Force and laws of motion notes (Part 2)

Description of Balanced and Unbalanced Forces

Notice when the diver jumps down on a diving board. The board springs back and forces the diver into the air. The action force exerted on the board by the diver causes a reaction force by the board equal and opposite to the force exerted by the diving board. These interacting forces are unbalanced and differ from the balanced forces. No motion occurs when the forces are balanced. If the diver stands quietly on the diving board, all the forces on the diver and the board are balanced. Neither the diver not the board moves.

GALILEO’S OBSERVATIONS

Galileo arrived at some important conclusion about motion of objects by observing their motion on an inclined plane.

Galileo observed that when a small marble ball rolls down an ideal, frictionless plane inclined on both sides.

Galileo concluded that an unbalanced external force is required to initiate the motion from state of rest, but no unbalanced net force is needed to sustain the uniform motion, objects move with a constant speed along a straight line when no force acts on them.

Newton`s laws of motion

Sir Isaac Newton was one of the greatest scientists. He was born in England. He was born in the same year that Galileo died. Newton studied in Trinity College, Cambridge. Newton worked his way in college. His work laid the foundations for modern science. While Newton was in college, he had new ideas about motion and state’s three laws of motion.

Newton’s laws of motion are used to define the concept of the force and for describing the motion and also used as the basis of classical mechanics.

First law

According to this law, a body continues to be in its state of rest or of uniform motion along a straight line, unless it is acted upon by some external force to change its state.

The law consists of three parts:

A body at rest continues to remain at rest until an external force is applied on the body to move it.
A body in uniform motion continues to move uniformly unless an external force is applied to change its speed.
A body moving along a straight line will continue to move along the same straight line unless an external force is applied on the body to change its direction of motion.

NEWTON’S FIRST LAW DEFINE FORCE

According to Newton’s first law of motion, a body continues to be in a state of rest or in a state of uniform motion along a straight line; unless an external force is applied on the body to change the state. This means that force applied on a body alone can change its state of rest or state of uniform motion along a straight line; we may define force as an external effort in the form of a push or pull which

Newton’s first law of motion is also called as Galileo’s law of inertia. This law states that everybody has some inertia.
Inertia is that property of body due to which it tries to remain in its initial state until the force is applied. Greater the inertia of body, greater will be the force required to change its state. Heavier object has more inertia than lighter objects. Such as: cricket ball has more inertia than rubber ball of same size. Thus, Newton’s first law of motion defines inertia and is rightly called the law of Inertia.

TYPES OF INERTIA

Inertia of rest: It is the inability of a body to change by itself, its state of rest. This means a body at rest remains at rest remains at rest and cannot start moving on its own. Rather, a body at rest opposes the forces which try to move it.

Such as: When a bus or train starts suddenly, the person sitting inside tends to fall backwards. This is because lower part of his body starts moving with the bus or train, but the upper part of the body tries to remain at rest, due to inertia of rest

Inertia of motion: It is the inability of a body to change by itself, its state of motion. This means a body in motion remains in motion and cannot stop on its own. Rather, a body in motion opposes the forces which try to stop it.

Such as: When a bus or train stops suddenly, a person sitting inside tends to fall forward. This is because lover part of his body comes to rest with the bus or train, but the upper part of his body tends to continue its motion, due to inertia of motion.

Inertia of direction: It is the inability of a body to change by itself its direction of motion, a body moving along a straight line will continue to move along the same direction unless some external force compels it to change the direction of motion. Rather, a body opposes the forces that try to change its direction of motion.

Such as: When a car rounds a curve suddenly, a person sitting inside is thrown outwards. This is because while the car turns, the person tries to maintain his original direction of motion due to inertia of direction.

Second law

According to this law, the rate of change of linear momentum of body is directly proportional to the external force applied on the body and this change takes place always in direction of force applied.

F (mv – mu)/t

F = m (v – u)/t

F = kma

F = ma (here k = 1 for SI UNIT)

Application of second law

Catching a cricket ball

To catch a fast cricket ball, a player pulls his hands backwards to prevent injury to his hands. By doing so, the player increases the time during which high velocity of the cricket ball reduces to zero. Thus the acceleration of the ball a =(v-u)/t is decreased, and therefore, the impact of catching the fast ball (F= ma) is reduced, the player has to apply a smaller force against the ball in order to stop it . The ball, in turn, exerts a smaller force on his hands and the hands are not injured.

High Jump

In the athletic event High Jump, the athletes are made to fall either on a cushioned bed or on a sand bed. This is done to avoid injury to the athlete. Falling on a cushioned bed or on a sand bed will increase the time during which high velocity of the athlete would be reduced to zero. This would decrease the rate of change of momentum of the athlete and hence the force on the athlete. The injury to the athlete is thus avoided.

Use of seat belts in cars

All the cars these days are provided with seat belts for the passengers, which are rightly called safety belts. The purpose of seat belts is to prevent injuries to the passengers in case of an accident or in case of sudden application of brakes. In both the case, the large momentum of the car reduces to zero in a very short interval of time resulting in the development of a large force causing injuries. The stretchable safety belts worn by the passengers of the car exert a force on their body and make the forward motion slower. The time taken by the passengers to fall forward increases. Therefore, rate of change of momentum of passengers is reduced. Hence, the stopping force acting on the passengers is reduced. They may not get injuries at all or they may get away with minor injuries.

NEWTON’S FIRST LAW OF MOTION IS A SPECIAL CASE OF NEWTON’S SECOND LAW

The body will continue to move with the same uniform velocity, u throughout the time t, when no external force is applied on the body. Further, if u=0, then v will also be zero. It means if the object is initially at rest, it will continue to be at rest, when no external force is applied on the body.

Third law

According to this law, to every action, there is always an equal and opposite reaction i.e. the forces of action and reaction are always equal and opposite.

3rd law of motion signifies that forces in nature always occur in pairs. A single isolated force is not possible.
Note Force of action and force of reaction always act on different bodies and hence they never cancel each other. So, each force produces its own effect.
3rd law of motion is applicable only when the bodies are at rest or they are in motion.

Walking

To walk on the ground, we push the ground backwards with our foot. As a reaction, the ground pushes our foot forward with the same force. It is forward reaction force of the ground that enables us to walk forward.

Walking becomes difficult when the ground is slippery or it is covered with snow or send. This is the force of action. The water pushes the swimmer forward with the same force (of reaction).

Recoiling of gun

When a bullet is fired from a gun, the gun recoils, the gun moves backwards through a small distance, giving jerk to the shoulder of the gun man. This is because on firing, the gun exerts some force on the bullet in forward direction. In turn, the bullet exerts an equal force on the gun reaction in the backward direction. The distance moved by the gun is small because gun is much heavier than the bullet.

Importance of 3 Laws of Motion

3 laws of motion form the backbone of mechanical science, and provide a deep insight to it. These 3 laws of motion are the most basic laws and holds true for all the cases.

Impulse

The effect of a force not only depends on its magnitude but also on the time for which the force acts. When a large force acts for a very short time, one more important parameter comes into play.

Impulse = Force X Time

I = F X T

Applications of impulse

While catching a moving cricket ball, a player lowers his hands after catching the ball.
Automobiles are provided with spring systems to reduce the damage to the vehicle when it receives a shock.
A man falling from a certain height gets injured more severely when he falls on concrete when compared to his falling on sand.
It is more difficult to catch a cricket ball when compared to a tennis ball.

Momentum

Momentum is another vector quantity which has the same direction as that of velocity. Momentum is a property of the body possessed by virtue of its mass and velocity. It is the product of mass of the body and its velocity.

Momentum = mass × velocity

When two bodies, a heavy one and a light one, are acted upon by the same force for the same time, the light body builds up a higher velocity than the heavy one. But the momentum they gain is the same in both cases. This important connection between force and momentum was recognised by Sir Isaac Newton and expressed by him in a second law of motion.
If a body is at rest, its velocity is zero and hence its momentum is also zero.
Momentum is a vector quantity.
SI unit is kg m/s.

Definition of law of conservation of momentum

Law of conservation of momentum is stated as when any two bodies act upon one another, their total momentum remains constant provided no external forces are acting. In other words, we can say that whenever one body gains momentum, then some other body lose an equal amount of momentum, that is, momentum is never created or destroyed. Therefore, law of conservation of momentum is also known as principle of conservation of momentum.

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