Newton's Third Law

Newton's third law: equation

When two particles interact, each exerts an equal force on the other. Though the magnitude of these forces is the same, their directions are opposite to each other. You can write the equation for this law as \(F_A = -F_B\) where A and B are variables indicating the objects.

In this equation, F_A represents the force applied by object 1 on object 2, while F_B represents the force applied by object 2 on object 1. The negative sign indicates that these forces are in opposite directions.

A frog swimming pushes the water back, and the water pushes its body forward. Sometimes this law isn't as obvious as it sounds in real life. Take a flying bird as an example, it almost looks like there is one object here, and no other objects for it to interact with. However, that isn't accurate – the bird's wings push the air down, and the air pushes the bird upwards.

Fig. 1 = Once example of Newton's third law is how a bird flies through the air.

Applications of Newton's third law

Applications of Newton's Third Law are ubiquitous in everyday life and in scientific fields. One common example is the act of walking: when we push the ground backward (the action), the ground pushes us forward with an equal force (the reaction).

Example one of Newton's third law

Let's look at a different example. When a gun is fired there is a forward force on the bullet. The bullet also exerts an equal and opposite force on the gun. You can perceive this in the recoil of the gun. But perhaps you are wondering why the gun doesn't recoil at the same acceleration as the bullet.

It is true that the gun recoils at a different acceleration than the bullet even though they have the same magnitude of force. This is possible, and was described in Newton's Second Law of motion which states that force is the product of mass and acceleration:

\[Force = mass \ \times \ acceleration\]

This also means that:

\[acceleration = \frac{force}{mass}\]

Therefore, if the mass is more, then there will be less acceleration.

Fig. 2 - The recoil of the gun is the reaction while the force of the bullet is the action.

Example two of Newton's third law

Imagine you are in a boat on the water with a ball in your hand, and you want to move east. You throw the ball in the opposite direction. You and the boat will move east like you wanted. But because the mass of the ball is much smaller than you and the boat, you are not going to move very far.

The ball possesses less mass and will have greater acceleration, comparatively. Though the amount of force is the same, if you decrease the mass, the acceleration is increased, and if you increase the mass, the acceleration decreases.

Example three of Newton's third law

The same principle can be applied to a balloon. Imagine you have a fully-inflated balloon and it has a hole in it somewhere. Gas is going to escape out of the opening and the balloon will fly in the opposite direction. That's how an object can be propelled using gas.

Fig. 3 - This ballon expels gas outward, and the reaction force propels the balloon forward.

Why Newton's third law is significant

A deep understanding of Newton's third law of motion has been of great use across almost all engineering disciplines. The balloon example is how we produce rockets. When a rocket is built, it takes into consideration where gases will burn to orchestrate its movement. The action force is the rapid disposal of burning gas from the back of the rocket. This exerts an equal reaction force on the rocket causing it to move upwards.

This law has a role to play in sports, too. It's important to understand that if you hit a tennis ball with a lot of force you should be prepared to receive a reaction from the ball. This allows you to take a proactive approach by positioning physically and psychologically, expecting the response. It can help prevent injuries, too.