Madhava Publications
Introduction
We have discussed motion and its different kinds like uniform motion and non-uniform motion. We have discussed accelerated motion where the speed of the objects varies with time. A moving body moves faster under acceleration and could stop also. One thing which we have not discussed there is Who governs all these motions?
We have seen that magnets attract iron kept at a distance without even physical contact with it. And the moon causes tides on the earth even from such a large distance. So we can conclude that there must be an external agency that governs all these and these agencies can even affect from a distance ( gravitational force and electromagnetic force).
Concept of force
From the previous discussion, we can conclude that an external agency is required to describe what governs different kinds of motion.
We call it force!. To stop a moving object, to start a body from rest, or change the speed of the moving body, all require a force.
Now the next question is that does a force is required to keep a body moving in uniform motion?
Aristotle said that a force is required to maintain the uniform motion of the body. His statement is based on the motion of the body we see in our daily life.
When a child throws a ball with some initial speed it eventually stops after moving some distance, also a car moving at a constant speed cannot maintain its motion when we turn off the engine of the car. So someone can conclude that force is necessary to even maintain the uniform motion. But this is not correct and thus this statement is called the Aristotle fallacy.
Force is a vector quantity whose unit is Newton.
Let us first try to understand what is the correct answer to the question: does a force is required to keep a body moving in uniform motion?
The answer is No ! Force is not required for the uniform motion of the object.
The ball which is moving comes to rest later due to an external force which is a friction force acting on it, in its opposite direction. So an external force is required to cancel the friction force to maintain the uniform motion of the object.
If there is no friction then there will be no force required to maintain the uniform motion of the body.
Inertia: resistance to change
Inertia is that property of any matter by virtue of which it always resists any change in its state.
If we are habitual to wake up late in the morning and suddenly we have to wake up early for work, both the body and the mind try to resist this change.
If we have our opinion on something and then we listen to someone else's opinion about the same thing which is different from ours, then our mind tries to stick to its own opinion rather than accepting the opinion of the other.
Inertia is basically everywhere. But in this chapter, we will restrict ourselves to the concept of mechanical inertia.
Mechanical inertia is the inertia of matter by virtue of which it resists any change in its motion or rest. This concept laid the formulation of Newton’s first law.
Newton’s First law
Statement: An object which is at rest will try to remain at rest and an object which is in uniform motion will continue to do so, until and unless an external force is applied to it. This is called Newton’s first law which is also known as the law of inertia.
- When no force is acting on the object then there will be zero acceleration then the object at rest will remain at rest and an object moving with uniform speed will continue moving with uniform speed.
But we all know there is gravity everywhere on the earth and also some opposing forces like friction and viscous drag (in fluids) are present everywhere. So how could it be possible to have zero force on any object?
- Since force is a vector quantity, a force in a particular direction can be canceled by another force of the same magnitude acting in opposite direction.
- So if we have the sum of all the forces acting on an object is zero. Then also we can apply Newton’s First law as there is no net force acting on the object.
Example: A car is moving with uniform speed on the road when the external force provided by the engine of the car is exactly equal to the frictional force acting between the road and the tires of the car during motion.
A book kept in the book remains at rest as the gravitational force by the earth is balanced by the normal force from the table in the opposite direction to the gravity.
I am putting this for fun just to help to remember Newton's First Law. An object at rest will remain at rest unless acted upon by another force.
Significance of the Newton’s first law
1. When we are sitting on a bike and it suddenly starts we get a jerk in the backward direction. Similarly when a moving bike stops we experience a jerk forward. This is true for any vehicle.
Explanation: When we are sitting on a bike our lower body is in contact with the bike but the upper body is not. When the bike starts, the lower body moves with the bike but the upper body resists the change in the state of rest and thus experiences a jerk backward.
2. When we place a playing card over a glass and a coin on the car. When we push the card, the card goes away but the coin falls into the glass.
Explanation: Here force is applied only on the card and thus moves away but the coin will try to remain at rest due to its inertia and thus falls into the glass as soon as the card is pushed away.
3. When we hold the trunk of the tree and try to shake it, fruits fall from it.
Explanation: when we shake the trunk, the whole tree starts to shake The little branch with which the fruit is connected also vibrates and the fruit will try to remain at rest due to its inertia and thus detaches from it and falls on the ground.
4. Newton's law of inertia is the law that tells us why we should wear seatbelts while driving.
5. Law of inertia tells us while you go flying over the handlebars if you stop the bicycle suddenly.
Momentum
The momentum of a body is defined as the product of the mass and velocity of that body. It is a vector quantity.
Let’s first discuss some common experiences related to motion in our daily life.
It is easier to put a car into motion than a loaded truck. Similarly, it would require greater force to stop a loaded truck moving at the same speed as a car at the same time.
Two stones, one lighter and the other heavier are dropped from the same height then it will be easier to catch the lighter stone than to catch the heavy stone.
From the above two discussions, we conclude that mass is one parameter that determines the effect of force on the motion.
A bullet fired from a gun can pierce human flesh before it stops and hence causes casualty. But the same bullet when thrown with hands does not harm much. This is because the stone fired from the gun has a much larger velocity than the bullet thrown by hands. Here we conclude that velocity is also a parameter that determines the effect of force on the motion.
As mass and velocity both are important parameters to describe the effect of force on the motion. Therefore a physical quantity which is the product of both mass and velocity (momentum) is a relevant variable of the motion
We can say that the greater the change in the momentum of a body, the greater the force will be needed. This statement laid the basis for the formulation of Newton's second law.
Newton’s second law of motion
Newton’s second law is a quantitative description of the changes that a force can produce in the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.
Statement: The rate of change of momentum of the body is directly proportional to the applied force and takes place in the direction in which force acts.
If a force F is applied on a body of mass ‘m’ for a time Δt, if the velocity of the body change from ‘v to v+Δv’
Change in momentum Δ p = m ( v +Δv ) - mv= mΔv
Rate of change of momentum = m Δv/ Δt
So according to newton’s second law
Here K= proportionality constant which is equal to 1 here.
So mathematically,
- S.I. unit of force is Newton .
- 1 N is the force that produces an acceleration of
- When F= 0 then acceleration is also zero. So we can say that Newton’s second law is consistent with Newton's first law.
- Now since F and acceleration is a vector quantity
So using Newton’s second law we have
- The second law of motion is applicable to a single particle. In the case of an extended object, we consider it equivalent to a point particle and all the forces are applied on a single point which is the center of mass.
- Any internal forces within the body itself are not included in the force.
- The second law of motion is a local equation. It means that Force F at a given point at an instant ‘t’ relates to the acceleration at that point in that instant.
The same force for the same time produces the same change in momentum for different bodies
Some examples of Newton’s Second law from daily life.
- Karate player breaking slabs of bricks
A karate player makes use of the second law of motion to perform the task of breaking a slab of bricks. Since, according to law, the force is proportional to the acceleration, the player tends to move his/her hands over the slab of bricks swiftly. This helps him/her to gain acceleration and produce a proportionate amount of force. The force is sufficient enough to break the bricks.
- It is easier to push an empty shopping cart than a full one because the full shopping cart has more mass than the empty one. This means that more force is required to push the shopping cart.
- Two people walking: of the two walking people, if one is heavier than the other, the one who weighs the heaviest walks slower because the acceleration of the one who weighs the lighter is more.
- Kick the ball: When we kick the ball we exert force in a specific direction, which is the direction the ball will move. In addition, the more forcefully the ball is kicked, the more force we apply to it and the further away the ball is.
- Racing cars: Reducing the weight of racing cars to increase their speed, engineers try to keep vehicle mass as low as possible, as a lower mass means more acceleration, and the higher the acceleration the greater the chances of winning the race.
- Objects falling under gravity: When an object falls in a free fall onto the ground, it accelerates because the force of gravity of the earth pulls it. The velocity of the object keeps on increasing as it falls and has its maximum value just before hitting the ground.
There are many examples that illustrate Newton's second law in our daily life.
Impulse
Sometimes a large force acts on a body for a very short instant of time and thus produces a finite momentum on the body. For example, when a ball hits the wall, it bounces back. The force on the ball acts for a very short duration yet the force is large enough to reverse the momentum of the ball. Another example could be when a ball hits the bat and bounces back.
Since the force is very large and the time duration is very small. It is difficult to take account of both so we talk about change in momentum in such cases. Change in momentum is called impulse
A large force acts for a very small time producing a finite change in momentum called Impulsive force. This is just like any other force in the mechanics.
Newton’s Third Law
Forces exist in two forms, either as a result of contact interactions, i.e., normal, tensional, frictional, and applied forces; or as a result of actions-at-a-distance interactions, existing in the form of electrical, electrical, and magnetic forces. In this law, Isaac Newton described any two objects that are interacting to be exerting mutual forces upon each other.
- If you punch the bench with your first with some force, your fist will also experience a force from the bench and it will get hurt.
- If you are reading this article while sitting on the chair, you are exerting a force on the chair and in return, the chair also exerts an equal force on you. These forces cancel each other in pairs and thus you are sitting comfortably on it.
“Forces come in pairs.”. The two equal forces exerted are of the same magnitude but in opposite directions, known as action and reaction forces. This led to the foundation of Newton’s third law.
Statement of Newton’s third law. To every action, there is an equal and opposite reaction.
In fact, the term action-reaction is a misnomer. There is nothing like one force is the cause and the other force is the effect. There is no cause-effect relation implied to the third law. Object A applies a force F on B and object B also applies a force F on A in the opposite direction at the same instant.
How Is Newton’s Third Law of Motion Useful in Our Real Life?
A variety of action-reaction force pairs are evident in nature, and in our real life. Here are 7 applications of Newton’s third law of motion:
- Walking: When you walk, you push the street; i.e., you apply an active force on the street’s ground, and the reaction force moves you forward.
- Gun Firing: when someone fires a gun, the action force pulls the bullet outside the gun, and the reaction force pushes the gun backward.
- Jumping from a boat: the action force is applied on the boat, and the reaction force pushes you to land. Parallelly, the action force pushes the boat backward.
- Slapping: when you slap someone, your hand feels pain and so does the cheek of the victim. The pain in the cheek is due to action force, and the pain in the palm is due to reaction force.
- Bouncing a ball: when a ball hits the ground, the ball applies an action force on the ground. The ground applies a reaction force and the ball bounces back.
- Flight motion of a bird: the wings of the bird push air downwards as an active force, and the air pushes the bird upwards as a reaction force.
- Swimming of a fish: the fish’s fins push water around it backward as an active force, and the water applies a reaction force by pushing the fins forward, thus the fish.
