force on object B, then object B simultaneously exerts a force of equal magnitude back on object A in the opposite direction.

These action-reaction pairs show up constantly in everyday life:

• Walking: Your foot pushes backward on the ground (action), and the ground pushes forward on your foot (reaction), propelling you forward.
• Swimming: Your hands push water backward (action), and the water pushes your hands and body forward (reaction), moving you through the water.
• Jumping: Your feet push down on the ground (action), and the ground pushes up on your feet (reaction), launching you upward.
• Sitting: Your body exerts a downward force on the chair (action), and the chair exerts an upward force on your body (reaction), supporting your weight.

Friction plays a crucial role in many of these situations. Without friction between your shoe and the ground, for instance, your foot would just slide backward and you wouldn't be able to walk. The ground can only push you forward because friction allows the surfaces to grip each other.

Force Calculations in Action-Reaction Pairs

Forces in an action-reaction pair are always equal in magnitude and opposite in direction:

$F_{A \text{ on } B} = -F_{B \text{ on } A}$

To find the reaction force, determine the action force and reverse its direction.

Example 1: A 70 kg person stands on the ground.

1. Calculate the gravitational force (weight) pulling the person down: $F = mg = 70 \text{ kg} \times 9.8 \text{ m/s}^2 = 686 \text{ N downward}$
2. The person's feet exert a 686 N force downward on the ground.
3. By Newton's Third Law, the ground exerts a 686 N normal force upward on the person.

Note: when the person jumps, they push down on the ground with a force greater than their weight (they're accelerating upward), and the ground pushes back with that same larger force. The 686 N calculation above only represents the person's weight while standing still, not the force needed to accelerate upward.

Example 2: You push a box against a wall with 50 N of force. The box exerts 50 N on the wall, and the wall pushes back on the box with 50 N in the opposite direction.

Example 3: A 0.5 kg bird pushes air downward with its wings. The air pushes the bird upward with an equal force. For the bird to hover, it needs to push air down with a force equal to its weight: $F = mg = 0.5 \text{ kg} \times 9.8 \text{ m/s}^2 = 4.9 \text{ N}$

The normal force is one of the most common reaction forces you'll encounter. Whenever an object rests on a surface, the surface pushes back with a normal force perpendicular to the surface.

Newton's Third Law in Physical Systems

Rocket Propulsion: Rockets work by expelling hot gases downward at high speed (action). Those gases push back on the rocket with an equal force upward (reaction). This is why rockets work in the vacuum of space: they don't need air to push against. They push against their own exhaust.

$F_{\text{gases on rocket}} = -F_{\text{rocket on gases}}$

Collisions: When two objects collide, they exert equal and opposite forces on each other for the same duration. This means the impulse (force × time) each object experiences is equal in magnitude and opposite in direction. If two cars collide head-on, both cars experience the same magnitude of force, regardless of their size. However, the smaller car experiences a greater acceleration because of its smaller mass (Newton's Second Law). This is why collisions between vehicles of different sizes are more dangerous for occupants of the smaller vehicle.

Fluid Propulsion: Vehicles that move through fluids use the same principle as rockets:

• A boat propeller pushes water backward, and the water pushes the boat forward.
• A jet engine expels air backward at high speed, and the air pushes the plane forward, generating thrust.

Types of Forces in Action-Reaction Pairs

Both contact and non-contact forces obey Newton's Third Law:

• Contact forces require objects to physically touch: normal force, friction, tension, and applied forces.
• Non-contact forces act at a distance: gravity, electromagnetic forces, and nuclear forces. For example, Earth pulls you downward with gravity, and you pull Earth upward with the exact same gravitational force. Earth just doesn't noticeably accelerate because its mass is enormous.