What is Newton’s Third Law of Motion?

A wise man once said, ‘You cannot be touched without being touched!’

No one understood the science in the statement better than Sir Isaac Newton. This understanding is represented in the form of Newton’s third law of motion.

In a football game, when two opponents stand in a line facing each other and the football is snapped, the two opponents crash into each other. When one opponent applies force on the other, force is felt on oneself also. So, there isn’t just one force in action here, there is a pair of forces. Newton was the first one to realize that forces always exist in pairs—no force exists in isolation.

Newton’s third law of motion deals with this fundamental characteristic of forces.

“Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.”

The third law is also termed as “action- reaction law” and is often stated as: “For every action, there is an equal and opposite reaction”.

This is how the third law of motion was defined by Sir Issac Newton.

Third Law of Motion in Real Life

Few examples to demonstrate third law of motion.

A swimmer pushes the wall of the pool backward under the water with a force F_feet . In response, the wall exerts an equal and opposite force F_wall on the swimmer. In Figure 1, it can be seen the force F_wall, enables the swimmer to kick start the swim and move forward.

Figure 2 illustrates an astronaut pushing a spacecraft in space with a force P to the left. In response the astronaut experiences a push backwards, i.e., a force P of equal magnitude to the right, in the opposite direction.

Now lets suppose that the mass of the spacecraft in Fig 2 is about 10000 kg and that of the astronaut is 100 kg. If the astronaut is capable of pushing the spaceship with a force of 50 N, lets estimate the accelerations produced in spacecraft and the astronaut, respectively.

Applying Newton’s second law, F=ma for spacecraft and the astronaut individually,

Spacecraft:
P=m_sa_s

50 N= 10000 kg x a_s

Acceleration produced in spacecraft, a_s = 50/10000 = 0.005 m/s²

Astronaut:
P=m_aa_a

50 N= 100 kg x a_a

Acceleration produced in astronaut, a_s = 50/100 = 0.5 m/s²

Although the action-reaction forces that acted on the spacecraft and the astronaut were the same, the forces did not create the same acceleration. This is primarily due to the huge difference in their masses. So in this case, because of the push exerted by the astronaut, the acceleration produced on himself is formidable enough to experience a considerable push back away from the spacecraft!

Application of Newton’s Third law

A tow bar connects the jeep in the front with the trailer to the rear bumper (Figure 3).

It contains a mechanism that can automatically trigger brakes on the trailer wheels as soon as the jeep applies its brakes. When the driver of the jeep applies the brakes, the jeep slows down. Due to inertia, the trailer at its rear continues to move forward and begins to push against the rear bumper of the jeep. In reaction, the jeep bumper pushes the tow bar backwards. This reaction force on the tow bar is deployed as a brake force on the braking pedal of the trailer. The trailer is almost instantaneously brought to rest along with the jeep.

The trailer is almost instantaneously brought to rest along with the jeep. In Figure  4, a boy pulls at one end of the rope. In the first case, the other end of the rope is connected to an inanimate object, i.e., a wall.  In the second case, the other end of the rope is connected to an elephant.

What force is exerted on the boy due to reactions by the wall and the elephant? Does the reaction force depend upon whether the object is animate or inanimate?

The answer is NO. The boy applies 100 N force in each case. The force is transmitted to the wall in the first case. The wall exerts the same force of 100 N on the rope that is transmitted to the boy’s hands.

Similarly, in the second case, the 100N force from the boy is transmitted to the elephant and the elephant exerts 100N on the rope, that is transmitted back to the boy’s hands.

So the boy experiences the same force whether the rope is connected to a wall or to an elephant as per Newton’s third law.

Third Law in Real Life

Rocket Principle

Simplest example based on rocket principle is a fully blown balloon made to slide using a straw on a thin horizontal string (Fig 5). As soon as the mouth of the fully blown balloon is released, the high-pressure air inside is released with a force towards the left. The escaping air pushes the balloon back as a reaction, so the balloon is propelled along the string in the opposite direction.

Similarly, a rocket, in its simplest form, can be considered as a chamber enclosing thousands of gallons of propellants kept under extremely high pressure. As soon as the rocket is launched, the gases produced by burning propellants escape from the bottom of the rocket downwards. In doing so, the escaping burnt gases provide a huge thrust that propels the rocket in the opposite direction that is upwards!

The Horse Cart Problem

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”

When applying Newton third law it is important to remember that the action and reaction forces act on two different bodies. The force exerted by the horse acts on the cart. The reaction force exerted by the cart, acts on the horse. Since the two forces act on two different bodies, they do not cancel each other.

The horizontal forces exerted on the cart include action force F exerted by the horse in the forward direction and friction force f due to ground acting backwards. Its only when F>f, that the cart experiences a net force forward. And that’s when it begins to accelerate in the forward direction.

Context and Application

This concept is applicable for students who are studying the following courses –

• Bachelors in Technology
• Masters in Technology
• Bachelors in Science in Physics
• Masters in Science in Physics

Practice Problems

Q1.When a horse pulls the wagon, the force that causes the wagon to move forward is the force that the

1. horse exerts on the wagon
2. the wagon exerts on horse
3. the ground exerts on the horse
4. horse exerts on the ground

Answer: the ground exerts on the horse

Explanation: The horse exerts a force on the ground when it pulls the wagon. So, according to Newton's third law of motion, the ground exerts an equal and opposite force on the horse enabling it to move forward. So, option (c) is correct.

Q2. A book placed on a table surface experiences a downward force of gravity due to earth. The book doesn’t accelerate downwards as this force is balanced by the ……………….  exerted on the book by the table surface.

a. contact force

b. centripetal force

c. centrifugal force

Answer: contact force

Explanation: Any object placed on a surface experiences a normal contact force directed opposite to the force of gravity due to the earth, which maintains it in stable equilibrium. So, the book doesn.t accelerate downwards as the downward force of gravity on it is balanced by the contact force exerted on the book by the surface. Hence, option (a) is correct.

Q3. A father and his daughter are facing each other on ice skates. With their hands they push off against one another. The ………………..experiences greater acceleration.

a. father

b. daughter

Answer: daughter

Explanation: When the father and daughter push off against one another, it is the daughter that experiences more acceleration as the force exerted by the father on the daughter is comparatively greater than the force exerted by the daughter on the father. So, option (b) is correct.

Q4. A rubber ball is dropped on the floor. The ……………force causes the ball to bounce back into the air.

a. normal reaction

b. friction

c. gravitational force

Answer: normal reaction

Explanation: The ball bounces back as the ground exerts a force of normal reaction on the ball due to the force exerted by ball on the ground. This is in accordance with Newton's third law of motion. Hence, option (a) is correct.

Q5. In a tug of war between two athletes, each athlete pulls the rope with a force of 100 N. If the rope does not move,   force that each athlete exerts against the ground is ……………….N.  

a. 0

b. 9.8

c. 100

Answer: 100

Explanation: As the athlete pulls the rope with a force of 100 N, he also pushes the ground with the force of the same magnitude. So, option (c) is correct.