CHAPTER - 1

CHAPTER - 1FORCEFORCE: It is an external agent which changes (or tends to change) either the state of rest or the state of motion of the body or the shape of the body.Rigid body : changes only state of rest or motion.Non-Rigid body: can change shape or state of rest or motion.Types of ForcesContact forces

Non-contact forcesContact force

The forces which act on bodies when they are in physical contact, are called contact forceTypes of Contact forces Frictional forceWhen a body slides on a rough surface, the force due to its roughness opposes the motion of the body and applies a force opposite to the direction of motion.This types of force is called the frictional force

Normal Reaction Force When a body is placed on a surface, it exerts a force equal to the weight of the body on the surface. The body does not fall because the surface also applies equal and opposite force on the body known as reaction force, this force is always perpendicular to the plane of the surface, so its called as Normal force

Tension Force in the string When an object is suspended by a string, the weight of the body acting in the vertically downwards direction is balanced by the force due to the string in the upwards direction. This force developed in the string is called the tension force T

Force due to a springA horizontally placed spring (fig a) in its original loose form does not exert any force on the object attached If its other end is either stretched or compressed, the spring is found to exert a force which is directly proportional to the displacement. This force is called the restoring force

Collision force When two bodies collide each body applies an equal and opposite force on the other body.This result in the motion in the bodies after collision

Non Contact ForceThe forces experienced by the bodies even without being physically touched, are called the non contact forces or the force at a distance.ExamplesGravitational force, electrostatic force and magnetic forceTypes of Non Contact forcesGravitational ForceWe know that, each and every object in the universe attracts each other. The force of attraction between them is called the gravitational force.

Due to the gravitational force earth pulls every object towards its centre.

Electrostatic ForceTwo like charges repel, while unlike attracts each other when they brought nearThe force between two charges even when they are on in contact, is called electrostatic force

Magnetic forceTwo likes poles of magnet repel while unlike poles attract each other.

The force between the two magnetic poles even they are not in contact is called the magnetic force

Effects of a ForceIt can start or stop the motion.

It can change the speed or the direction of the motion or both.

It can change the size or shape of the bodyNewton`s Laws of motion First Law -> A body continues to be in its state of rest or of uniform motion in a straight line unless an external unbalanced force is applied on it.

First law also gives us the definition of force in a qualitative way.Newton`s Second LawThe rate of change of momentum of a body is directly proportional to the force applied on it and the change takes place in the direction of force appliedF = ma

Relationship between F , m and a.

Units of Force1 newton = 1kg x 1 m/s2 1 dyne = 1 g x 1cm/s2 Relation between newton and dyne1N = 105dyne Gravitational unit of force1kgf = 9.8 N1 gf = 980 dyne

Newton's Third Law To every action, there is always an equal and opposite reaction

Action and reaction forces act on different objects.

Types of motionTranslational motionWhen sufficient is applied on a stationary rigid body it begins to move in a straight line along the direction of force.This straight line motion of the body is called Translational motionRotational motionIf the body is pivoted at one point and due to some other point begins to rotate about the axis passing through the fixed point the motion of the body is called rotational motionMoment of force (Torque) Moment of force or torque on a rigid body is define as the product of magnitude of the force and its perpendicular distance from the axis of rotation of the bodyIt is also known as the turning effect of the force.The turning effect of force acting on a body about an axis is called the moment of force or torqueTorque Moment of force about the point O= Force x Perpendicular distance of force from the point O= F x d S I unit- Nm1Nm = 105dyne x 100cm = 107dyne cm cgs unit dyne cm

Factors affecting the TorqueThe magnitude of the force applied andThe distance of line of action of the force from the axis of rotation

Some examples of Torque

Equilibrium of BodiesWhen a number of forces acting on a body produced no change in its state of rest or motion, the body is said to be in equilibrium

Kinds of EquilibriumStatic equilibriumWhen a body remains in the state of rest under the influence of the applied forces, the body is in static equilibriumDynamic equilibrium When a body remains in the same state of motion like linear or rotational motion, under the influence of the applied forces. The body is said to be in dynamic equilibriumPrinciple of Moment If numbers of forces acting on a rigid body keeps it in equilibrium, then the sum total of the clockwise moment about the turning point is equal to the sum total of the anti-clockwise moments.

Or, the sum total of all the moments about the turning point is zero

Anticlockwise moments = F1 x d1Clockwise moments= F2 x d2From definition, when the scale is in horizontal equilibrium A.C.W moment = C.W moments F1 x d1 = F2 x d2From the above principle, if the Body is stationary algebraic sum of all the moments is zeroThe beam balance works on the principle of moments.

SOLVING PROBLEMS RELATED TO PRINCIPLE OF MOMENTSStep 1: Identify what are the forces that will give rise to clockwise / anticlockwise momentStep 2: Find the clockwise / anticlockwise momentStep 3: Equate the clockwise and anticlockwise moments

2910N30N6mdFind the value of d.WORKED EXAMPLE30Step 1: Identify what are the forces that will give rise to clockwise / anticlockwise moment316N30N6mdFind the value of d.WORKED EXAMPLEAnticlockwise momentClockwise moment32Step 2: Find the clockwise / anticlockwise moment336N30N6mdClockwise moment = Force x distance between force and pivot= 30 x d= 30d NmWORKED EXAMPLEAnticlockwise momentClockwise momentAnticlockwise moment= Force x distance between force and pivot= 6 x 6= 36 Nm

Find the value of d.Solution:34Step 3: Equate the clockwise and anticlockwise moments356N30N6mdFind the value of d.Solution:Clockwise moment = Force x distance between force and pivot= 30 x d= 30d NmAnticlockwise moment= Force x distance between force and pivot= 6 x 6= 36 NmUsing the principle of moments,Clockwise moment = Anti-clockwise moment30d = 36d = 36 30d = 1.2 m

WORKED EXAMPLEAnticlockwise momentClockwise moment36Points to note:The unit for force must be in Newtons, the unit for distance must be in metres.The distance must measured from the force to the pivot.37Example 1:A metre scale is supported at the centre. It is balanced by two weights

A and B as shown in figure below, find the distance of B from the pivot.

Clockwise moment and anticlockwise moment about 50 cm divisions are equal.

Suggested answer :20 x d = 40 x 20Therefore, Hence the 20 N force of B is acting from 90 cm mark.38Example 2:The illustration in figure below shows a uniform metre rule weighing 30 N pivoted on a wedge placed under the 40 cm mark and carrying a weight of 70 N hanging from the 10 cm mark. The ruler is balanced horizontally by a weight W hanging from the 100 cm mark. Calculate the value of the weight W.

Suggested answer :

W x (100 - 40) + 30 (50 - 40) = 70 x (40 - 10) 60 x W + 30 x 10 = 70 x 30 60 W = 2100 - 300Therefore,

39Couple When two equal and opposite parallel forces act at equal distance on either side of the point of rotation of the body, the sum of their moments form a couple

Let a body be free to rotate about O Two forces each of magnitude F acts at point A & B where OA=OBMoment of force at A : F x OA (anticlockwise direction)Moment of force at B : F x OB (clockwise direction)The sum of CW and ACW moment or couple = F(OA + OB) = F x AB

Some examples of couple actionOpening or closing of the water tap,Driving the pedal of a bicycle.Turning a steering wheelOpening or tightening the cap in a bottleCentre of GravityCentre of gravity of a body is that imaginary point through which the entire weight of the body acts irrespective of the position of the body

Centre of gravity of regular shape bodies

Centre of gravity of an irregular lamina

Uniform Circular Motion The motion of a body around a circular path with uniform speed, but variable velocity, such that its acted upon by a uniform acceleration is called circular motion

Few examples of uniform circular motion

Centripetal Force A force which is directed towards the centre of a circular path and always acts at right angles to the direction of motion, along the circular path is called Centripetal forceThe magnitude of Centripetal force is given by

The magnitude of Centripetal force is given by

WhereF-> Centripetal forcem- > mass of the bodyr -> distance from the axis of rotationv-> velocity of the body

Centrifugal force A force acting away from the centre of circular path is called the centrifugal force This is a pseudo force that actually does not exist in nature.

Centripetal and centrifugal forces are equal in magnitude but opposite in the direction

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