Chapter -9  Force  &  Laws of Motion

   1.   Force:

Force may be defined as a pull or push which changes or tends to changes the state of rest or state of motion of a body.

•         If force is applied directly on a body then force is called contact force and if force is applied without actual contact from a distance then it is called action at a distance.

   2.  Effect Produced By  Force:

1. Force can change speed of an object:- 

 e.g.:- A ball thrown with a larger force will have larger speed and force  applied on breaks of a car makes car speed slow down.

2. Force can change direction of motion of an object:-

e.g.:- Force applied on the steering wheel of a car changes the direction of motion of car.

3. Force can change the shape of an object:-

            e.g.:- By pushing the rubber ball we can change its shape. 

Balanced forces & unbalanced forces

•         Balanced forces: 

Forces are said to be balanced forces if they cancel one another and their resultant force is zero.

•         Unbalanced forces: 

When two opposite forces acting on a body, move a body in the direction of the greater force or forces which brings motion in a body are called as unbalanced forces. 

1. Aristotle’s Fallacy: 

According to Aristotle’s Law of motion, an external force is necessary to keep a body moving with uniform velocity i.e. according to this law a body will not remains in motion without a external force. This was proved wrong by Galileo law of inertia.

2. Galileo’s Law of Inertia:

On the basis of a series of experiment performed by Galileo, he gave the law of inertia. According to this law, it is inability of a body to change the state of rest or uniform motion of a body without the help of any external force.

Question: 2 how is the inertia of a body measured?

Inertia of a body is measured by the mass of the body; greater is the amount of mass greater is the inertia of the body. e.g.:- It is easy to change the position of football than a stone of same size because the mass of football is smaller than the mass of the stone. It does not depend on the shape of the body.

Inertia: 
The inability of a material body by virtue of which it cannot change its state of rest or uniform motion is called inertia. Inertia means resistance to change.

Question:  Which of the following has more inertia:
(a) a rubber ball and a stone of the same size?
(b) a bicycle and a train?
(c) a five-rupees coin and a one-rupee coin?
Answer:
(a) A stone of the same size
(b) a train
(c) a five-rupees coin
As the mass of an object is a measure of its inertia, objects with more mass have more inertia. 

Different Types of Inertia:

1. Inertia of rest

2.  Inertia of motion

3.  Inertia of direction 

1. Inertia of rest: 

The inability of a body changes its state of rest called inertia of rest:- 

Why a person falls backward when bus suddenly starts moving forward? 

when bus starts moving forward then the lower part of the body starts moving forward while the upper part is in rest due to this the person falls backward. 

Question . Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.
Answer: When the tree’s branch is shaken vigorously the branch attains motion but the leaves stay at rest. Due to the inertia of rest, the leaves tend to remain in its position and hence detaches from the tree to fall down. 

2.Inertia of motion

The inability of a body changes its state of rest motion is called inertia of motion:-

•         Why a person falls backward when bus suddenly stops. 

This is due reason that when bus, suddenly stops then lower part of the body comes into rest while  the upper part is still in the motion due to this person falls forward. 

Question 4. Explain why it is dangerous to jump out of a moving bus.

Answer: While moving in a bus our body is in motion. On jumping out of a moving bus our feet touches the ground and come to rest. While the upper part of our body stays in motion and moves forward due to inertia of motion and hence we can fall in forward direction.
Hence, to avoid this we need to run forward in the direction of bus. 

3. Inertia of direction

The inability of a body changes itself its direction of motion is called inertia of direction 

Q. Why a person sitting inside the bus experience force acting away from the center of curved path when a bus takes a sharp turn?

Ans. This is due to reason that the body of person does not like to change its direction of motion.

Question:  how is the inertia of a body measured?  Inertia of a body is measured by the mass of the body; greater is the amount of mass greater is the inertia of the body.

 e.g.:- It is easy to change the position of football than a stone of same size because the mass of football is smaller than the mass of the stone. It does not depend on the shape of the body.

Momentum

The quantity of motion possessed by the body is called the momentum. It is equal to product of mass and velocity of the body.

   Or     

  Or   

Momentum is vector quantity. Its direction is same as that of velocity. The S.I. unit of momentum =  .

      Different cases of Momentum:

1. when two object each of mass  moves with velocity and  such that  then

 Or  

As        

Hence equal massive bodies having larger velocity will have larger momentum.

When two objects of masses  such that  moves with same velocity then

As   

Hence the two bodies having same velocities will have larger momentum which have larger mass.

3. When two bodies have equal linear momentum

Then      

Or   

Or  

If   

Thus velocities of the bodies are inversely proportional to masses of the bodies i.e. heavier body will have smaller velocity and smaller body will have larger velocity.

How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 ms^-2. 

Ans:   m=10kg ,  h=80cm= 0.8m , a= 10m/s^2  , u=0 

Momentum 

Newton’s Laws of Motion

Newton’s First Law of Motion: 

A body in rest will remain in rest or a body is in motion will remain in motion till any external force is applied on the body.

How Newton’s first law defines force? 

•         According to Newton’s first law, force is external agency which changes the state of rest or uniform motion of the body. Hence this law gives the qualitative definition of force.

•         Newton’s first law sometimes called law of inertia.

Question Using a horizontal force of 200 N, we intend to move a wooden cabinet across a floor at a constant velocity. What is the friction force that will be exerted on the cabinet? 

As the wooden cabinet moves across the floor at a constant velocity and the force applied is 200 N. Hence the frictional force that will be exerted on the cabinet will be less than 200 N. 

Newton’s Laws of Motion

Newton’s First Law of Motion: 

A body in rest will remain in rest or a body is in motion will remain in motion till any external force is applied on the body.

How Newton’s first law defines force? 

•         According to Newton’s first law, force is external agency which changes the state of rest or uniform motion of the body. Hence this law gives the qualitative definition of force.

•         Newton’s first law sometimes called law of inertia.

Newton’s Second Law of Motion: 

According to Newton’s second law of motion, the rate of change of linear momentum is directly proportional to applied force.

Mathematically

or     ()

Or 

Or 

Or 

Where

Force is a vector quantity. Its dimensional formula is 

Unit of Force: 

There are two types of unit of Force

1.                       Absolute Unit of Force:

 An absolute unit of force is defined as the force which produces unit acceleration in unit mass of a body.

In S.I. absolute unit of force is Newton

 ()

 In absolute unit of force is dyne (1 dyne)

2.                   Gravitational Units of Force:

A gravitational unit of force is defined as the force which produces   (acceleration on due to gravity) acceleration in a body of unit mass.

In S.I. the gravitational unit of force is Kilogram weight  or Kilogram force 

In  the gravitational unit of force is gram weight  or gram force 

Relation between Newton and dyne

Or 

Difference between Gravitational unit and absolute unit of force:

     The absolute units of force remains the same throughout the universe but the Gravitational unit depends upon  so changes from place to place.

     A gravitational unit is  times the corresponding absolute unit. Gravitational unit is also called weight or practical unit of force.

Question.  An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of 1.7 ms^-2? 

Ans:  ,   ,    

The force between the vehicle and road is

=-2550N

Question . A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 tones (Hint : 1 tone = 1000 kg). 

Ans:      ,

        ,  

Question.  A stone of 1kg is thrown with a velocity of 20 ms~1 across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice? 

Ans:      ,   

     ,  

So  

1.                     Newton’s Third Law of Motion:

It states that to every action, there is always an equal and opposite reaction.

Suppose  is the amount of force exerted by body   on body

  Is the amount of force on   due to  

then from Newton’s Third law of motion

I.e. Force on 

e.g.: During swimming a person pushes water back word then the water pushes person in forward direction.

     Here Newton’s third law shows that a single force cannot exist in nature, the force exists in pairs.

     Newton’s third law of motion is applicable irrespective of the nature of the forces.

     Action and reaction always acts on the different bodies.

     The force of action and reaction cannot cancel each other because act on different bodies.

     No action act occurs in the absence of reaction.

Illustrations of Newton’s Third Law of Motion:

•                      A book kept on table exert a force  due to  weight on the table in down ward direction  due to which a equal and opposite force is Act on book due to table in upward direction. Hence both remain in equilibrium.
•               While walking, we press the ground in backward direction, them the ground exerts an equal and opposite force on us due to which we walks.
•           It is difficult to walk on slippery ground or sand because we are unable to exert force due to which reaction is not sufficient to walk.

Question . If action is always equal to the reaction, explain how a horse can pull a cart?
Answer: The third law of motion states that action is always equal to the reaction but they act on two different bodies.
In this case the horse exerts a force on the ground with its feet while walking, the ground exerts an equal and opposite force on the feet of the horse, which enables the horse to move forward and the cart is pulled by the horse. 

Law of Conservation of Linear Momentum

According to law of conservation of linear momentum if there is no any external force is acting on an isolated system then the linear momentum of the system remains constant.

If  is the external force acting on the system

then    =  

For isolated system

 F = 0   

Thus in absence of external force the linear momentum of isolated system remains constant.

Application of Law of  Conservation of Linear Momentum:

•         While firing a bullet, the gun should be hold tight to the shoulder because as we know the recoiling gun can hit the shoulder. If the gun is hold tight to the body then gun and body becomes a isolated system of large mass and recoil velocity becomes small.

•          Rocket and Jet planes work on the principle of conservation of linear momentum:-In rockets and Jet planes the fuels impart momentum in downward direction due to which rocket get a momentum in upward direction.

•         When a men jumps out of a boat to the shore, the boat moves slightly away from the shore becomes initially total momentum of both is zero, but during jumping man acquire a momentum in forward direction due to which boat acquire momentum  in backward direction so it happens.

• Recoil of gun: suppose a bullet of mass m is fired   from a gun of mass M. initially both are in rest but after firing suppose v is the velocity of bullet and V is the velocity of gun. Then from conservation of linear momentum

Or 

Or 

Here   sign show that both bullet and gun moves in opposite direction and clearly

. So bullet moves faster from heavy gun. 

Question: 17 A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 ms^-1 what is the recoil speed of the gun? 
Answer:  m = 0.02 kg, M = 100 kg, v = 80 ms^-1, V =?

 So        
here negative sign indicates that the gun moves in a direction opposite to the direction of motion of bullet.

Question. From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m/s. Calculate the initial recoil velocity of the rifle. 

Mass of rifle 

Mass of bullet 

Velocity of bullet = 

Recoil velocity of rifle =?

According to law of conservation of momentum

= 

Question . An object of mass 100 kg is accelerated uniformly from a velocity of 5 ms^-1 to 8 ms^-1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Ans:      ,    

    ,      

Question . Class V students were playing cricket with the cork hall in the school campus. Charu a senior student told them about the accidents that can occur due to cork ball in the campus and also advised them to bring soft cosco ball to play the game.
(a) Why it was safe to play with soft ball and not with hard cork ball?
(b) A player pulls his hands backwards after holding the ball shot at high speed. Why?
(c) What value of Charu is seen in this act?
Answer:
(a) The soft ball will have less inertia as compared to the heavy ball and it would not hurt the players.
(b) By pulling the hand backwards it reduces the force exerted by the ball on hands.
(c) Charu showed the value of being responsible and helpful by nature. 

Question. Saksham saw his karate expert friend breaking a slate. He tried to break the slate but Saksham’s friend stopped him from doing so and told him that it would hurt; one needs lot of practice in doing so.
(a) How can a karate expert break the slate without any injury to his hand?
(b) What is Newton’s third law of motion?
(c) What value of Saksham’s friend, is seen in the above case?
Answer:
(a) A karate player applies the blow with large velocity in a very short interval of time on the slate, therefore large force is exerted on the slate and it breaks.
(b) To every action there is an equal and opposite reaction, both act on different bodies.
Saksham’s friend showed the value of being responsible and caring friend.