1

Newton's laws of motion

2

Born: 4 Jan 1643 in Woolsthorpe, Lincolnshire, EnglandDied: 31 March 1727 in London, England

Let us dedicate ournext one hourto the great scientist & mathematician

“Sir Isaac Newton”

3

Summary

Distance: total length of travel

Displacement: change in position

Average speed: distance / time

Average velocity: displacement / time

Instantaneous velocity: average velocity measured over an infinitesimally small time

4

Summary Instantaneous acceleration: average acceleration measured over an infinitesimally small time Average acceleration: change in velocity divided by change in time Deceleration: velocity and acceleration have opposite signs Equatiojna of motion: equations of motion relate position, velocity, acceleration, and time Freely falling objects: constant acceleration

g = 9.81 m/s2

5

Newton

For an object to CHANGE its motion we need force

Newtons mechanics applies for motion in

an inertial frame of reference!

???????

6

NEWTONS 1st LAW MOTION –LAW OF INERTIA • Mass occupies space Inertial property• Unless acted upon by external imbalanced

force mass continues to be in state of rest (velocity=0 ) or uniform motion in straight line ie.

• Without force Velocity and/or Direction of motion does not change•Eg – A rolling ball will continue to roll with same velocity for ever on a frictionless surface

7

Inertia( Measure of mass) More mass more inertia

• Season & tennis ball:, • Inertia at rest

• Suddenly Starting or stopping train• Cleaning carpet by heating• Fruits/ flowers fall down when we shake tree• Pile of carom coins• Coin over card

• Inertia of motion • Jumping from running train, Car stops suddenly• Ball thrown up in running train• Start by fast bowler / long jump athlete

8

9

Inertia of coin stack

10

Will these objects fall down if we pull table cloth suddenly

11

12

Examples of Inertia of motion

13

14

15

16

• Concept of force

17

ForceForce causes acceleration?Force: push or pullForce is a vector – it has magnitude and direction

18

Calibrating Spring ForceTwo equal weights exert twice the force of one; this is used for calibration of a spring:

We can measure force by using spring balance

19

Points to Remember about force:1.Force must have an agent that produces

it;2.Contact force will act at the point of

contact3.The normal force acts only

perpendicular to the surface in contact;

4.The friction force acts only parallel to the surface in contact;

5.The tension force from a string or rope acts only along the line of the string or rope.

20

• Force is needed to change an object's motion

21

• Weight is measure of earth’s gravitational force

• In space weight will be zero but mass will not change

• Newton's laws will be still valid

22

NEWTONS 2st LAW – Measurability

– By definition three terms are involved, namely•Force , Mass & Velocity

– Hence a new term ,Momentum is defined as• Momentum P = Mass Velocity = mv

–‘ P ‘ does not change if there is no external force.This is called law of conservation of momentum

Inertial property

• Definition Rate of change of momentum is proportional

to the applied external imbalance force & takes place in direction of force

24

Normal application : Only velocity changes

M M

U VF

.t sec

F

Newton made the constant of proportionality one by suitably selecting the units and hence the formula becomes F = aM

t1

F M V – M U

Now Mass is constant

t1

F ( V – U)M

F aM

25

ImpulseChange in momentum may be produced by a force acting for a instantaneously for short time) , it is called impulse

26

Soft bed

Hard surface

Why glass breaks when it falls on hard face ?

27

Observe long jump of athlete

Why do athlete jump on soft sand & not on hard surface ?

28

29

Acceleration vs. ForceAcceleration is proportional to force:

1 1F a

1 12 2F a

30

Kg x m /sec2

Kg

31

Force is vector quantity

32

33

34

Kg x m /sec2

Kg

35

36

A solid object resists the action of force which compresses .This is called normal force. It always acts outward and perpendicular to the surface of the compressed object. The symbol for the normal force is n.

Normal Force (Denoted by n )

n

37

Type of Forces:( Normal force )

38

Type of Forces:( Normal force )

39

The normal force may be equal to, greater than, or less than the weight.

40

Units: Mass has SI units of kg, and acceleration has SI units of m/s2. We define the SI unit of force as:1 newton = 1 N = 1kg m/s2.

41

Example: Accelerated Mass

A net force of 3.0 N produces an acceleration of 2.0 m/s2 on an object of unknown mass. What is the mass of the object?

1 21

(3.0 N)= 1.5 kg(2.0 m/s )

Fma

m1

42

Example:Three Forces

Mira, Lata, and Kamal push a 600kg boat, each exerting a 100 N force parallel to the dock.(a) What is the acceleration of the boat if they all push in the same direction?

3 x 100 = 300 N .a = F / M = 300 N / 600Kg = 0.5 m / sec2

DOCK

43

Mira, Lata, and Kamal push a 600kg boat, each exerting a 100 N force parallel to the dock.(b) What is the acceleration if Mira & Lata pushes in the opposite direction from Kamal?

Example: Three Forces

100 – 100 – 100 = – 100N.a = F / M = -100 N / 600Kg = - 0.167 m / sec2

DOCK

44

Typical Forces

45

Newton’s third law

.

• For every action (force) there is a reaction (force)

• Action (force) and reaction forces are in opposite direction and act on two different bodies

46

Newton’s Third Law of MotionSome action-reaction pairs:

ActionReaction

47

Action

Reaction

Action Reaction

ActionReaction

Reaction

F

Two forces act on man F & -F will cancel each other hence man will not move

F

Action

Understanding action-reaction pairs:Will man move?

48

49

Understanding action-reaction pairs:Will man move if he is on skates ?

Action

Action

ActionReaction

GroundReaction

If man stand on skates, ground reaction F will not be there. Hence man will move back due to cupboard reaction force

Action

CupboardReaction

F

No ground reaction

50

Understanding action-reaction pairs:Will coup bard move?

Action

Reaction

Action Reaction

ActionReaction

Reaction

Two forces act on cupboard F & -F will cancel each other hence it will not move

51

Example: Pulling a Rope

A student pulls horizontally with a force of 100 N on a rope that is attached to a wall.

Two students pulls on opposite ends of a rope with forces of 100 N each.

1 2

52

Example --- Action

The man pushes ground back ward –ActionAction acts on ground

53

Example --- reaction

The ground pushes man forward –ReactionReaction acts on man

Note: If ground will not give reaction man can not move forward

54

Example --- Action & reaction

The man pushes ground back ward –ActionAction acts on ground

The ground pushes man forward –ReactionReaction acts on man

Note: If ground will give reaction man can

move forward

55

Action Reaction

If ground is slippery ground can not give reaction & tire will slip

Tier exerts force on ground--Action

Hence no action

If ground is slippery no action,hence no reaction

Ground exerts force on wheel ---Reaction –hence tractor moves

Hence tractor will not move

56

Action :Gases moving out under high pressure

Rocket engine

Reaction :Reaction acts on plane due to which it moves

Rocket engine can work in vacuum as it is having its own oxygen supply but jet engine cannot work in vacuum

57

Action: Rotating Fan pushes water

Reaction : Water pushes the fan back & hence ship moves forward

For breaking the motion of propeller fan is reversed & reaction force decelerates the ship

58

59

60

61

Recoiling of gun

62

Airplane has landed at point ‘A’ & came to halt point ‘B’

A B

u = 400m/sec a = -50m/sec2

V= 0m/sec

63

Time Velocity Distance Acc0 400 0 -501 350 375 -502 300 700 -503 250 975 -504 200 1200 -505 150 1375 -506 100 1500 -507 50 1575 -508 0 1600 -50

U = 400 m/sec, V = 0 , a = -50m/sec2

V =u +at s =ut + ½ at2

64

400350

300250

200150

10050

0050

100150200250300350400450

0 1 2 3 4 5 6 7 8 9

Time in sec

Velo

cty

m/s

ec

Velocity time graph

65

0

375

700

9751200

13751500 1575 1600

0200400600800

10001200140016001800

0 1 2 3 4 5 6 7 8 9

Time sec

Dis

tanc

e m

eter

sDistance time graph

66

-60

-50

-40

-30

-20

-10

00 2 4 6 8 10

Time sec

Acc

m/s

ec^2

Acc time graph

67

Free fall upward motion

68

• A force of F = 7.50 N pushes three boxes to the left.  The boxes have masses = 1.30 kg, 3.20 kg, = 4.90 kg.                                                    

•What is the magnitude of the contact force between boxes 2 and 3 (in N)?

g = 10m/sec2

F23?

4.875

EX 1

69

g = 10m/sec2

4.875

F23?

Total mass moving = 1.3 +3.2 + 4.875 =9.375 kg

.a = F/M =7.5/9.375 = 0.8m /sec2 for all masses

70

g = 10m/sec2

F23?

.a = = 0.8m /sec2 for all masses

Force F23 is pushing blocks 1 & 2 = 4.5kg

4.875

F23 = f x a = 4.5 x 0.8 = 3.6 N

Find contact force between 1 & 2 Ans = 1.04 N

71

Ex2

Masses 1.0 kg, 2.0 kg are connected by a string & kept on a frictionless table. They are connected by a string and pulley to a hanging mass 3.0 kg as shown. System is released from rest . Find acceleration of the system in m/ sec2 ?Find tension in stirng at point 1 (T1)

g = 10m/sec2

T1 .a ?

72

Ex2

g = 10m/sec2

.a ?

Net force = m3 x g = 3 x 10 = 30 N Force acting is weight of mass m3

Net moving mass = m1+ m2+ m3 = 6 Kg Net a = F / (m1+ m2+ m3) = 30 / 6 Kg = 5m/sec2

F

T1

73

Ex2

g = 10m/sec2

.a ?

T1 = m1 x 5 = 1 x 5 = 5 N

Force T1 produces accn = 5m/sec2 in mass m1

F

T1

74

You ask the talking horse, to pull a wagon. He replies that he would be glad to, but the laws of physics will not permit it. From Newton’s 3rd Law, if he pulls the wagon, wagon will pull him back with equal reaction force, so the net force on him will be zero and the wagon cannot move.  What would you reply? Explain

Ex 3

75

When you convince him on his first point the lezzy smart horse says “ the road below wheels is oily. It will not give any reaction .Hence I am not be able to pull the car”  What would you reply? Explain

Ex 3

Oily surface

76

When you convince him on his second point the smart horse says “ the road below my feet is oily. It will not give any reaction .Hence I am not be able to pull the car”  What would you reply? Explain

Ex 3

Oily surface

77

An object moves with a constant velocity. Is it safe to conclude that no forces act on the object?  Why or why not?

The constant velocity implies that the acceleration is zero, and from Newton's 2nd Law we can infer that the net force on the object is also zero.  However, there could be many forces acting on the object, as long as their vector sum is zero, leading to zero net force

78

END

79

Mass changing with velocity• Mass increases with velocity• However increase in mass is noticeable only

at speed comparable with light speed ie more than 106m/sec (light speed 3 * 108 m/sec)

• Formula is m = mo / √1- (v2/c2), c = velocity of light, m= mass at velocity v, mo= rest mass

• In case of atomic particles moving near to speed the increase is mass can be measured in lab

• However Newton's law are still valid• For all normal situation mass can be

considered constant .