FORCE AND LAWS OF MOTION, Class IX, Part 4

 If a boy wearing roller skates stands facing a wall and pushes the wall with his hands, the boy finds himself moving backward, away from the wall. It appears as if the wall also pushes the boy away.

When the boy exerts a force on the wall by pushing it with his hands, then the wall exerts an equal force on the boy in the opposite direction. Since the boy is wearing roller skates, the opposite force exerted by the wall makes him backward, the boy on roller skates is exerting force on the wall towards the left side. The wall exerts an equal force on the boy towards the right side. Due to this, the boy moves in the backward direction.

From this discussion, we conclude that when a boy exerts a force on the wall, the wall exerts an equal and opposite force on the boy. This is just an illustration of Newton’s third law of motion.

Whenever one body exerts a force on another body, the second body exerts an equal and opposite force on the second body. The force exerted by the first body on the second body is known as “action” and the force exerted by the second body on the first body is known as “reaction”.

It should be noted that “action” and “reaction” are just forces. We can now write another definition of Newton’s third law of motion. To every action, there is an equal and opposite reaction. Action Force and reaction force act on two different bodies, but they act simultaneously.

We will now describe a simple experiment to prove Newton’s third law of motion, that is to prove that action force and reaction force are always equal and opposite.

We make two similar spring balances A and B and join them hook to hook. The other end of spring balance B is attached to a hook H fixed in a wall. Let us pull the free end of the spring balance A to the right side by our hand. We find that both the spring balance shows the same force of 4 N (Newton). This can be explained as follows.
When we pull the balance A, it exerts a force of 4 N (Newton) on the balance B. the balance B pulls the balance A with an equal force of 4 N (Newton), but in the opposite direction. In other words, when balance A exerts a force of action on balance B, balance B exerts an equal and opposite force of reaction on balance A. Since both the spring balances show the reading of 4N, we conclude that the action and reaction force is equal in magnitude. We find that the action force is acting towards the east and the reaction force towards the west. Thus, action and reaction forces act in opposite directions.

                Action and Reaction Act-On Two Different Bodies

Suppose a book is resting on the ground. The book is exerting a downward force of its weight on the ground. The downward weight of the book is balanced by an equal, upward force supplied by the ground. Now the force exerted by the weight of the book is “action and it acts on the ground whereas the force exerted by the ground on the book is the reaction and it acts on the book. Since the book is in equilibrium under the action of two forces, it neither goes up nor goes down the action of the book must be equal and opposite to the reaction of the ground. It is obvious that the action of the book acts on the ground and the reaction of the ground acts on the book. Thus action and reaction act on two different bodies.

              Some examples to illustrate Newton’s Law of Motion

When we walk on the ground, then our foot pushes the ground backward and in return, the ground pushes our foot forward. The forward reaction exerted by the ground on our feet makes us walk forward.

 If however, the ground is slippery or if there is all ice it becomes very difficult to walk. This is due to the fact that on the slippery ground or Ice the friction is much less and we cannot exert a backward action force on slippery ground or ice which would produce a forward reaction force on us. 

A swimmer pushes the water backward or applies force on the water backward with his hands and feet to move in the forward direction in the water. It is the equal and opposite reaction to this force that pushes the swimmer forward. Please note that though action and reaction forces are equal in magnitude they do not produce an equal acceleration in the two bodies on which they act. This is because the two bodies on which action and reaction force act usually have different masses. So the acceleration produces will be more in the body having less mass whereas the acceleration produces will be less the body having more mass.

                                            Why does the gun recoils?

                             

When a bullet is fired from a gun, the force sending the bullet forward is equal to the force sending the gun backward. But due to the high mass of the gun, it moves only a little distance backward and gives a backward jerk or kick to the shoulder of the gunman. The gun is said to have recoiled.

                           The flying of jet airplanes and rockets

                                           

Jet airplanes utilize the principle of action and reaction. In modern jet aircraft. In the modern jet aircraft, the hot gases obtained by the rapid burning of fuel rush out of a jet (a nozzle) at the rear end (back end) of the aircraft at a great speed. The equal and opposite reaction of the backward going gases pushes the aircraft forward at a great speed.

The rockets also work on the principle of action and reaction. In a rocket, the hot gases produced by the rapid burning of fuel rush out of a jet at the bottom of the rocket at a very high speed. 

The equal and the opposite reaction force of the downward going gases pushes the rocket upward with a great speed. Please note that a rocket can propel itself even in vacuum or outer space because it doesn’t require air for obtaining uplift or for burning its fuel. This is not so in the case of a jet aircraft. A jet aircraft cannot fly in outer space (where there is no air) because it needs air to provide uplift and also to burn its fuel.

                                     The case of a boat and the ship

                                     

During the rowing of a boat, the boatman pushes the water backward with the oars. The water exerts an equal and opposite push on the boat move forward. In fact, the harder the boatman pushes back the water with oars, the greater is the reaction force exerted by water and the faster the boat moves forward.

                          

It is a common experience that when a man jumps out of a boat to the bank of the river the boat moves backward, away from him. This is due to the fact that to step out of the boat, the man presses the boat with his foot in the backward direction. The push of the man on the boat is the action force. The boat exerts an equal force on the man in the forward direction which enables him to move forward. This force exerted by the boat on the man is the reaction force. Since the boat is floating on water and fixed, it moves backward due to the action force exerted by man.

                                    The Case of Horse Pulling a Cart

According to the third law of motion, the horse exerts some force on the cart, and the cart exerts an equal and opposite force on the horse. So at first glance, it seems that the forces being equal and opposite cancel out and hence the cart would not move. But it should be noted that it is only the force on the cart which determines whether the cart will move or not and that the force exerted by the cart on the horse affects the horse alone. Thus if the horse is able to apply enough force to overcome the frictional present, the cart will move so to make the cart move, the horse vends forward and pushes the ground with its feet. When the forward reaction force of the horse is greater than the backward push, or opposing frictional forces of the wheels, the cart moves.

                   CONSERVATION OF MOMENTUM

When two or more bodies act upon one another, their total momentum remains constant provide no external force is acting. The law of conservation of momentum means that whenever one body gains momentum, then some other body must lose an equal amount of momentum. This law can also be stated as Momentum is neither created nor destroyed. The law of conservation of momentum is also known as the principle of conservation of momentum.

 The principle of conservation of momentum is in accord with Newton’s third law of motion which says that action and reaction (force) are equal and opposite. We will now take an example to prove the law of conservation of momentum.

Suppose two bodies, are moving in the same direction (forward east) but with different speeds or velocities let the mass of the first body be m and its velocity be u so that its initial momentum is m u and reaction (forces) are equal and opposite.

Let the mass of the first body be m₁ and its velocity be u₁ so that its initial momentum is m₁u₁.
If the mass of the second body is m₂ and its velocity is u₂ so that the initial momentum of the car is m₂ u₂.
Thus the total the momentum of first and the second body before the collision is m₁ u₁  + m₂ u2.

It is obvious that the total momentum of the bodies before and after the collision is the same. This means that the momentum of the two bodies remains constant or conserved. And this result proves the law of conservation of momentum.