9FORCE AND LAWS OF MOTION

Chapter

In our everyday life we observe that someeffort is required to put a stationary

objectinto motion or to stop a moving object.

Weordinarily experience this as a muscular

effortand say that we must push or hit or pull

onan object to change its state of motion.

Theconcept of force is based on this push, hit

orpull.

A force can be seen.A force can be judged only by the effect which it can produce in various bodies (objects) around us.A force can produce the following effects:

1. A force can move a stationary body.2. A force can stop a moving body3. A force can change the speed of the moving body4. A force can change the direction of the moving body5. A force can change the shape (and size) of a body

Effect of force

*If the resultant of all the force acting on a body is zero , the force are called the balanced force.*Please note that the force of our push on the book is balanced by force of friction, and the force of gravity is balanced by the force of reaction of the ground.

Balanced Force

If the resultant of all force acting on a body is not zero, the force are called unbalanced forcePlease note that when an unbalanced force acts on a body, it produce motion in the body. Another point is to be noted that an unbalanced force can also stops a moving body.

Unbalanced Force

Newton has given three laws to describe the motion of bodies.These laws are known as Newton’s laws of motion. The newton’s laws of motion give a precise definition of force and establish a relationship between the force applied on the body and the state of motion acquired by it. We will now discuss these law’s of motion and consider some of their important application. Let us start with first law of motion………

NEWTON’S LAWS OF MOTION

Some of the bodies (or object) around us are at rest that is they are stationary ,whereas other are in motion. Newton's first law describe the behavior of such bodies which are in a state of rest or of uniform motion in a straight line. According to the Newton’s first law of motion :*A body at rest will remain at rest, and a body in motion will continue in motion in a straight with uniform speed, unless it is compelled by an external force to change its state of rest or of uniform motion.*It should be noted that Newton’s first law of motion is also some times called Galileo’s laws of motion

NEWTON’S FIRST LAW OF MOTION

Let us take some examples to make the first law of motion more clear. Suppose a book is lying on the table. It is at rest. The book will not move by itself that is, it cannot change its position of rest by itself. It can change its state of rest only when compelled by external force that is our hands,that is, when we lift the book from the table. Thus, the position of rest of the book has been changed by external force of our hand. And this observation support the first part of the first law of motion. Before external force After external force

*The tendency of a body to remain at rest (stationary) or, if moving, to continue moving in a straight line, is called inertia.*Inertia is that property of a body due to which it resists a change in its state of rest or of uniform motion.*Greater the inertia of a body, greater will be the force required to bring a change in its state of rest or of uniform motion.*In fact mass is measure of the inertia of a body*If the body has more mass, it has more inertia *That is, heavier object has more inertia than lighter objects*For example: 1.the stone has more inertia than a rubber ball 2.A cricket ball has more inertia than a rubber ball of the same size.

Inertia and mass

From the above discussion we conclude that to overcome the inertia and make a body move from rest , we must apply an external force.we can illustrate the Newton’s first law of motion or property of inertia of a body with simple experiment describe below:

Take an empty glass tumbler and put it on a table. Cover the tumbler by a stiff playing card over its mouth. Now place a coin on the card as shown in fig. Give a sudden, sharp horizontal flick to the card with a finger. The card moves along the direction of flick but coin is found to fall vertically into the glass tumbler due to its inertia of rest.

*We will now consider the second part of the first laws of motion which say that a body in uniform motion will continue to move unless a force compels it to change its state of uniform motion in a straight line.

*At first site it would be appear wrong that a body moving at uniform speed in a straight line will continue to move for ever without coming to rest. Because if we stop pedaling a bicycle , which is moving at a uniform speed, the bicycle does not go on moving for ever, it comes to rest after some time.

*The moving bicycle has been compelled to change its state of uniform motion by external force of air resistance and friction. If there were no air resistance and no friction to oppose the motion of a bicycle, then according to the first law of motion a moving bicycle will go on motion for ever. It will not stop by itself.

In order to understand the Newton’s second law of motion, we should first know the meaning of term momentum:We know that a cricket ball is much heavier than a tennis ball. suppose we throw a cricket ball and a tennis ball, both with the same velocity. It is found that more force is required to stop the cricket ball (which has more mass) and less force is required to stop the tennis ball (which has less mass).*so we conclude that force required to stop the moving ball is directly proportional to its mass

MOMENTUM

Now if we throw two cricket balls of the same size at different speed or velocity. It will be found that more force is required to stop the cricket ball which is moving with higher velocity and less force is required to stop the cricket ball moving with lower velocity*So we conclude that the force required to stop a moving body is directly proportional to its mass.

more force required to stop the ball moving with higher velocity

Less force required to stop the ball moving with lower velocity

Thus, the quantity of motion in a body depends on the mass and velocity of the body. This gives the other term known as ‘’Momentum’’. The momentum on a body is defined as product of mass and velocity.Thus, Momentum = mass x velocityOr, p = m x v where p = momentum m = mass of the body v = velocity (or speed) of the body *It is clear that if a body at rest its velocity is zero and hence its momentum is also zero.*Now mass is measured in kg and velocity is measured in m/sSo the SI unit of momentum is kg.m/s or kg.ms-1

When two bodies a heavy one and a light one, are acted upon the same force for the same time, the light body attains a high velocity than the heavy one. But the momentum gained by both the body is the same the link between force and momentum is expressed in Newton’s second law of motion.*According to the Newton’s second law of motion: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force act

NEWTON’S SECOND LAW OF MOTION

The rate of change of momentum of a body can be obtain by dividing ‘’change in momentum” by time ‘’taken for this change’’*So Newton’s second law of motion can be expressed as: change in momentum Time taken for change

Force ∝

Consider a body of mass m having initial velocity u. the initial momentum of the body will be mu. Suppose a force f acts on this body for time t and causes the final velocity to become v. The final momentum of the body will be mv. Now, the change in momentum of this body is mv-mu and time taken for change is t. so according to the newton's law of motion: mv-mu or f ∝ m(v-u) t tBut v-u represent change in velocity which is known as acceleration.

tso by wring a in the above relation we get : f ∝ m x a Thus, f = k x m x a (k constant) force = mass x acceleration

f ∝

Thus Newton’s second law of motion gives relationship between force and acceleration. when a force acts on a body it produces acceleration in the body, the acceleration produce may be positive or negative.*Acceleration produce in the body is directly proportional to the force acting on it and inversely proportional to the mass of the body.*if the mass of the body is doubled its acceleration will be halved. And if mass is halved then the acceleration will get doubled (provided the force remain the same)*The SI unit of force is Newton which is denoted by N. a newton is that force which when acting on a body of mass 1 kg produces an acceleration 1m/s in it. We have just seen that: f = m x a 1 newton = 1kg x 1 m/s2

2

Sample problem : calculate the force required to impart to a car velocity of 30 m/s in 10 seconds starting from rest. The mass of the car is 1500 kg .Solution : here mass, m= 1500 kgLet us calculate the value of acceleration using the first equation of motion: Now, initial velocity u = 0 final velocity v = 30 m/s time taken t = 10sNow putting these value in the equation : v = u + at 30 = 0 + a x 10 10a = 30c a = 30 m/s2 acceleration, a = 3 m/s2 10

Now, putting m = 1500kg a = 3m/s2 in equation:

we get f = m x a f = 1500 x 3N f= 4500N

Thus the force required in this case is of 4500 newtons.

When a body exerts a force on the wall, the exerts an equal and opposite force on the body. This is just illustration of Newton’s third law of motion.*According to the newton’s third law of motion : whenever one body exerts a force on another body, the second body exerts equal and opposite force on the first 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.

NEWTON’S THIRD LAW OF MOTION

To every action there is an equal and opposite reaction. Action and reaction acts on two different bodies but they act simultaneously. we will now describe a simple experiment to prove the Newton’s third law of motion, that is, to prove that action and reaction are always equal and opposite.*We take two similar spring balance A and B and join them hook to hook as shown in figure. The another end of spring balance B is attached to hook H fixed in a wall. Let pull the free end of the spring balance A to right side of our hand. We find that both the

H

Reaction 4 N

Action 4 N

spring balances shows the same reading. For example, in figure, both the spring balances show the same reading of 4N. This can be explained as follows:When we pull the balance B, It exerts a force of 4N on the balance A. The balance A pulls the balance B with equal force of 4N,but in opposite direction.

*We conclude that the action and reaction forces are equal in magnitude. In the figure we find that the action force is acting toward the east and the reaction force is acting toward west. Thus action and reaction forces act in opposite directions.

Action and reaction acts on two different bodies.

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

According to the laws of conservation of momentum: When one or more bodies act upon one another, their total momentum remains constant (or conserved ) provided no external force are acting. The law of conservation of momentum means that whenever one body gains momentum, then some other body must loose an equal amount of momentum. This law can also be stated as: Momentum is never created or destroyed.

CONSERVATION OF MOMENTUM

Schoolboy 'genius' solves puzzles posed by Sir Isaac Newton that have baffled mathematicians for 350 years

Shouryya Ray put the historical breakthrough down to 'schoolboy naivety'

Modest Shouryya began solving complicated equations as a six year old but says he's no genius

A 16-year-old has managed to crack puzzles which have baffled the world of maths for more than 350 years.

Shouryya Ray has been hailed a genius after working out the problems set by Sir Isaac Newton. 

The schoolboy, from Dresden, Germany, solved two fundamental particle dynamics theories which physicists have previously been able to calculate only by using powerful computers.

His solutions mean that scientists can now calculate the flight path of a thrown ball and then predict how it will hit and bounce off a wall.Shouryya only came across the problems during a school trip to Dresden University where professors claimed they were uncrack able.'I just asked myself, 'Why not?',' explained Shouryya.'I think it was just schoolboy naivety. I didn't believe there couldn't be a solution,' he added.

MADE BY MD ZAKARIA AND MEMBERS OF OUR GROUP :

1. MD ZAKARIA2. VIKASH KUMAR SHARMA 3. AMIT CHAUHAN4. PUSHKAR SINGH JANTWNAL5. ANKIT TIWARI