# Newton’s Third Law of Motion : Concept of Action Reaction Pair

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### Statement:

• To every action, there is always equal, opposite and simultaneous reaction.

#### Explanation: • Let us consider a block of metal kept on the table. The weight of the block acts vertically downward. Thus the block tries to push the surface of the table downward by a force which is equal to its weight. This is action.
• Now the surface of table pushes the block vertically upward which is the reaction.
• Here it should be noted that action and reaction act simultaneously. The action is on the table while the reaction is on the block. Thus action and reaction act on two different bodies. Hence though action and reaction are equal they can not cancel each others effect.

### Examples to Illustrate Action Reaction Pair:

• To explain the third law of motion we can take an example of the working of a rocket. When the fuel of rocket is ignited the combustion of fuels takes place. The hot gases produced in the chemical reaction are pushed out through the small hole at the bottom (tail) of the rocket with very high velocity. Thus the action is in downward. Now, these outgoing gases produce an equal and opposite force on the rocket, which constitutes the reaction. Under the effect of upward reaction, the rocket is propelled upward. The jet engine also works on the same principle, the difference is that the rocket has to carry oxygen or oxidizing agent with it to propel because it has to go out of the atmosphere of the Earth where oxygen is not available. While planes with jet engines fly in Earth,s atmosphere, hence they need not carry oxygen with them. • Let us sit on a chair in front of a wall and push the wall with our legs. We will find that the chair is pushed backward. When we are pushing the wall we are applying action force, now the wall will put equal and opposite reaction on us and the chair is pushed backward.
• When we walk on the ground, as our foot pushes down (action) the ground, the ground pushes up (reaction) which is equal and opposite. This reaction is responsible for our forward movement. If the ground is not able to give a required reaction, then our foot sinks in it as in the case of sand, mud, water etc. If we push the ground harder we can jump into the air. • Two-wheeled blocks of the same kind are at rest on the top of a smooth surface of a table. They are tied with a thread with each other. A compressed spring is placed between the two blocks. When the thread is cut the blocks move in the opposite direction. • If we attach a spring balance to the hook on the wall and its hook is engaged with a hook of another spring balance and apply a pull on the second spring balance that both of the spring balance show the same reading but in opposite direction.
• The ball bounces back on hitting the ground. A ball strikes the ground with certain force (Action) and the ground pushes back the ball with equal force(Reaction) • A gun recoils when a shot is fired from it. Initially both the bullet and gun are at rest, thus the total momentum of the system is constant. When a shot is fired, the bullet moves forward pushing the gun backward. This phenomenon is called the recoil of the gun. Due to recoiling of the gun, a backward jerk is experienced on the shoulders by the shooter. Hence to avoid injury he has to hold the rifle holding tight on shoulders. • When a boy jumps from the boat to the bank. The boat moves in the direction opposite to jump. In order to jump out of the boat, he has to push the ground (surface of the boat) with greater force (action). During Now the boat is in water, thus it is representing the non-rigid surface. Thus the boat moves backward under the action of pushing force. • While swimming, the swimmer pushes the water backward with his hands. The action of pushing water backward give rise to a reaction in the opposite direction which results in the swimmer moving forward.
• While hammering a nail. a force is experienced on the hand holding the hammer. When a nail is hammered a force is applied to it (action) due to which the nail applies equal and opposite reaction on the hammer.
• When moving train collides with a stationary one, the former experiences a reverse motion. The moving train applies a force on the stationary train and in return, the stationary train put a reaction which is equal and opposite to the former train.
• A person falling from a certain height on a hard surface gets hurt more seriously than when he falls on a soft surface. By Newton’s third law of motion “to every action, there is always equal, opposite and simultaneous reaction. Thus when the person falls on the surface its weight (action) acts on the surface in turn the surface puts equal and opposite reaction on the person. Now the hard surface is rigid it transfers complete reaction without absorbing any impact (energy). Thus hard surface put more reaction on the person. While the soft surface is elastic it transfers part of reaction absorbing some impact (energy). Thus soft surface put less reaction on the person. Thus hard surface is providing greater reaction than the soft surface. Hence, the person falling from a certain height on a hard surface gets hurt more seriously than when he falls on a soft surface.

#### Motion is a relative concept and not an absolute one:

• Motion is always with respect to the observer. Consider a person A is standing in a train moving in the north direction with a uniform velocity of 5 m/s in a straight line. Let us consider another person B standing on the ground.
• Now B as an observer would say that he himself is stationary and the person A is moving in the north direction with a uniform velocity of 5 m/s.
• Now A as an observer would say that he himself is stationary and the person B is moving in the south direction with a uniform velocity of 5 m/s.
• Thus there is a difference in the interpretation of motion of each other it is because their states of motion are different. It is to be noted that both are in the state of uniform motion with respect to earth. Thus we can say that the motion is a relative concept and not the absolute one.

#### Reference Frame:

• It is a system of co-ordinate axes with reference to which position or motion of an object in space is described. The rectangular Cartesian coordinate system of axes is considered as the simplest reference system.
• If (x, y, z) are the coordinates of the point in this system of reference, then the position vector of the particle w.r.t. the origin is given by ### Concept of Inertial and Non-Inertial Reference Frames:

• The reference frame which is at rest or moving with uniform velocity with respect to earth is called inertial reference frame.
• The reference frame which is moving with uniform acceleration w.r.t. earth is called non-inertial reference frame.
• Newton’s laws of motion are applicable in inertial reference frame only. Newton’s laws of motion are not applicable in non-inertial reference frame
• The force in an inertial reference frame is a real force. To apply Newton’s laws of motion in non-inertial reference frame we have to consider the existence of an imaginary force called pseudo force. • Let us consider two persons A and B traveling by train with uniform velocity 5 m/s towards right as shown. There is a third observer C standing on the ground near the track. observer A and B are moving with uniform velocity w.r.t. earth similarly observer C is at rest w.r.t. earth. Hence A, B, C are the inertial frame of reference. We shall ask an opinion of motion of each observer. A will say that he is stationary, B is stationary and C is moving backward with uniform velocity 5 m/s and no force is acting on him. The opinion of B will be similar. But C will say he is stationary and B and C are moving towards the right with uniform velocity 5 m/s. No force acts on them. Then who is correct. Everybody is correct because the motion is always with respect to the state of the observer. Thus Newton’s laws are not violated. • Let us consider same two persons A and B traveling by train with uniform acceleration 5 m/s² towards the right as shown. There is a third observer C standing on the ground near the track. observer A and B are moving with uniform acceleration w.r.t. earth while observer C is at rest w.r.t. earth. Hence A and B are the non-inertial frame of reference, while C is still inertial frame of reference. We shall ask the opinion of motion of each observer. C will say he is stationary and B and C are moving towards the right with uniform acceleration 5 m/s². Necessary force for acceleration is provided by the engine of the train. Thus he is not violating Newton’s laws of motion. A or B will say that he is stationary and C is moving backward with uniform acceleration 5 m/s² and no force is acting on C. It is a contradiction to Newton’s laws of motion because he is saying acceleration is there but no force present to cause it. Thus Newton’s laws of motion are violated in the non inertial reference frame. To correct A and B the observer in non-inertial reference frame, imaginary or hypothetical force acts on C. This force is called pseudo force.

#### Examples of Pseudo Forces:

• An object revolving in a circle experiences a centrifugal force directed radially outward. This force tends to move the object away from the centre. This centrifugal force is a pseudo force because the circular motion accelerated motion. Thus the object is in acceleration w.r.t. earth. The reference frames which are moving with acceleration with respect to earth are called non-inertial reference frames.
• When bus negotiates a curve on the right side, the passengers are pushed on the left side and if the bus negotiates a curve on left side passengers are pushed on the right side. As the bus is negotiating a curve the passengers are in accelerated motion. Thus they constitute the non-inertial reference frame.

#### Characteristics of Inertial Reference System:

• The reference frames which are at rest or moving with uniform motion with respect to earth are called as inertial reference frames.
• Newton’s laws of motion are applicable in inertial reference frames
• Concept of pseudo force is not required in inertial reference frames.
• A person sitting in a car moving with uniform motion in a straight line is the inertial frame of reference.

#### Characteristics of Non-inertial Reference System:

• The reference frames which are moving with acceleration with respect to earth are called non-inertial reference frames.
• Newton’s laws of motion are not applicable in non-inertial reference frames.
• To apply Newton’s laws of motion in non-inertial reference frames we have to consider the existence of an imaginary force called pseudo force.
• A person sitting in a car negotiating a curve is non-inertial frame of reference.
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