FORCE AND LAWS OF MOTION

1. FORCE AND LAWS OF MOTION Galileo Galilei (1564 – 1642) Sir Issac Newton (1643 -1727)

2. Force • Effects of Force • Balanced Forces • Unbalanced Forces • Newton’s First Law of Motion (Inertia) • Momentum • Newton’s Second Law of Motion • F = ma • Applications of Second Law of Motion • Newton’s Third Law of Motion • Applications of Third Law of Motion • Law of Conservation of Momentum Created by C. Mani, Deputy Commissioner, KVS RO Gurgaon

3. F F Force Push Pull A push or pull on a body is called force.

4. Push or Pull? Pull Push or Pull?

5. Push

6. Push

7. F F Effects of Force A body at rest can be moved by a force. A body in motion can be stopped by a force.

8. A body in motion can be changed in its direction of motion by a force.

9. F F F F A body (spring) can be changed (stretched) in its shape or size by a force. A body (spring) can be changed (compressed) in its shape or size by a force.

10. Effects of Force: Revisit • A force can move a stationary body. • A force can stop a moving body. • A force can change the speed of a moving body. • A force can change the direction of a moving body. • A force can change the shape (and size) of a body. Force A force is an influencing agency which tends to move a stationary body or which tends to stop a moving body or which tends to change the velocity (speed or and direction) of a moving body or which tends to change the shape (and size) of a body.

11. Reaction (R) (Exerted by the table) F F Weight (W) (Force of gravity) Balanced Forces If the resultant of all the forces acting on a body is zero, the forces are called balanced forces. The block on the table is acted upon by many forces. Since the block is at rest, the normal reaction R must be equal and opposite to its weight W. Force ‘F’ applied by the left hand is being balanced by the force ‘F’ applied by the right hand.

12. Note: • When a body at rest is acted upon by balanced forces, the body is not displaced. i.e. the body remains stationary. • When balanced forces act on a body moving with constant velocity (uniform motion), they do not produce any acceleration on the body. i.e., the body continues to move with the same speed and direction. • Eg.When rain drops fall from clouds at a greater height, the drops at first gain velocity due to gravity of the earth. • After falling through some height, a stage called equilibrium occurs when downward weight of the drops is balanced by the upward forces such as upthrust and viscous force. • The net force acting on the drops will be zero and hence no more acceleration is produced on the drops. • Therefore, the rain drops move with constant velocity which was last gained by the drops just before reaching equilibrium condition.

13. Can you imagine the speed of the rain drops while reaching the surface of the earth, if they continue to move only under the action of gravity? Suppose the clouds are at the height (h) of 3 km (3000 m). Acceleration due to gravity (g) is 9.8 m/s2. Initial velocity (u) = 0 m/s. Then, final velocity is given byv2 = u2 + 2gh i.e. v2 = 02 + 9.8 x 3000 => v = 171.5 m/s = 617 km/h A rain drop with such a high velocity is faster than a bullet and can pierce through a human skull ! • Though the balanced forces cannot produce motion in a stationary body or stop a moving body, they can, however, change the shape of the body. Eg. When a ball is pressed between the hands the forces are balanced but the ball is changed in its shape and size.

14. Lift Thrust Drag Weight Unbalanced Forces If the resultant of all the forces acting on a body is not zero, the forces are called unbalanced forces. Unbalanced forces can move a stationary body or they can stop a moving body. When we talk of a force acting on a body, we usually mean an unbalanced force. When the total force on the plane is in one direction, the force is called “unbalanced”. An unbalanced force changes the motion of the plane. For instance, when thrust is greater than drag, it is the unbalanced force that causes the plane to speed up, or accelerate. In addition, as the velocity of the plane increases, the lift force increases and becomes the unbalanced force that causes the plane to fly.

15. Reaction (R) f Weight (W) F ≤ f F > f Since the block is at rest, the normal reaction R must be equal and opposite to its weight W. As long as the applied force F is less than the frictional force, the block is not moved. When the applied force is just equal to the friction, the body may move with uniform velocity. When the applied force is greater than the friction, the body moves with acceleration.

16. F F NEWTON’S LAWS OF MOTION The block remains at rest….. unless and until it is acted upon by an external force. The ball continues to be in uniform motion…… unless and until it is acted upon by an external force. NEWTON’S FIRST LAW OF MOTION A body at rest will remain at rest, and a body in uniform motion will continue to be in uniform motion, unless and until it is compelled by an external force to change its state of rest or of uniform motion.

17. Inertia Inertia is the inherent property of a body due to which it resists a change in its state of rest or of uniform motion. Inertia can be understood in parts, viz. inertia of rest and inertia of motion. Mass is a measure of the inertia of a body. Heavier objects have more inertia than lighter objects. Eg. 1. A stone of size of a football has more inertia than football. 2. A cricket ball has more inertia than a rubber ball of the same size. Inertia of rest

18. Examples of Inertia of rest: • A passenger in a bus jerks backward when the bus starts suddenly because the passenger tends to be in inertia of rest whereas the bus is moved away forcefully. • When a bed sheet is flicked away suddenly dust particles fall away as they tend to be in inertia of rest. • When a branch of a tree carrying a mango is suddenly flicked mango falls off due to inertia of rest.

19. Examples of inertia of motion: • A passenger in a bus jerks forward when the bus stops suddenly because the passenger tends to be in inertia of motion whereas the bus is stopped forcefully. • An athlete after reaching the finishing point can not stop suddenly or if he stops suddenly then he falls toppling head down. • A car takes some time and moves through some more distance before coming to rest even after the application of brakes. • A rotating fan continues to do so for some more time even after the current is switched off. • An oscillating simple pendulum bob does not halt at the mean position but continues to move further. • When a car or bus turns around a sharp corner, we tend to fall sideways because of our inertia to continue to move in a straight line. • It is dangerous to jump out of a moving bus because the jumping man’s body is in the state of inertia of motion but the legs are suddenly stopped by the ground and hence he topples down.

20. MOMENTUM Momentum is the quantity of motion in a body and it depends on its mass and velocity. Momentum of a body is defined as the product of its mass and velocity. i.e. Momentum = mass x velocity or p = m x v • Momentum is directly proportional to mass. If a cricket ball and a tennis ball move with same velocity, momentum of cricket ball is more because its mass is larger than that of the tennis ball. • Momentum is directly proportional to velocity. If two cricket balls move with different velocities, then the momentum of the ball with greater velocity possesses more momentum. • If a body is at rest, its velocity is zero and hence its momentum is zero. • But, every moving body possesses momentum. • Momentum is a vector quantity. • SI unit of momentum is kg m/s or kg ms-1. • CGS unit of momentum is g cm/s g cms-1.

21. Change in momentum Force α Time taken Δp F α t mv - mu F α t m(v – u) F α t (v – u) m x a F α since a = t K m a F = K x 1 x 1 1 = m a F = NEWTON’S SECOND LAW OF MOTION The rate of change of momentum of a body is directly proportional to the applied force, and takes place in the direction in which the force acts. If force of 1 N applied on a body of mass 1 kg produces an acceleration of 1 m/s2 on the body, then or K = 1 Force = mass x acceleration

22. F Acceleration a = m 100 g The acceleration produced in a body is directly proportional to the force acting on it and inversely proportional to the mass of the body. • Force is a vector quantity. • Force can cause acceleration or deceleration. Eg.: Accelerator of a car accelerates it and brakes decelerate it. • SI unit of force is ‘newton’. • One ‘newton’ is defined as that force which when acting on a body of mass 1 kg produces an acceleration of 1 m/s2 in it. Place an 100 g on your outstretched palm. The force you feel is nearly 1 newton !

23. Applications of Newton’s Second Law of motion • A cricket player (fielder) moves his hands backwards on catching a fast moving cricket ball. A fast moving cricket ball has a large momentum. In stopping the cricket ball, its momentum has to be reduced to zero. When a player moves his hands back, the time taken to stop the ball increases and hence the rate of change of momentum decreases. i.e. the force exerted by the ball on the hands decreases. So, the hands of the player do not get hurt.

24. A high jumping or long jumping athlete is provided either a cushion or a heap of sand on the ground to fall upon. • The cushion or sand helps to increase the time in which the momentum comes to zero. This decreases the rate of change of momentum and hence the force. So, the athlete does not get hurt. • Packing materials like thermocoal, corrugated sheets, bubbled plastic sheet, straw, paper strands, etc. are used while packing glassware, chinaware, electronic devices, etc. • These materials help to increase the time in which the momentum comes to zero when jolting and jerking take place. This decreases the rate of change of momentum and hence the force. So, the articles do not get broken.

25. NEWTON’S THIRD LAW OF MOTION To every action there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs - equal and opposite (action-reaction) force pairs. • Note: • Action and reaction are just forces. • The forces always occur in pairs. • Action and reaction do not act on the same body. • Action and reaction act on different bodies but simultaneously. • Though action and reaction forces are equal in magnitude but they do not produce equal acceleration in the two bodies on which they act.

26. F F 60 60 60 40 40 40 80 80 80 20 20 20 100 100 100 0 0 0 0 100 20 60 80 40 Examples / Applications of Newton’s Third Law of motion Reaction = 58 gwt Action = 58 gwt

27. F F Action Reaction

28. F F Force on gun (Reaction) Force on bullet (Action) Recoil of a gun

29. Identify Action and Reaction

30. Forward Motion Vertical component of reaction Reaction Reaction Horizontal component of reaction Action Weight Weight

31. Action Reaction

32. Horse and Cart Problem A horse is urged to pull a cart. The horse refuses to try, citing Newton’s third law as his defence. “The pull of me on the cart is equal but opposite to the pull of the cart on me. If I can never exert a greater force (action and reaction are always equal) on the cart than it exerts on me, how can I ever set the cart moving?”, asks the horse. How would you reply?

33. RC TCH THC V Reaction R f H WC Action WH Why don’t you educate the Horse properly? Weight of the cart ‘WC’ is balanced by Reaction ‘RC’ on the cart offered by the ground. Forward pull of the horse on the cart ‘THC’ is balanced by the Reaction pull of the cart on the horse ‘TCH’. If the horse pushes the ground in a slanting manner (Action), the Reaction offered by the ground is resolved into Vertical and Horizontal components. The Vertical component ‘V’ balances the weight of the horse ‘WH’. If the Horizontal component ‘H’ is greater than the Friction ‘f’, then the horse-cart system will move forward with acceleration.

34. LAW OF CONSERVATION OF MOMENTUM When two or more bodies act upon one another, their total momentum remains constant provided no external forces are acting on them.

35. Suppose a big and a small car move in the same direction with different velocities. Let the mass of the bigger car be ‘m1’ and its initial velocity is ‘u1’. Let the mass of the smaller car be ‘m2’ and its initial velocity is ‘u2’ such that u2 < u1. Suppose both the cars collide for a short time ‘t’. Due to the collision, the velocities will change. Let the velocities after the collision be v1 and v2 respectively.

36. F1 = m2a2 v2 – u2 v1 – u1 F1 = m2 x F2 = m1 x t t F2 = m1a1 v2 – u2 v1 – u1 m2 x = - m1 x t t m1u1+ m2u2 = m1v1 +m2v2 Suppose that during collision, the bigger car exerts a force F1 on the smaller car and in turn, the smaller car exerts a force F2 on the bigger one. When the force F1 acts on the smaller car, its velocity changes from u2 to v2. When the force F2 acts on the bigger car, its velocity changes from u1 to v1. According to Newton’s third law,F1 = - F2 Cancelling t on both sides, we get m2(v2 – u2) = m1(v1 – u1) m2v2 – m2u2 = m1v1 – m1u1 Initial momentum of the bigger car = m1u1 Initial momentum of the smaller car = m2u2 Final momentum of the bigger car = m1v1 Final momentum of the smaller car = m2v2 Total momentum before collision = Total momentum after collision

37. Recoil of a Test Tube (Activity) Wait…..water is getting heated ! Here, the event of popping up of the cork is considered as collision. Total momentum before collision is zero.Total momentum after collision also must be zero.Hence, the velocities of the test tube and the cork are adjusting themselves.i.e. the cork and the tube fly away in opposite directions; also note that the velocity of the cork (lighter) is faster than that of the test tube (heavier).

38. Acknowledgement • The objects copied from various sites: • Pictures of Galileo, Newton • Apple Tree • Aeroplane • 5 Rupee coin • Rocket • Body of the car • Spirit Lamp