Table of Contents

Notes

 

Q1. Define dynamics?

Ans: Dynamics:

The branch of mechanics that deals with the study of the motion of an object and the cause of its motion is called dynamics.

 

 

 

Q2. Define Force.

Ans: 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 force is newton

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

 

 

 

Q3. Define inertia. Experiment to understand inertia?

OR

          What is the law of inertia?

Ans: See Q # 3.4 from Exercise.

 

 

 

Q4. Put a one-rupee coin over a piece of card paper placed on an empty glass. Push the card with a sudden stroke of a finger. The card will move ahead while coin falls in the glass. Why it does do?

Ans: Due to inertia card will continue its motion in the forward direction while coin will remain at rest and will fall in the glass.

 

 

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Q5. Define Momentum.

Ans: 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.

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

 

 

 

Q6. A bullet has very small inertia due to its small mass. But why does its impact is so strong when it is fired from the gun?

Ans: According to the law of conservation of momentum, the mass of the bullet is much smaller than the gun therefore the recoil is much greater than the velocity of the gun. Therefore, the impact of the bullet is very strong.

 

 

 

Q7. Why the impact of the loaded truck on a body coming it’s the way is very large even if the truck is moving slowly.

Ans: Greater is the mass of truck, greater will be its momentum. Therefore, the loaded truck has a large impact.

 

 

 

Q8. Explain Newton’s first law of motion by a practical example of daily life?

Ans: Newton’s laws of motion:

          A body continues its state of rest or uniform motion in the straight line provided no net force acts on it.

Examples:

Case I (Part I):

According to Newton’s first law of motion, a body at rest remains at rest provided no net force acts on it. This part of the law is true as we observe that objects do not move by themselves unless someone moves them. For example, a book lying on a table remains at rest as long as no net force acts on it.

Case II (Part II):

Similarly, a moving object does not stop moving by itself. A ball rolled on a rough ground stops earlier than that rolled on smooth ground. It is because rough surfaces offer greater friction. If there would be no force to oppose the motion of a body then the moving body would never stop.

 

 

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Q9. Why newton’s first law of motion is also known as the law of inertia?

Ans: Since Newton’s first law of motion deals with the inertial property of matter, therefore, Newton’s first law of motion is also known as the law of inertia.

 

 

 

Q10. Why the passengers standing in a bus fall forward when the driver applies brakes suddenly?

Ans: The passengers standing in a bus fall forward when its driver applies brakes suddenly. It is because the upper parts of their bodies tend to continue their motion, while lower parts of their bodies in contact with the bus stop with it. Hence, they fall forward.

 

 

 

Q11. When a bus takes a sharp turn, passengers fall in an outward direction. Why?

Ans: When a bus takes a sharp turn, passengers fall in the outward direction. It is due to inertia that they want to continue their motion in a straight line and thus fall outwards.

 

 

 

Q12. Define net force?

Ans: Net force:

            The net force is the resultant of all the forces acting on a body.

 

 

 

Q13. State and prove Newton’s second law of motion.

                                  Or

Show that F = ma.

Ans: Newton’s second law of motion:

           When a net force acts on a body, it produces acceleration in the body in the direction of the net force. The magnitude of this acceleration is directly proportional to the net force acting on the body and inversely proportional to its mass.

 Derivation of formula F = ma:

          If a force produces an acceleration ‘a’ in a body of mass ‘m’, then we can state mathematically that

a ∝   F………..(i)

and                                                      a ∝   ……….(ii)

By combining (i) and (ii)

Or                                                         a ∝

Or                                                          F ∝ ma

Putting k as proportionality constant, we get

F = kma ………(iii)

In SI units, the value of k comes out to be 1. Thus Eq. (iii)

F = ma

 

 

 

Q14. Define SI units of force?

Ans: SI units of force:

           SI unit of force is newton (N).

Newton (1 N):

One newton (1 N) is the force that produces an acceleration of 1 ms – 2   in a body of mass of 1 kg.

Thus, a force of one newton can be expressed as

1 N = 1 kg  x 1 ms – 2

Or                                                      1 N = 1 kgms – 2

 

 

 

Q15. Differentiate between mass and weight.

Ans: See Q # 3.3(i) from Exercise

 

DO YOU KNOW?

          When a bus takes a sharp turn, passengers fall in the outward direction. It is due to inertia that they want to continue their motion in a straight line and thus fall outwards.

 

 

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Q16.Explain Newton’s third law of motion by practical examples of daily life?

Ans: Newton’s third law of motion:

To every action, there is always an equal but opposite reaction.

Explanation:

Newton’s third law of motion deals with the reaction of a body when a force acts on it. Let a body A exerts a force on another body B, the 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.

Examples:

A book lying on a table:

           Consider a book lying on a table. The weight of the book is acting on the table in the downward direction. This is the action. The reaction of the table acts on the book in the upward direction.

An air-filled balloon:

            Take an air-filled balloon. When the balloon is set free, the air inside it rushes out and the balloon moves forward. In this example, the action is by the balloon that pushes the air out of it when set free. The reaction of the air which escapes out from the balloon acts on the balloon. It is due to this reaction of the escaping air that moves the balloon forward.

Taking off a rocket:

A rocket such moves on the same principle. When its fuel burns, hot gases escape out from its tail with a very high speed. The reaction of these gases on the rocket causes it to move opposite to the gases rushing out of its tail.

 

Quick Quiz

 

Stretch out your palm and hold a book in it.

  1. How much force do you need to prevent the book from falling?

Ans:  The force which is needed to prevent the book from falling is equal to the weight of the book, i.e. R = W

 

 

 

  1. Which is the action?

Ans:  The weight of the book acting in a downward direction is called action.

 

 

 

  1. Is there any reaction? If yes, then what is its direction?

Ans:  Yes, the force applied to prevent the book from falling is called the reactional force. The reactional force is acting in the upward direction. Opposite to weight of the book i.e.  R = W

 

 

 

Q17. What do you know about tension and acceleration in a string?

Ans: Tension and acceleration in a string:

             Consider a block supported by a string. The upper end of the string is fixed on a stand. Let w be the weight of the block. The block pulls the string downwards by its weight. This causes a tension T in the string. The tension T in the string is acting upwards at the block. As the block is at rest, therefore, the weight of the block acting downwards must be balanced by the upwards tension T in the string. Thus, the tension T in the string must be equal and opposite to the weight w of the block.

 

 

 

Q18. Calculate the tension and acceleration in the string during motion of bodies connected by the string and passing over friction pulley using the second law of motion?

Ans: Vertical motion of two bodies attached to the ends of a string that passes over the frictionless pulley:

Suppose two bodies A and B having masses m1 and m2 respectively are connected to two ends of an inextensible string which passes over a frictionless pulley. If m1 is greater than m2, then body A will move downward and the body B will move upward.

Two forces are acting on the body A:

  •  Its weight w1 = m1g
  • Tension of string T1 acting upward.

Since body A will move downward, hence its weight m1g is greater than the tension T in the string.

Net force acing on body A = m1g – T

                 According to Newton’s second law of motion:

                                     m1g –  T = m1a ……….. (i)

Two forces are acting on the body B:

  • Its weight w2 = m2g, acting downward.
  • Tension of string T acting upward.

As body moves upward, hence its weight m2g is less than the tension T in the

string.

Net force acting on body B =  T  –  m2g

        According to Newton’s second law of motion:

T  –  m2g = m2a ……….. (ii)

Adding Eq. (i) and Eq. (ii), we get acceleration a.

m1g –  m2g = m1a + m2a

(m1 – m2)g = (m1 + m2)a

Magnitude of acceleration = a =  g…………(iii)

Putting the value of a in Eq. (ii), we get

T  –  m2g = m2(  g)

T  =   m2g +  m2(  g)

T =   m2g

T =   m2g

Magnitude of tension = T =    g

    Note:

    Atwood machine:

The above arrangement is also known as the Atwood machine. It can be used to find the acceleration g due to gravity using Eq. (iii)

g =  a

 

DO YOU KNOW

An Atwood machine is an arrangement of two objects of unequal masses. Both the objects are attached to the ends of a string. The string passes over a frictionless pulley. This arrangement is sometimes used to find the acceleration due to gravity.

 

 

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Q19. Calculate the tension and acceleration in a string during motion of two bodies attached to the ends of a string that passes over a frictionless pulley such that one body moves vertically and the other moves on a smooth horizontal surface:

Ans: Motion of two bodies attached to the ends of a string that passes over a frictionless pulley such that one body moves vertically and the other moves on a smooth horizontal surface:

Consider two bodies A and B of masses m1 and m2 respectively attached to the ends of an inextensible string.

Let the body A moves downwards with an acceleration a. Since the string is inextensible, therefore, body B also moves over the horizontal surface with the same acceleration a. As the pulley is frictionless, hence tension T will be the same throughout the string. Since body A moves downwards, therefore, its weight m1g is greater than the tension T in the string.

\       Net force acing on body A = m1g – T

                 According to Newton’s second law of motion:

m1g – T = m1a ……….. (i)

The forces acting on body B are:

  1. Weight m2g of the body B acting downward.
  2. Reaction R of the horizontal surface acting on body B in the upwards direction.
  3. Tension T in the string pulling the body B horizontally over the smooth surface.

As body B has no vertical motion, hence resultant of vertical forces (m2g and R) must be zero. Thus, the net force acting on body B is T.

According to Newton’s second law of motion;

T = m2a …………..(ii)

Adding Eq. (i) and (ii), we get acceleration a as

m1g – m2a = m1a

m1g = m1a + m2a

m1g = a (m1 + m2)

a =  g……….(iii)

      Putting the value of a in equation (ii) to get tension T as

T =  g

 

 

 

Q20. Show the relationship between momentum and force OR Derive Newton’s Second Law of motion with the help of momentum.

OR

Prove that F = ΔP/t .

OR

How can you relate a force with the change of momentum of a body?

Ans.     See Q # 3. 7 from Exercise

 

 

 

Q21.    Show that Ns = Kg m/s    OR     Ns = Kg ms – 1

Ans:     L.H.S = N s = (1kg x 1 ms – 2 ) x s = Kg  x  ms – 2 + 1  = Kg  x  ms – 1 = Kg ms – 1

 

 

USEFUL INFORMATION

Fragile objects such as glasswares etc. are packed with suitable materials such as Styrofoam rings, balls, polythene sheets with air sacks etc.

The air enclosed in the cavities of these materials makes them flexible and soft. During any mishap, they increase the impact time on fragile objects. An increase in impact time lowers the rate of change of momentum and hence lessens the impact of force. This lowers the possible damage due to an accident.

 

 

USEFUL INFORMATION

In an accident at high speed, the impact force is very large due to the extremely short stopping time. For safety purposes, vehicles have rigid cages for passengers with crumple zones at their front and rear ends.

During an accident, crumple zones collapse. This increases the impact time by providing extra time for crumpling. The impact of force is highly reduced and saves passengers from severe injuries.

 

 

USEFUL INFORMATION

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

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

 

 

 

Q22.   Define System and Isolated system?

Ans:  System:

            A system is a group of bodies within certain boundaries.

Isolated system:

           An isolated system is a group of interacting bodies on which no external force is acting. The momentum of an isolated system is always conserved. This is the Law of Conservation of Momentum.

 

 

 

Q23:    What is the law of conservation of momentum?

OR

            State and explain the law of conservation of momentum?

Ans:     See Q # 3.11 from Exercise.

 

 

 

Q24.    When a gun is fired, it recoils. Why?

Ans:     See Q # 3.13 from Exercise.

 

 

 

Q25.    Under which principle rockets and jet engines works?

Ans:     Working of rockets and jet engines:

              Rockets and jet engines also work on the same principle. In these machines, hot gases produced by burning of fuel rush out with large momentum. The machines gain equal and opposite momentum. This enables them to move with very high velocities.

 

 

 

Q26.    What do you know about friction?

Ans.    Friction:

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

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

Factors 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.

Examples:

              Rub your palm over different surfaces such as table, carpet, polished marble surface, brick, etc. You will find smoother is the surface, easier it is to move over the surface. Moreover, harder you press your palm over the surface, more difficult would it be to move.

 

 

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Q27:    Have you noticed why a moving ball stops?

Ans:     Moving ball stops due to the force of friction.

 

 

 

Q28.    Why bicycle stops when the cyclist stops peddling?

Ans:     Bicycle stops die to force of friction.

 

 

 

Q29.    Why friction opposes motion?

OR

            Give the microscopic concept of friction?

Ans:     Microscopic concept of friction:

             No surface is perfectly smooth. A surface that appears smooth has pits and bumps that can be seen under a microscope. The figure shows two wooden blocks with their polished surfaces in contact.

                      

A magnified view of two smooth surfaces in contact shows the gaps and contacts between them. The contact points between the two surfaces form a sort of cold-welds. These cold welds resist the surfaces from sliding over each other. Adding weight over the upper block increases the force pressing the surfaces together and hence, increases the resistance. Thus, greater is the pressing force greater will be the friction between the sliding surfaces.

 

 

Tidbits

Pushing the opposite walls by palms and feet increases friction. This enables the boy to move up the walls

 

 

 

Q30.   What you know about limiting force of friction?

Ans:    See Q # 3.18 (ii) from Exercises

 

 

 

Q31.   What do you know about the coefficient of friction?

Ans:    Coefficient of friction (µ):

            The ratio between the force of limiting friction Fs and the normal reaction R is constant. This constant is called the coefficient of friction and is represented by µ

Thus              µ =                       (i)

Or                   = µ R                        (ii)

If m be the mass of the block, then for horizontal surface,

R = mg                          (iii)

Hence            = µ mg                    (iv)

 

 

 

Q32.   Describe the situations in which force of friction is needed.

Ans:    See Q # 3.14 from Exercise.

 

 

 

Q33.   Describe coefficient of friction ( µ ) between some common materials?

Ans:    Coefficient of friction ( µ )between some common materials:

            

                 Materials                           µs
Glass and Glass 0.9
Glass and Metal 0.5 – 0.7
Ice and Wood 0.05
Iron and Iron 1.0
Rubber and Concrete 0.6
Steel and Steel 0.8
Tyre and Road, dry 1
Tyre and Road, wet 0.2
Wood and Wood 0.25 – 0.6
Wood and Metal 0.2 – 0.6
Wood and Concrete 0.62

 

QUICK QUIZ

 

  1. Which shoes offer less friction?

Ans: The smooth surface shoe offers less friction.

 

 

 

  1. Which shoe is better for walking on dry track?

Ans:  The smooth surface shoe is better for walking on dry track.

 

 

 

  1. Which shoes are better for jogging?

Ans:  The rough surface shoe is better for jogging.

 

 

 

  1. Which sole will wear out early?

Ans:  The smooth surface sole will wear out early.

 

 

 

Q34. Why rolling friction is less than sliding friction?

                                               OR

         Demonstrate that rolling friction is less than sliding friction?

Ans:      See Q # 3.17 from Exercise.

 

 

 

Q35. The first thing about a wheel is that it rolls as it moves rather than to slide. This greatly reduces friction. Why?

Ans: When the axle of a wheel is pushed, the force of friction between the wheel and the ground at the point of contact provides the reaction force. The reaction force acts at the contact points of the wheel in a direction opposite to the applied force. The wheel rolls without rupturing the cold welds. That is why the rolling friction is extremely small than sliding friction.

 

 

 

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Q36. Why ball bearing or roller bearings are used to reduce friction?

Ans: The fact that rolling friction is less than sliding friction is applied in ball bearings or roller bearings to reduce losses due to friction.

 

 

 

Q37.Friction is ‘necessary evil’. Comment.

Ans: In certain cases, we need friction while in certain other we have to reduce friction. It means friction has some advantages as well as disadvantages. It is difficult to walk on ice because of less friction. A nail stays in the wood because of friction. Similarly, we can tie the knot because of this force. A horse will not be able to pull wagon unless friction furnishes him a secure foot-hold.

Friction causes energy lost and reduces the efficiency of machines. Friction causes rapid wear and tear.

In short, we can say that friction is necessary for every-day activities. Thus, the statement that “friction is necessary evil” is correct.

The wheel would not recoil on pushing it if there would be no friction between the wheel and the ground. Thus, friction is desirable for wheels to roll over a surface.

 

 

 

Q38. Why it is dangerous to drive on a wet road?

Ans: It is dangerous to drive on a wet road because of the friction between the road and the tyres are very small. This increases the chance of slipping the tyres from the road. The threading on tyres is designed to increase friction. Thus, threading improves road grip and make it safer to drive even on a wet road.

 

 

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Q39. Why a cyclist applies brakes to stop his/her bicycle?

Ans: A cyclist applies brakes to stop his/her bicycle. As soon as brakes are applied, the wheels stop rolling and begin to slide over the road. Since sliding friction is much greater than rolling friction. Therefore, the cycle stops very quickly.

 

 

QUICK QUIZ

 

  1. Why is it easy to roll a cylindrical eraser on a paper sheet than to slide it?

Ans: The fact that rolling friction is less than sliding friction. Cylindrical eraser is a rolling body and can easily roll on a paper sheet than to slide it. Because rolling friction is the force of friction between a rolling body and a surface over which it rolls.

 

 

 

  1. Do we roll or slide eraser to remove the pencil work from our notebook?

Ans: The fact that sliding friction is greater than rolling friction. We slide the eraser to remove the pencil work from our notebook.

 

 

 

Q40.    Explain breaking force and skidding of vehicles?

Ans:     See Q # 3.18 (iii & iv) from Exercise.

 

Mini Exercise

 

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

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

 

 

 

  • In which case it is easy for the tyre to roll over?

  1. Rough ground

  2. Smooth ground

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

 

 

 

Q41.   Describe the situation in daily life in which friction is most desirable?

Ans:    Sometimes friction is most desirable. We cannot write if there would be no friction between paper and pencil. Friction enables us to walk on the ground. We cannot run on slippery ground.

            A slippery ground offers very little friction. Hence, anybody who tries to run on a slippery ground may meet an accident. Similarly, it is dangerous to apply brakes with full force to stop a fast-moving vehicle on a slippery road.

Birds could not fly if there is no air resistance. The reaction of pushed air enables birds to fly. Thus, in many situations, we need friction while in other situations we need to reduce it as much as possible.

 

 

 

Q42. Write a dream during which you are driving a car and suddenly the friction disappears. What happened next…?

Ans: If suddenly the friction disappears then we cannot stop the car. Nothing would be steady on the ground, car would be just sliding and sliding.

 

 

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Q43. Describe the advantages of friction?

Ans: Advantages of friction in daily life:

  1. It enables animals to walk or crawl without slipping.
  2. It stops cars, trains, bicycles, MRT trains etc.
  3. It enables us to hold things firmly with our hands.
  4. It prevents objects from sliding down a slope.
  5. It allows nails to hold things.

 

 

 

Q44. What are the disadvantages of friction?

Ans: Problems caused by friction:

  1. It causes energy lost and reduces the efficiency of machines.
  2. It causes rapid wear and tear of the moving parts of machines.

Most of our useful energy is lost as heat and sound due to friction between various moving parts of machines. In machines, friction also causes wear and tear on their moving parts.

 

 

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Q45. What are the methods to reduce friction?

Ans: See Q # 3.16 from Exercise.

 

DO YOU KNOW

 

Friction is highly desirable when climbing up a hill.

 

 

 

Q46.   Define uniform circular motion?

Ans:    Uniform circular motion:

            The motion of an object in a circular path is known as circular motion. The motion of the moon around the Earth is circular motion.

 

 

 

Q47. Define the centripetal force. Derive the relation of centripetal force on a body moving in a circle?

Ans: Centripetal Force:

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

Examples:

Let us study the centripetal forces in the following examples:

  • A stone tied to one end of a string rotating in a circle. The tension in the string provides the necessary centripetal force. It keeps the stone to remain in the circle. If the string is not strong enough to provide the necessary tension, it breaks and the stone moves away along a tangent to the circle
  • The moon revolves around the Earth. The gravitational force of the Earth provides the necessary centripetal force.

Derivation of centripetal Force:

Let a body of mass m moves with uniform speed v in a circle of radius r. The acceleration ac produced by the centripetal force Fc is given by

Centripetal acceleration ac =   ……..(i)

According to Newton’s second law of motion, the centripetal force Fc is given by

Fc = m ac …………….(ii)

Fc =   ……………(iii)

Factors on which centripetal force depends:

Equation Fc =   shows that the centripetal force needed by a body moving in a circle depends on:

  1. The mass m of the body
  2. Square of its velocity v
  3. Reciprocal to the radius r of the circle.

 

 

 

Q48.   What is the centrifugal force? Explain.

Ans:    Centrifugal force:

            The centripetal force pulls the object towards the centre of the circle. As a reaction, another force appears at the centre of the circle which is equal in magnitude to the centripetal force but opposite in direction. This outward reaction is called centrifugal force

According to Newton’s third law of motion, there exists a reaction to this centripetal force. The centripetal reaction that pulls the string outward is sometimes called the centrifugal force

Example:

                If we whirl a piece of stone tied to one end of a string, the stone is pulled inwards due to centripetal force transmitted to it through the string. As a reaction, the stone pulls our hand outwards, and this outward reaction force on our hand is the centrifugal force.

 

DO YOU KNOW?

While the coaster cars move around the loop, the track provides centripetal force preventing them to move away from the circle.

 

 

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Q49.   Identify the use of centripetal force in (i) safe driving by banking roads (ii) washing machine dryer (iii) cream separator.

Ans:    i.    Banking of the roads:

           The curvature of the road must be inclined to control the centrifugal force of the vehicle.

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

Explanation:

When a car takes a turn, the centripetal force is needed to keep it in 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.

  1. Washing machine dryer:

       The dryer of a washing machine is basket spinners. They have a perforated wall having large numbers of fine holes in the cylindrical rotor. The lid of the cylindrical container is closed after putting wet clothes in it. When it spins at high speed, the water from wet clothes is forced out through these holes due to lack of centripetal force.

iii.    Cream Separator:

        Most modern plants use a separator to control the fat contents of various products. A separator is a high-speed spinner. It acts on the same principle of centrifuge machines. The bowl spins at 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.

 

 

SUMMARY

 

  1. A force is a push or pull. It moves or tends to move, stops or tends to stop the motion of a body.
  2. Inertia: Inertia of a body is its property due to which it resists any change in its state of rest or uniform motion in a straight line.
  3. Momentum: Momentum of a body is the quantity of motion possessed by the body. Momentum of a body is equal to the product of its mass and velocity.
  4. Friction: The force that opposes the motion of a body is called friction.
  5. Newton’s first law of motion: Newton’s first law of motion states that a body continues its state of rest or uniform motion in a straight line provided no net force acts on it.
  6. Newton’s second law of motion: Newton’s second law of motion states that when a net force acts on a body, it produces acceleration in the body in the direction of the net force. The magnitude of this acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F = ma.
  7. Unit of Force: SI unit of force is newton (N). It is defined as the force which produces an acceleration of 1 ms – 2 in a body of mass 1 kg
  8. Mass: Mass of a body is the quantity of matter possessed by it. It is a scalar quantity. SI unit of mass is kilogram (kg).
  9. Weight: Weight of a body is the force of gravity acting on it. It is a vector quantity. SI unit of weight is Newton (N).
  10. Newton’s third law of motion: Newton’s third law of motion states that to every action there is always an equal and opposite reaction.
  11. The acceleration and tension in a system of two bodies attached to the ends of a string that passes over a frictionless pulley such that both move vertically is given by:

a =  g            T =    g

  1. The acceleration and tension in a system of two bodies attached to the ends of a string that passes over a frictionless pulley such that one moves vertically and the moves on a smooth horizontal surface are given by:

a =  g            T =  g   

  1. Law of conservation of momentum: Law of conservation of momentum states that the momentum of an isolated system of two or more than two interacting bodies remains constant.
  2. Friction:  A force between the sliding objects which opposes the relative motion between them is called friction.
  3. 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.
  4. The friction causes loss of energy in machines and much work has to be done in overcoming it. Moreover, friction leads to much wear and tear on the moving parts of the machine. The friction can be reduced by:

(i) Smoothing the sliding surfaces in contact.

(ii) Using lubricants between sliding surfaces.

(iii) Using ball bearings or roller bearings.

  1. Circular motion: The motion of a body moving along a circular path is called circular motion.
  2. Centripetal force: The force which keeps the body to move in a circular path is called the centripetal force and is given by:

Fc =

  1. Centrifugal force: According to Newton’s third law of motion, there exists a   reaction to the centripetal force. The centripetal reaction that pulls the string outward is sometimes called the centrifugal force.