Exercise

(i) Inertia:

The inertia of a body is its property due to which it any change in its state of rest or motion.

Galileo related the inertia of a body with its mass; the greater is the mass of a body greater its inertia.

Inertia $\propto$ mass of the body

(ii) Momentum:

The momentum of a body is the quantity of motion it possesses due to its mass and velocity.

The momentum P of a body is given by the product of its mass m and velocity v. Thus

P = mv

Momentum is a vector quantity. Its SI unit is $kgms^{-1}$

The momentum of a system depends on its mass and velocity.

(iii) Force:

A force moves or tends to move stops or tends to stop the motion of a body. The force can also change the direction of motion of a body.

F = ma

Si unit of a force in the newton.

Note:  A force can also change the shape or size of a body on which It acts.

(iv) Force of friction:

Friction:

The force, that opposes the motion of moving objects is called friction.

Friction is a force that comes into action as soon as the body is pushed or pulled over a surface.

Factor on which friction depends:

In the case of solids, the force of friction between two bodies depends upon many factors such as the nature of the two surfaces in contact and the pressing force between them.

(v) Centripetal force:

Centripetal force is a force that keeps a body moving in a circle.

The centre-seeking force is called the centripetal force. It keeps the body moving in a circle. Centripetal force always acts perpendicular to the motion of the body

$Fc =\frac{mv^2}{r}$ 

Mass and weight:

Action and reaction:

Newton’s third law of motion deals with the reaction of a body when a force act on it. Let body A exerts a force on another body B. Body B reacts against this force and exerts a force on body A. The force exerted by body A on B is the action force whereas the force exerted by body B on A is called the reaction force.

Note that action and reaction forces act on different bodies.

Example:

Action and reaction forces act on different objects and in opposite directions. For example, if the rocket pushes the gas out, the gas pushes back against the missile. The forces on different objects (the gas, and the rocket, respectively), and in opposite direction.

Sliding friction:

A force between the sliding objects which opposes the relative motion between them is called sliding friction.

Rolling friction:

Rolling friction is the force of friction between a rolling body and a surface over which it rolls. Rolling friction is lesser than the sliding friction.

Inertia:

The inertia of a body is its property due to which it any change in its state of rest or motion.

Galileo related the inertia of a body with its mass, the greater the mass of a body greater its inertia.

Inertia ∝   mass of the body

Experiment:

Take a glass and cover it with a piece of cardboard. Place a coin on the cardboard. Now kick the card horizontally, with a jerk of your finger.

The coin does not move with the cardboard due to inertia. The coin falls into the glass as the card flicks away.

Experiment:

Cut a strip of paper. Place it on the table. Stack a few coins at one end. Pull out the paper strip under the coins with a jerk.       

Coins stacked over remain undisturbed on pulling the paper strip quickly

Coins stacked over remain undisturbed on pulling the paper strip quickly due to inertia.

Because of the friction force due to air acting on the upper part of the body the person travelingling on the roof of running bus try to turn over which is dangerous for the passenger while traveling on the lower portion remains at rest w.r.t the roof of the bus due to inertia.

An inward net force is required to make a turn in a circle. This inward net forc+e requirement is known as a centripetal force requirement. In the absence of any net force, an object in motion(such as a passenger) continues in motion in a straight line at a constant speed. Due to the absence of necessary centripetal force, a passenger moves outward when a bus takes a turn.

Force and momentum:

         Consider a body of mass m moving with initial velocity vi, let a force acts on the body which produces an acceleration an in it. This changes the velocity of the body. Let its final velocity after time t become vf. If pi and pf be the initial momentum and final momentum of the body related to initial and final velocities respectively then

                      Pi=mvi

                      Pf=mvf

Or 

           Change in momentum = final momentum – initial momentum

Or

                 P=mv

           Thus the rate of change in momentum is given by:

$\frac{pf \:, \: pi}{t} =\frac{mvf \: - mvi}{t}$

              Since $\frac{vf \:- \: vi}{t}$ is the rate of change of velocity equal to the acceleration a produced by the force F

$\frac{pf \:, \: pi}{t}$ = ma

According to Newton’s second law of motion,

           F= ma

Or $\frac{pf \:, \: pi}{t}$ = F …………… (I)

Equation (I) also defines force and states Newton’s second law of motion as:

When a force acts on a body, it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.

Tension in the rope and its force pull equally at both ends if no forces act on the rope except its ends, and the rope itself is in equilibrium, then the tension is the same throughout the rope.

         ∑F = 0 

Action and reactions (forces acting on an object) are always equal and opposite

When the object is at equilibrium. When we apply external force to pull, push and twist, the equilibrium is disturbed means now the magnitude of action (force provided by you) and reaction (force provided by the objects) are not equal. That is why it is possible to twist, pull, move and push the object in the direction of applied force.

First, when the horse pulls o the cart, the cart exerts an equal but opposite reaction on the horse, the action and reaction. If this was the only force in action then the force and cart would indeed remain stationary.

However, there is another force between the force and the ground. The horse’s hooves press down on the ground and the ground pushes back on the horse.

If the reaction force of the ground is greater than the reaction force of the cart on the horse, then the horse will move forward. The cart will move forward when the force exerted on it by the horse is greater than the frictional force between the cart and the ground.

Law of conservation of momentum:

The momentum of an isolated system of two or, more two interacting bodies remains constant.

Example:

Consider the example of an air-filled balloon as described under the third law of motion. In this case, the balloon and the air inside it form a system. Before releasing the balloon, the system was at rest and hence the initial momentum of the system was zero. As soon as the balloon is set free, air escapes out of it with some velocity. The air coming out of it possesses momentum. To conserve momentum, the balloon moves in a direction opposite to that of air rushing out.

Explanation: 

Law of conservation of momentum applies to all objects in the universe. A rocket and jet engine are taking off. The recoil of a gun is an example that demonstrates the importance of the law of conservation of momentum.

Case I:

Consider an isolated system of two spheres of masses m₁ and m₂. They are moving in a straight line with initial velocities u₁ and u₂ respectively such that u₁ is greater than u₂. The sphere of mass m₁ approaches the sphere of mass m₂ as they mThe initial

The initial momentum of mass m₁ =m₁u₁

The initial momentum of mass m₂ =m₂u₂

The total initial momentum of the system before collision = m₁u₁+m2u2 ………(i)

Case II:

After sometimes mass m₁ hit m₂ with some force. According to newton's third law of motion, m₂ exerts an equal and opposite reaction force on m₁. Let their velocities become v₁ and v₂ respectively after the collision. Then

Final momentum of mass m₁ = m₁u₁

Final momentum of mass m₂ = m₂u₂

Total final momentum of the system before collision = m₁u₁+m₂u₂ ………(ii)

According to the Law of conservation of momentum:

 [ total initial momentum of the system before collison] = [ total initial momentum of the system before system]

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂......... (iii)

Equation (iii) shows that the momentum of an isolated system before and after collisions remains the same which is the law of conservation of momentum. The Law of conservation of momentum is important and has vast applications.

Recoils of gun:

         Consider a system of gun and a bullet. Before firing the gun, both the gun and build are at rest, so the total momentum of the system is zero. As the gun is fired, a bullet shoots out the gun and acquires momentum. To conserve the momentum of the system, the gun recoils.

            According to the law of conservation of momentum, the total momentum of the gun and the bullet will also be zero after the gun is fired. Let m be the mass of the gun and v be its velocity on firing the gun, M be the mass of the gun and V be the velocity with which it recoils. Thus the total momentum of the gun and the bullet after the gun is fired will be.

[total momentum of the gun and the bullet after the un is fired]= MV + mv……(i)

According to the law of conservation of momentum,

 (total momentum of the gun and the bullet=  (total momentum of the gun and the after the gun is fired)  bullet before the gun is fired)

       MV+ mv=0

Or            MV = -mv

Hence V=$\frac{m}{M}v$ ......(ii)

Equation (ii) gives the velocity V of the gun. The negative sign indicates that the velocity of the gun is opposite to the velocity of the bullet i.e, the gun recoils. Since the mass of the gun is much larger than the bullet, therefore the recoil is much smaller than the velocity of the bullet.

Friction is needed to walk on the ground.

1. It is risky to run on a wet floor with shoes that have smooth soles. Athletes use special shoes that have extraordinary ground grip. Such shoes prevent them from slipping while running fast.
2. To stop our bicycle we will apply brakes. The rubber pads pressed against the rims provide friction. It is the friction that stops the bicycle.

The friction can be reduced by lubricating the sliding surfaces. The oil helps slick(polish) the two surfaces so that the molecular surfaces become easier to side on with less friction.

Methods of reducing friction:

1. The friction can be reduced by making the sliding surfaces smooth.
2. The friction can be reduced by making the fast-moving objects streamlined. shape (fish shape) such as cars, airplanes, etc. this causes the smooth flow of air and thus minimizes air resistance at high speeds.
3. The friction can be reduced by using ball bearings or roller bearings because the rolling friction is lesser than the sliding friction.
4. The friction can be reduced by lubricating the sliding surfaces.

DO YOU KNOW

Friction is highly desirable when climbing up a hill.

Sliding friction:

 A force between the sliding objects which opposes the relative motion between them is called sliding friction.

Rolling friction:

Rolling friction is the force of friction between the rolling body and the surface over which it rolls. Rolling friction is lesser than the sliding friction.

Explanation:

When a certain body rolls over the surface of another body, it has contact with the surface only at a single point. As there is no relative motion between the two bodies at this point, therefore sliding friction is zero. However, practically the wheel is compressed a little temporarily at the contact point of the two surfaces under pressure. Because of that little sliding friction, rolling friction is produced.

But when a body moves over the surface of another body, there is relative motion between the two surfaces, thus, friction has some maximum value. That is why the rolling friction is less than sliding friction. The rolling friction is 100 times less than sliding friction.

(i) Tension in a string:

“the force exerted by a string when it is subjected to pull is called tension in the string”

If a person is holding a block of weight W attached to the end of a string, a force is experienced by him. This force is known as Tension. When the body is at rest, the magnitude of tension is equal to the weight of the body suspended by the string Tension and the weight acts in the opposite direction.

Unit of tension:                                                                           

In S.I. system: newton

In C.G.S. system: dyne

In the F.P.S. system: the pound

(ii) Braking force:

Friction between a rotating component (the drum or disc) and a stationary force is called braking force.

1. The diameter of the disc
2. The friction material
3. The size of the pad friction face
4. The force used to clamp the pads onto the disc
5. The greater the diameter of the disc, the further from the centre of the wheel the braking force can be applied. This, in turn, will generate a greater force, or torque, on the disc.

(iii) Seatbelts:

In case of an accident, a person not wearing a seatbelt will continue moving until stopped by something before him, This something may be a windscreen another passenger or the back of the seat in front of him/her. Seatbelts are useful in two ways.

1. They provide an external force to a person wearing a seatbelt.
2. additional time is required for stretching seatbelts. This prolongs the stopping time for momentum to change and reduces the effect of collision.

(iv) Banking of roads:

The curvature of the road must be inclined to control the Centrifugal force of the Vehicle.

Banking of road means to make the road slide towards the centre of curvature with an angle. It is helpful because the velocity of the car is more or there is less friction between the tyres and the road which reduces the danger of the car moving out of the circular track. 

Explanation:

When a car takes a turn, the centripetal force is needed to keep it on its curved track. The friction between the tyres and the road provides the necessary centripetal force. The car would skid if the force of friction between the tyres and the road is not sufficient enough particularly when the roads are wet. This problem is solved by the banking of curved roads.

(v) Cream separator:                

Most modern plants use a separator to control the fact contents of various products. A separator is a high-speed spinner. It acts on the same principle as centrifuge machines. The bowl spins at a very high speed causing the heavier contents of milk to move outward in the bowl pushing the lighter contents inward towards the spinning axis

Cream or butterfat is lighter than other components in milk. Therefore, skim milk, which is denser than cream is collected at the outer wall of the bowl. The lighter part (cream) is pushed towards the centre from where it is collected through a pipe.

The limiting force of friction:

       the maximum value of friction is known as the force limiting friction(Fs). It depends on the normal reaction (pressing force) between the two surfaces in contact Fs=µR

Skidding of vehicles:

       Skids usually occur while driving the clutch is suddenly engaged or disengaged, the brakes are applied too hard, the vehicle accelerates too quickly or the steering wheel is turned too sharply. These can create a situation where power, either too much or too little, causes a loss of traction.

          If the brakes are applied too strongly, the wheels of the car will lock up (stop turning) and the car will skid due to its large momentum. It will lose its directional control which may result in an accident. To reduce the chance of skidding, it is advisable not to apply brakes too hard that lock up their rolling motion, especially at high speed.

Mini Exercise:

1. In which case do you need smaller force and why?

Ans:  In the case of rolling friction we need a smaller force. Because the rolling friction is lesser than sliding friction.

2. In which case it is easy for the tire to roll over?

1. Rough ground
2. Smooth ground

Ans:  On the smooth ground, it is easy for the tire to roll over due to less friction.

If there was no friction then we could not walk, we would keep slipping. Nothing would be steady on the ground, many things would be just sliding and sliding.

The dryer of a washing machine is a basket spinner. They have a perforated wall having large numbers of fine holes in the cylindrical rotor. The lid of the speed, the water from wet clothes is forced out through these holes due to lack of centripetal force.