Class 9 science notes Force and laws of motion

Topic covered : Types of inertia, Second law, third law, Importance of 3 Laws of Motion and much more Class 9 science notes Force and laws of motion

TYPES OF INERTIA

1. 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

1. 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.

1. 3rd law of motion signifies that forces in nature always occur in pairs.  A single isolated force is not possible.
2. 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.
3. 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.

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.

DERIVATION FOR LAW OF CONSERVATION OF MOMENTUM

Suppose two bodies a truck and car are moving in the same direction but with different speeds. 

 Let,

             Mass of the truck = M₁       

             Mass of the car = M₂

             Velocity of the truck = U₁

             Velocity of the car = U₂

             We know, momentum = mass x velocity

             Initial momentum of truck = M₁U₁

             Initial momentum of car = M₂U₂

            Total momentum = momentum of truck + car

                                               = M₁U₁ + M₂U₂                      ———- (1)

          Suppose after time t, car and the truck collide each other,

          Let,

                 Velocity of the truck after collision = V₁

                 Velocity of the car after collision = V₂

                 Final momentum of truck = M₁V₁

                 Final momentum of car = M₂ V₂

                Total momentum after collision =  M₁V₁ + M₂V₂

1. Acceleration of car (A₂) =  V₂ – U₂/T

                     Force F₁ of the truck acts on the car for time t,

                          F₁ = mass x acceleration

                                 = M₂ X [ V₂ – U₂/T ]

• Acceleration of truck (A₁) = V₁ – U₁/T

                     Force F₂ of the car reacts on the truck for time t,

                          F₂ = mass x acceleration

                               = M₁ X [ V₁ – U₁/T ]

The force F₁ exerted by the truck is the ‘action’ and the force F₂ exerted by the car is the ‘reaction’

According to Newton’s third law of motion, action and reaction are equal and opposite,

F₁ = – F₂ 

M₂ X [ V₂ – U₂/T ] = – M₁ X [ V₁ – U₁/T ]

                   M₁(V₁-U₁) = – [M₂ (V₂ – U₂)]

                    M₁ V₁ – M₁ U₁ = – M₂V₂ + M₂U₂

                    M₁V₁ + M₂V₂ = M₁U₁ + M₂U₂

Total momentum after collision = Total momentum before collision