CHAPTER - 1

1. CHAPTER - 1 FORCE

2. FORCE: 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.

3. Types of Forces • Contact forces • Non-contact forces

4. Contact force The forces which act on bodies when they are in physical contact, are called contact force

5. Types of Contact forces Frictional force When 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

6. 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

7. 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

8. Force due to a spring A 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

9. 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

10. Non Contact Force The forces experienced by the bodies even without being physically touched, are called the non contact forces or the force at a distance. Examples Gravitational force, electrostatic force and magnetic force

11. Types of Non Contact forces Gravitational Force We 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.

12. Electrostatic Force Two like charges repel, while unlike attracts each other when they brought near The force between two charges even when they are on in contact, is called electrostatic force

13. Magnetic force Two 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

14. Effects of a Force • It 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 body

15. Newton`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.

16. Newton`s Second Law The 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 applied F = ma

17. Relationship between F , m and a.

18. Units of Force • 1 newton = 1kg x 1 m/s2 • 1 dyne = 1 g x 1cm/s2 Relation between newton and dyne • 1N = 105dyne Gravitational unit of force • 1kgf = 9.8 N • 1 gf = 980 dyne

19. Newton's Third Law To every action, there is always an equal and opposite reaction Action and reaction forces act on different objects.

20. Types of motion Translational motion When 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 motion Rotational motion If 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 motion

21. Moment 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 body It 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 torque

22. Torque Moment of force about the point O = Force x Perpendicular distance of force from the point O = F x d S I unit- Nm 1Nm = 105dyne x 100cm = 107dyne cm cgs unit – dyne cm

23. Factors affecting the Torque • The magnitude of the force applied and • The distance of line of action of the force from the axis of rotation

24. Some examples of Torque

25. Equilibrium of Bodies When 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

26. Kinds of Equilibrium Static equilibrium When a body remains in the state of rest under the influence of the applied forces, the body is in static equilibrium Dynamic 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 equilibrium

27. Principle 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

28. Anticlockwise moments = F1 x d1 Clockwise moments = F2 x d2 From definition, when the scale is in horizontal equilibrium A.C.W moment = C.W moments F1 x d1 = F2 x d2 From the above principle, if the Body is stationary algebraic sum of all the moments is zero The beam balance works on the principle of moments.

29. SOLVING PROBLEMS RELATED TO PRINCIPLE OF MOMENTS Step 1: Identify what are the forces that will give rise to clockwise / anticlockwise moment Step 2: Find the clockwise / anticlockwise moment Step 3: Equate the clockwise and anticlockwise moments

30. 6m d 30N 10N WORKED EXAMPLE Find the value of d.

31. Step 1: Identify what are the forces that will give rise to clockwise / anticlockwise moment

32. 6m d 30N 6N WORKED EXAMPLE Anticlockwise moment Clockwise moment Find the value of d.

33. Step 2: Find the clockwise / anticlockwise moment

34. 6m d 30N 6N WORKED EXAMPLE Anticlockwise moment Clockwise moment Find the value of d. Solution: Clockwise moment = Force x distance between force and pivot = 30 x d = 30d Nm Anticlockwise moment = Force x distance between force and pivot = 6 x 6 = 36 Nm

35. Step 3: Equate the clockwise and anticlockwise moments

36. 6m d 30N 6N WORKED EXAMPLE Anticlockwise moment Clockwise moment Find the value of d. Solution: Clockwise moment = Force x distance between force and pivot = 30 x d = 30d Nm Anticlockwise moment = Force x distance between force and pivot = 6 x 6 = 36 Nm Using the principle of moments, Clockwise moment = Anti-clockwise moment 30d = 36 d = 36  30 d = 1.2 m

37. Points 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.

38. Example 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 20 Therefore, Hence the 20 N force of B is acting from 90 cm mark.

39. Example 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 - 300 Therefore,

40. Couple 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

41. Let a body be free to rotate about O Two forces each of magnitude F acts at point A & B where OA=OB Moment 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

42. Some examples of couple action • Opening or closing of the water tap, • Driving the pedal of a bicycle. • Turning a steering wheel • Opening or tightening the cap in a bottle

43. Centre of Gravity Centre 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

44. Centre of gravity of regular shape bodies

45. Centre of gravity of an irregular lamina

46. 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

47. Few examples of uniform circular motion

48. 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 force The magnitude of Centripetal force is given by

49. The magnitude of Centripetal force is given by Where F-> Centripetal force m- > mass of the body r -> distance from the axis of rotation v-> velocity of the body

50. 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.