Force Resultant Force Balanced And Unbalanced Forces Galileo's Observation and Origin of Newtonian Mechanics Inertia : Inertia is Classified as:

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1 FORCE AND LAWS OF MOTION Force : An agent that change or try to change the state of an object is called force. A force may be i. Push ii. Pull iii. Gravitational force iv. Frictional force The force applied on a body can bring about the following changes: ft It can change the state of rest of a body or change its position ft It can change the speed of the body ft It can change the direction of motion of a body Resultant Force The resultant force is that single force which when acting on a body produces the same effect as that produced by a number of forces. For example, several people can jointly move a boulder but a strong person can move the same boulder all by himself. That is, the force applied by the strong man produces the same effect as that produced by the net force applied by all. The force applied by the strong man is the resultant force. Balanced And Unbalanced Forces : Forces which do not cause any change in state of rest or of uniform motion along a straight line are called balanced forces. The resultant of balanced forces is always equal to zero (because the forces are equal and opposite) The forces acting on a body produce any change in state of rest or motion, then the forces are said to be unbalanced Force. An unbalanced force acting on an object changes its speed or direction. The resultant of unbalanced forces is always greater than zero. Galileo's Observation and Origin of Newtonian Mechanics Aristotle and other medieval thinkers believed that the natural state of bodies is the state of rest. Galileo opposed this concept. Galileo observed that, when a ball was made to roll down an inclined plane, its speed increased. An Object Moving Down an Inclined Plane with Increasing Speed Similarly, when it was made to roll up the inclined plane, its speed decreased. An Object Moving Upward with Decreasing Speed He then tried rolling it on a horizantal plane. Galileo repeated this experiment by making the surface very smooth. He observed that the ball continued to move for a longer time. Galileo suggested that the speed of the ball moving on a horizontal plane would remain constant in the absence of an external force or force of friction Galileo suggested that the natural tendency of all bodies is to oppose a change in their state of rest or motion Inertia : All objects have a tendency to continue in their state of rest or of uniform motion until an external force acts on it. Or,Ttendency of an object to resist any change in its state of rest or of uniform motion is called inertia. Or, Inertia can be defined as the property of matter by virtue of which it opposes any change in its state of rest or of uniform motion along a straight line. Inertia is Classified as: Inertia of rest Inertia of motion Inertia of direction Examples of Inertia of Rest A passenger standing in a bus leans backwards when the bus starts all of a sudden Fruits fall down when the branches of a tree are shaken * Dust particles on a carpet falls when we beat the carpet with a stick Examples of Inertia of Motion #A passenger standing in a moving bus leans forward when the bus stops all of a sudden #A man carelessly alighting from a moving train leans forward Example of Inertia of Direction #The water particles sticking to the cycle tyre are found to fly off tangentially Whenever a driver is negotiating a curve, the passengers experience a force acting away from the centre of the curve Inertia of a body depends upon its mass. That is, massive objects possess more inertia than lighter ones. Newton's First Law of Motion : A body continues to be in a state of rest or of uniform motion along a straight line unless an external force acts upon it. This means that every object has a tendency to resist any change in its state of rest or motion. This tendency is inertia. This law is also known as law of inertia. Newton's first law of motion gives a gualitative definition of force. Momentum : The momentum of an object is defined as the product of its mass and its velocity. Momentum is a vector guantity and its direction will be same as that of velocity. It is represented by p. p = mv where, m is the mass of the object, v is its velocity. SI unit of momentum is kg m/s. Newton's Second Law of Motion : Newton's second law of motion states that rate of change of momentum is directly proportional to applied force and takes place in the same direction as the applied force. Explanation Consider a body of mass m, having an initial velocity u. Let the body be acted upon by some force F for time t, such that its final velocity is vr^ Initial momentum = m u Final momentum = m v Change in momentum in time t = m(v - u) m(v-u) ITI--- Change in momentum in unit time = t But, (acceleration) Change in momentum in unit time = ma According to Newton's secom^tew j Rate of change of momentum F m.a F = Km.a (K is the constant of proportionality) If a body has unit mass and unit acceleration, such that force possessed by it is also one unit then 1 = K x 1 * 1 or K = 1 F = ma Or, Force = mass x acceleration Unit of Force F = ma«xe know that SI unit of mass is kg and acceleration is m/s 2. SI unit of force is kgm/s 2

2 But 1 kgm/s 2 is defined as 1 Newton in honour of Sir Issac Newton. 1 N = 1 kgm/s 2 One Newton force is that force which produces an acceleration of 1 m/s 2 on an object of mass 1 kg. Impulse : Mathematical representation of Newton's second law of motion is P _ mv - mu t or Ft = mv- mu When the time of application of force is short then Ft is defined as impulse. Impulse is a large force acting for a short duration. SI unit of impulse = N s or kg m/s. Example for an impulsive force When we kick a football, the kick lasts only for a fraction of a second. The force, which we apply on a football, is an example for impulsive force Applications of Newton's Second Law of Motion : In a cricket match a fielder moves his arms back while trying to catch a cricket ball because if he tries to stop the fast moving ball suddenly then the speed decreases to zero in a very short time. Therefore the retardation of the ball will be very large. As a result the fielder has to apply a larger force to stop the ball. Thus, if he tries to stop a fast moving cricket ball the fielder may get hurt as the ball exerts a great pressure on the hands but if he tries to stop it gradually by moving his arms back then the velocity decreases gradually in a longer interval of time and hence retardation decreases. Thus the force exerted by ball on the hand decreases and the fielder does not get hurt. Newton's Third Law of Motion reaction". : "To every action there is an equal and opposite Some of the situations in daily life to illustrate Newton's third law of motion. When we walk on the ground, then our foot pushes the groun^ttackward (action force) and the ground in turn exerts a force on the foot (reaction force) pushing the foot forward When a man jumps from a diving board he pushes the board (action force) and the board in turn pushes the man forward in the opposite direction (reaction force) The birds, while flying, push the air downwards with the help of their wings (action force) and the air in turn exerts a force on the bird in the upward direction (reaction force) A swimmer pushes the water in the backward direction (action force) and the water exerts a force on the swimmer (reaction force) which pushes him forward Law of Conservation of Momentum : if a group of bodies are exerting force on each other, i.e., interacting with each other, their total momentum remains conserved before and after the interaction provided there is no external force acting on them. Two bodies A and B of masses m 1 and m 2 are moving in the same direction with initial velocities u1 and u2. They make a direct collision. Let us assume that after collision they continue moving in the same direction. Let the collision last for a very short interval of time 't' seconds. During collision, A exerts a force on B. At the same time, B exerts a force on A. Due to these action and reaction forces the velocities of A and B get changed. After collision, let v1 and v2 be the velocities of the bodies A and B respectively. The force exerted on A=m1a1 [According to Newton's II law of motion] A, Therefore, force exerted on B = m2a2 According to Newton's third law of motion, these two forces are equal and opposite. i.e., F1 = -F2 i.e., total momentum before collision is equal to the total momentum after collision, which is nothing but law of conservation of momentum. Applications of Law of Conservation of Momentum, Newton's Third Law of Motion

3 ft Recoil of a Gun When a bullet is fired from a gun, the gases produced in the barrel exerts a tremendous force on the bullet (action force). As a result, the bullet moves forward with a great velocity called the muzzle velocity. The bullet at the same time exerts an equal force on the gun in the opposite direction (reaction force). Due to this the gun moves backwards. This backward motion of the gun is called the recoil of the gun. The velocity with which the gun moves backwards is called the recoil velocity. Force of Friction : The force of friction or simply friction is that force which opposes the motion of an object over another object in contact with it. The maximum value of the force of friction, which comes into play when a body just begins to move over the surface of another body is known as the limiting friction. The force required to keep the body in steady motion after the motion has once started is called the sliding friction. The sliding friction is smaller than the limiting friction. Rolling Friction When a body rolls over a surface, the frictional force developed between the surfaces is called rolling friction. Friction can be Decreased by the following methods : By Using Lubricants Like Oil, Grease or Graphite Powder Lubricants like oil or grease can reduce friction. The lubricants form a thin film between the moving parts and fill the tiny pores and depressions on the surfaces. This makes the surfaces smooth and reduces the friction Friction can be Increased by By making both the surfaces very rough By making irregular projections and depressions like those we see on the tyres Advantages of Friction Due to friction we are able to walk on the surface of the Earth The brakes applied in automobiles work only due to friction Nails, screws and the wooden boards are held together due to force of friction The fibres of thread are held together due to force of friction Disadvantages of Force of Friction In overcoming the friction, a lot of energy is wasted in the form of heat. Friction causes wear and tear of the moving parts Due to friction, speed of automobiles cannot be increased beyond a certain limit TEXTBOOK QUESTIONS A Questions given on page number 118 of the Textbook. Q.l. Which of the following has more inertia : a) a rubber ball and a stone of the same size? (h) a bicycle and a train? (c) a five rupees coin and a one rupee coin? Ans. ( a ) A stone of same size has more inertia than a rubber ball of same size. A train has much more inertia than a bicycle. A five rupees coin has more inertia than a one-rupee coin. Q.2. In the following example, try to identify the number of times the velocity of the ball changes : "A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team." Also identify the agent supplying the force in each case. Ans. In the given example, the velocity of ball changes four times as explained below : When a football player kicks the football to another player of his team. Force is applied by the first player. When the second player kicks the football towards the goal of rival team. Force is applied by the second player. When the goalkeeper of the opposite team collects the football. Force is applied by t he goalkeeper. 4. When goalkeeper kicks the ball towards a player of his own team. Force is even now applied by the goalkeeper. Q.3. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch. Ans. Initially the whole tree is in a state of rest. When we vigorously shake a branch of the tree, we apply force on it and the branch comes in a state of motion. However, the leaves tend to maintain their rest position due to inertia of rest. As a result some leaves may get detache d from the branch of tree. Q.4. Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest? Ans. When driver of a moving bus applies brakes suddenly, the bus slows down but our body tends t o continue in the same state of motion due to the inertia of motion. Consequently, we may fall in forward direction or may collide with the panels in front. When driver of a bus accelerates it from rest, the bus gains speed but our body tends to remain in its state of rest due to the inertia of rest. Consequently, we may fall backward or experience a backward push.

4 B] Questions given on page number of the Textbook. Q.l. If action is always equal to the reaction, explain how a horse can pull a cart. Ans. When a horse wants to pull a cart, the horse pushes the road below backward with his legs. The road exerts an equal and opposite force on the horse legs due to which horse moves forward and pulls the cart along with him. Q.2. Explain, why is it difficult for a firemen to hold a hose, which ejects large amounts of water at a high velocity. Ans. When the hose pipe of firemen ejects large amounts of water at a high velocity, it carries a high forward momentum. In accordance with the law of conservation of momentum, the hose pipe experiences an equal momentum in backward direction. Thus, the hose tends to recoil backward. It is due to this reason that fireman finds it difficult to hold the hose. Q.3. From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s - '. Calculate the initial recoil velocity of the rifle. Ans. Here mass of rifle M= 4 kg, mass of bullet m = 50 g = = 0.05 kg, and initial velocity The negative sign indicates that the direction of motion of rifle is opposite to the motion of bullet. Q.4. Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m s" 1 and 1 m s~\ respectively. They collide and after the collision, the first object moves at a velocity of 1.67 in s - 1. Determine the velocity of the second object. Ans. Here mass of 1st object m ] = 100 g = 0.1 kg, mass of 2nd object m-, = 200 g = 0.2 kg, initial velocity of 1st object (before collision) M, = 2 m s~\ intial velocity of 2nd object (before collision), u 0 = 1 m s~', and final velocity of 1st object (after collision) v, = 1.67 m s~'. Let after collision the 2nd object moves with a velocity v,. Then in accordance with the conservation law of momentum, total momentum of system before collision = total momentum of system after collision TEXTBOOK EXERCISES Q.l. An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on the magnitude and direction of the velocity. If no, provide a reason. Ans. When an object experiences a net zero external unbalanced force, in accordance with second law of motion its acceleration is zero. If the object was initially in a state of motion, then in accordance with the first law of motion, the object will continue to move in the same direction with same speed. It means that the object may be travelling with a non-zero velocity but the magnitude as well as direction of velocity must remain unchanged or constant throughout. Q.2. When a carpet is beaten with a stick, dust comes out of it. Explain. Ans. Initially the carpet was in a state of rest. On beating with a stick the carpet conies in a state of motion. But dust present in it tends to remain in rest due to inertia of rest and hence comes out of the carpet. Q.3. Why is it advised to tie any luggage kept on the roof of a bus with a rope? Ans. If luggage is kept on the roof of a bus untied, then as driver of bus starts and accelerates the bus, the luggage will try to maintain its rest position due to inertia of rest. Consequently, the luggage experiences a backward push and may fall from the roof of the bus. It is, therefore advised to tie the luggage tightly using a rope. Q.4. A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to rest. The ball slows to a stop because the batsman did not hit the ball hard enough. velocity is proportional to the force exerted on the ball, (t) there is a force on the ball opposing the motion. (d) there is no unbalanced force on the ball, so the ball would want to come to rest. Ans. (c) There is a force

5 on the ball opposing the motion. Explanation : When ball is rolling on a level ground, a force of friction nets on it in a direction opposite to that of motion. Due to the backward force of friction ball gradually slows down and comes to rest after covering some distance. Q.5. A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find the acceleration. Find the force acting on it if its mass is 7 metric tonnes. [Hint: 1 metric tonne = 1000 kg Ans. Here mass of truck m = 7 metric tonnes = 7000 kg, initial velocity of truck u = 0, total distance covered by truck s = 400 m, time t = 20 s. Force acting on the truck F' - ma = 7000 x 2 = N Q.6. A stone of 1 kg is thrown with a velocity of 20 m s" 1 across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice? Ans. Here mass of stone m = 1 kg, initial velocity of stone u = 20 m s -1, final velocity of stone v = 0 and total distance covered by the stone s = 50 m. Using the relation v 2 - u 2 = las, we Force f = ma = l x(-4) = - 4 N The -ve sign of force means that force is opposing the motion of stone. Q.7. A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of N and the track offers a friction force of 5000 N, then calculate : (0 the net accelerating force ; ( i f ) the acceleration of the train ; and (iii) the force of wagon 1 on wagon 2. Ans. (i) The total force exerted by the engine on the train F [ = N and the forced of friction acting on train due to track F^= N (Force F 0 is negative because force of friction always opposes the motion).-. Net accelerating force acting on the train F= ± F 2 = = N ( i i i ) When engine is pulling the train, the first wagon will exert a force on 2nd wagon which is just sufficient to pull 2nd wagon and wagons joined behind 2nd wagon. It means it will have to p u l l in a l l 4 wagons of total mass M' = 2000 x 4 = 8000 kg..-. Force of wagon I on wagon 2, P = M'a = 8000 x 3.5 = N Q.8 An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of 1.7 m s -2? Ans. Here mass of automobile vehicle m = 1500 kg Acceleration produced by the force a = -1.7 m s~ 2.". Force acting on vehicle due to road F = ma = 1500 x( ) = N The -ve sign of force indicates that the force is in a direction opposite to that of motion of automobile vehicle. Q.9. What is the momentum of an object of mass m, moving with a velocity v? (a) (mv) 2 (b) mv 2 (c) ymv 2 (d) mv Ans. (d) mv. [Hint : Momentum of an object is given by the product of its mass ( m ) and velocity (v)] Q.10. Using a horizontal force of 200 N, we intend to move a wooden cabinet across a floor at a constant velocity. What is the friction force that will be exerted on the cabinet?

6 Ans. Here Horizontal forces applied f, = 200 N. As the cabinet is moving across a floor at a constant velocity, its acceleration is zero i.e, a = 0. Net unbalanced accelerating force acting on cabinet F = 0 The -ve sign means that force of friction is acting in a direction opposite of that of force applied on the cabinet. Q.ll. Two objects, each of mass 1.5 kg, are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 m s _1 before the collision during which they stick together. What will be the velocity of the combined object after collision? Ans. Here mass of given objects m { = m 2 = 1.5 kg As the objects are moving with equal speeds in mutually opposite directions along a s traight line, hence u l = m s^1 but u 7 = m s~'. As the two objects stick together due to collision, their final velocity will be the same. Let V = v 2 = v (say) Using conservation law of momentum, we have It means that after collision both the balls will be in a state of rest. Q.12. According to the third law of motion when we push on an object, the object pushes back on us with an equal and opposite force. If the object is a massive truck parked along the roadside, it will probably not move. A student justifies this by answering that the two opposite and equal forces cancel each other. Comment on this logic and explain why the truck does not move. Ans. The logic given by the student is wrong because forces of action and reaction act on two different bodies and never cancel each other. The truck does not move because the force applied on it is very small and is being balanced by t h e force of friction acting on t h e truck clue to road. As the truck is massive one, it has large inertia and to bring it into motion we require an extremely high force, which a single person cannot apply. Q.13. A hockey ball of mass 200 g travelling at 10 m s" 1 is struck by a hockey stick so as to return it along its original path with a velocity at 5 m s _I. Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick. Ans. Here it is given that mass of hockey ball m = 200 g = 0.2 kg, initial velocity of ball u = 10 ms" 1 and the final velocity of ball after struck by hockey stick v = - 5 m s _l. Here v has been taken as negative because the direction of motion of ball is reversed now. Change in momentum of hockey ball = mv - mu = in (v - it) = 0.2 [(-5)-(+10)] = -3 k g ms - ' -ve sign means that change in momentum is in a direction opposite to that of original motion of the hockey ball. Q.14. A bullet of mass 10 g travelling horizontally with a velocity of 150 m s -1 strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also, calculate the magnitude of the force exerted by the wooden block on the bullet. Ans. Here mass of bullet m = 10 g = ^ kg = 0.01 kg, initial velocity of the bullet u = 150 m s" 1, final velocity of the bullet v = 0 and time t = 0.03 s.

7 The -ve sign of force shows that the force is a retarding force or it is opposing the motion. Q.15. An object of mass 1 kg travelling in a straight line with a velocity of 10 m s -1 collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object. Ans. Here mass of the object m x = 1 kg, mass of block m, = 5 kg, initial velocity of object w, Q.16. An object of mass 100 kg is accelerated uniformly from a velocity of 5 in s"' to 8 m s" 1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted in the object Ans. Here mass of the object in = 100 kg, initial velocity it = 5 m s ' and final velocity v - 8 m s ' and time t - 6 s Initial momentum of the object p, = mu x 5 = 500 kg m s and final momentum of the object p, = mv = 100 x 8 = 800 kg m s Q.17. Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions. Ans. When the insect hit the windshield of car, collision had taken place between the insect and the motorcar. In the collision, force applied by the insect on car and force applied by th e car on insect are equal in magnitude but opposite in directions. Infact the two forces are action and reaction forces. Total momentum of car and insect system remains constant. Hence, change in momentum of insect during collision has same magnitude as the change in momentum of car. Thus, Rahul is correct. The real cause of death of insect was its extremely small mass. For a given force (or given change in momentum) the insect experienced a large negative acceleration and got stuck on the wind screen. Q.18. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s -2. Ans. Here mass of the dumb-bell m = 10 kg

8 ADDITIONAL EXERCISES What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero? What do you infer about the forces acting on the object? Q.A.I. The following is the distance-time table of an object in motion : Time in seconds Distance in metres Thus, it is clear that the acceleration is increasing with time. ( b ) As force acting on an object F = ma, hence it is clear that force is directly proportional to acceleration. It means that force acting on the object is increasing with time. Q.A.2. Two persons manage to push a motorcar of mass 1200 kg at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of 0.2 m s~~ 2. With what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort) Ans. Let each person applies a force F on a motorcar of mass m = 1200 kg. When two persons push the car, they just manage to move if at a uniform velocity. It means that their combined force 2F is just balanced by force of friction due to road and car moves with a uniform velocity. When three persons push the car, they apply a total force 3F on the car. Now net unbalanced force on the car = force applied by the persons - frictional force = 3 F - 2 F = F As now acceleration a = 0.2 m s~ 2, hence

9 F = = 1200 x 0.2 = 240 N Hence each person pushes the car with a force of 240 "N. Q.A.3. A hammer of mass 500 g, moving at 50 m s~', strikes a nail. The nail stops the hammer in a very short time of 0.01 s. What is the force of the nail on the hammer? Ans. Mass of hammer m = 500 g = 0.5 kg, initial velocity of hammer u = 50 m s"' 1, final velocity of hammer v = 0 and time / = 0.01 s. -ve sign of force suggests that the force is opposing the motion of hammer. Q.A.4. A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required. Ans. Here mass of motor car m = 1200 kg, initial velocity of car u = 90 km/h = 25 m s _l, final velocity of car v = 18 km/h = 5 m s"' and time t = 4 s. -ve sign of acceleration, change in momentum and force suggests that the force is opposing the motion of motorcar. Q.A.5. A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision and both of them come to a halt after that. If the collision lasts for I s : Which vehicle experiences the greater force of impact? Which vehicle experiences the greater change in momentum? Which vehicle experiences the greater acceleration? Why is the car likely to suffer more damage than the truck? Ans. (a) During head on collision forces applied by truck and car are action -reaction forces. Hence, both vehicles experience same (equal) force of impact. Here initial velocity of both car and truck is same equal to v and final velocity of both is zero. But mass of truck is much more than that of car, hence change in momentum of truck is more than change in momentum of car.( F For same force of impact, the acceleration of car will have a greater magnitude v a = v m because its mass is less. Car suffers more damage than the truck. As for car acceleration is more, its velocity falls to zero in a shorter time and, consequently, its momentum changes in a shorter time. OTHER IMPORTANT QUESTIONS (A) Very Short Answer Type Questions (One Mark Each) Q.l. What can a force acting on an object do? Ans. Force may change the magnitude or direction of velocity of object. It may also change the shape a nd size of the object. Q.2. Give an example to show that force can change shape and size of an object. Ans. Force applied on a spring may stretch/compress it. Force applied on an inflated balloon may deform it. Q.3. A person applies some force on an almirah but it does not move. Why? Aus. The force applied by the man is balanced by force of friction acting on almirah d u e to floor and net unbalanced force is zero. Q.4. What is inertia? Ans. Natural tendency of a body to maintain its state of rest or of uniform motion along a straight line by

10 itself. Q.5. What is a measure of inertia? Ans. The mass of an object. Q.6. Does inertia of an object depend on any other factor other than mass? Ans. No, it does not. Q.7. Why does a body of small mass require small initial effort to put it in motion? Ans. Because its inertia is small on account of its small mass. Q.8. Are Newton's first law of motion and Galileo's law of inertia same or different? Ans. Same. Q.9. What is the mathematical formula for momentum? Ans. Momentum of an object = Mass x Velocity. Q.10. What is the unit of momentum? Ans. Kilogram-metre (second)"" 1 or kg m s~ l. Q.ll. If you jerk a piece of paper under a book quick enough, the book does not move. Why? Ans. On account of its inertia of rest. Q.12. An old person standing in a moving bus falls forward when the driver suddenly stops the bus at a red light signal. Why? Ans. The old person falls forward due to his inertia of motion. Q.13. Why does an electric fan continue to rotate for sometime even after the electric current is switched off? Ans. Due to inertia of motion. Q.14. Why does a bicycle begin to slow down, when the rider stops pedalling? Ans. On account of force of friction acting on bicycle due to the road. Q.15. A body is moving on a smooth frictionless level surface with a speed of 15 m s _1 along a given direction. Does any force act on it? Why? Ans. No force acts on it because its motion is uniform and there is no ot her cause affecting the motion. Q.16. A body is moving on a rough level road with a speed of 15 m s along a given direction. Does any force is needed? Why? Ans. Yes, a constant force is needed to maintain the motion. The force is needed to balance the force of friction acting due to the road. Q.17. A body is acted upon by a number of external forces. Can it remain at rest even now? Ans. Yes, provided the resultant of all the external forces is zero. Q.18. A car and a motorbike both are running with the same speed. Which of the two has greater momentum and Why? Ans. The car because its mass is more. Q.19. A light rubber ball and a cricket ball both are projected with equal velocities. Whose momentum is more and why? Ans. The cricket b a l l because its mass is more than that of rubber ball. Q.20. A car and a truck have same momentum. Whose velocity is more and why? Ans. Velocity of car is more for same momentum as the truck has, because its mass is less than that of truck. Q.21. A passenger sitting in a car at rest pushes it from within. Will the car start moving? Ans. No, because there is no external force. An internal force cannot produce motion. Q.22. On shaking the branches of a Jaitnin tree, the Jamuns fall on ground. Why? Ans. Jamuns fall on ground on account of their inertia of rest. Q.23. Give the magnitude and direction of net force acting on a gas filled balloon lying stationary in sky at a height /». Ans. Zero. Q.24. If the net force acting on a body be zero, does it necessarily mean that the body must remain in rest position? Ans. No, if net force is zero then the body is either at rest or in a state of uniform motion along a given direction. Q.25. What is the relationship between force applied on a body and the resulting acceleration caused in it? Ans. Force (F) = Mass ( m ) x Acceleration (a). Q.26. What force is needed to produce an acceleration of 2 m s -2 in a body of mass 3 kg? Ans. F = m a = 3x2 = 6 N. Q.27. A force of 10 N produces an acceleration of 2.5 m s" 2 when applied on an object. What is the mass of the object? F I O N Ans. Mass m = = = = 4 kg. a 2.5 m s~ 2 Q.28. Name the SI unit of force. Ans. A newton ( IN ) Q.29. Define one newton force. Ans. Q.30. Two masses are in the ratio 1 : 4. What is the ratio of their inertia?

11 Ans. 1 :4. Q.31. Can balanced forces cause motion? Ans. No, they cannot. Q.32. When a motor car makes a sharp turn at a high speed, in what direction a passenger sitting in it experiences a push? Ans. In a straight line outward. Q.33. Why does a passenger sitting in a moving car slip to one side of the seat when the car takes a sharp turn? Ans. On account of its tendency to continue in its straight line motion (or on account of its inertia of direction). Q.34. An athlete runs for few steps before taking a long jump. Why? Ans. So as to gain momentum which helps him in taking a longer jump. Q.35. What is the relation between action and reaction forces? Ans. Their magnitudes are equal but directions are opposite. Q.36. Do action-reaction forces act on the same object? Ans. No, they act on different objects. Q.37. In which direction a swimmer applies force while swimming? Ans. The swimmer pushes the water backward. Q.38. How is a swimmer able to swim forward in a tank, although he is pushing water backward? Ans. Because tank water pushes the swimmer forward. Q.39. When action and reaction forces are equal and opposite, why don't they cancel each other? Ans. Because they are acting on two different bodies. Q.40. Which law of motion explains walking of a man on the ground? Ans. The third law of motion. Q.41. Which law of motion is involved in rocket propulsion? Ans. The third law of motion. Q.42. In which direction should a passenger run before trying to catch a train running slowly along a platform? Ans. In the direction of motion of train. Q.43. Which law of motion is the real law of motion? Ans. The second law of motion. Q.44. State conservation law of momentum. Ans. Q.45. Is conservation law of momentum always true? Ans. Yes, it is always true and never fails. Q.46. Why do splinters of an exploded cracker spread in different directions? Ans. So as to conserve its total momentum. Q.47. Why does a vehicle stop on applying brakes? Ans. Because brakes apply a force which opposes motion. Q.48. In which direction does a rowing boat move when a sailor jumps out of it? Ans. In backward direction. Q.49. What is the net force acting on a cork piece floating freely on water? Ans. Zero. Q.50. A person rubs his coat vigorously by using a brush so as to remove dust from the coat. How? Ans. On rubbing the coat comes into motion but dust particles present on it tend to maintain their state of rest due to inertia property and hence fall behind. (B-l) Short Answer Type Questions (Two Marks Each) Q.l. What do you mean by the term 'force'? Ans. Force is that external push or pull which is required to change the state of rest or of uniform motion along a straight line. Thus, force is needed to start motion, to accelerate a body in motion, to slow down a moving body, to stop a moving body or to change the direction of motion of the body. Force may also cause change in shape or size of a body. Q.2. Give few examples of different types of forces. Ans. 1. When we throw a ball, we apply force due to muscular effort of our arm. A body falling freely from the top of a tower is falling unde r the effect of force of gravity. Planets revolve around the sun due to gravitational force acting between the sun and planets. A ball moving on the floor stops after covering some distance due to force of friction acting on the ball due to floor. Q.3. What do you mean by balanced forces? Illustrate by giving one example.

12 Ans. Balanced forces are the forces which balance one another and the net (resultant) force acting on the object is zero. Consider a wooden block or a brick A placed on a horizontal table surface. Let us apply forces F, and F, on the block in mutually opposite directions as shown in Fig. 9.01, so that the block does not move from its rest position. Obviously, it means that net effect of F ] and F 2 taken together is zero. Thus, F, and F, are balancing each other. Q.4. What do you mean by the term 'unbalanced forces'? Ans. If the forces acting on an object do not balance each other but have a finite resultant, then the forces are said to be unbalanced forces. An unbalanced force is needed to change the state of re st or of uniform motion of an object. Q.5. Briefly state Galileo's concept of motion. Ans. On the basis of his experimental studies Galileo deduced that "any object moves with constant speed when no force acts on it". In other words, "no net force is neede d to sustain the uniform motion of an object". Q.6. State Newton's first law of motion. How does it agree with Galileo's observations? Ans. For statement of Newton's first law of motion Newton's first law of motion completely agrees with Galileo's observations. Q.7. Give a simple experiment to illustrate the inertia of rest. Ans. Take an empty glass tumbler and put it on a table. Cover the tumbler by a stiff playing card over its mouth. Now place a coin on the card as shown in Fig Give a sudden, sharp horizontal flick to the card with a finger. The card moves along the direction of flick but coin is found to fall vertically into the glass tumbler due to its inertia of rest. Q.8. Give the magnitude and direction of net force on : a rain drop falling down with a constant speed, a book placed on the table, a kite skillfully held stationary in the sky. Ans. (a) Net force is zero because magnitude and direction of velocity both are constant. Net force is zero because book is at rest. Net force is zero because the kite has been held stationary in the sky. Q.9. When a quilt or blanket is vigorously shaken, the dust falls off. Why? Ans. Initially quilt or blanket is at rest. When it is shaken vigorously, it comes in a state of motion. However, dust particles present in it tend to remain at rest due to inertia and fall off. Q.10. When a horse suddenly starts running, a careless rider falls backwards. Why? Ans. Initially, the horse and rider both are in a state of rest. When the horse suddenly starts running, he comes into a state of motion but rider tends to maintain his state of rest and experiences a backward pull. If the rider is careless, he may fall backward on the ground due to this pull. Q.ll. A horse rider falls forward when the horse suddenly stops. Why? Ans. Here initially horse and the rider both are in a state of motion. When horse suddenly stops, he comes to rest but the rider tends to maintain its state of motion due to inertia property. As a result, rider experiences a forward push and may even fall on the ground with his head in forward direction. Q.12. A fast medium bowler runs for quite some distance before delivering a ball. Explain, why? Ans. When a fast medium bowler wants to deliver a ball, he runs for quite some distance before actually delivering the ball. By running the bowler as well as ball acquires a state of motion and due to this inertia of motion balls moves at a faster speed. Q.13. A naughty boy hits a mango tree with a stone and the mango falls down. How? Ans. The mango tree is in a state of rest. When the stone thrown by a naughty boy strikes the tree just above a mango lying down, that part of branch comes into a state of motion. However, the mango tends to maintain its state of rest and falls down. Q.14. When a racer suddenly stops after completing the race, he falls in forward direction. Why? Ans. When a racer suddenly, stops after successfully completing a race, he falls in forward direction. When he stops suddenly, his feet come to rest but upper parts of body tend to maintain their state of motion. Consequently, he experiences a forward push and may fall in the forward direction.

13 Q.15. A passenger jumping on platform from a still running train falls with his head in the forward direction. Why? Ans. Q.16. Sparks coming out of a grinding stone move tangentially. How? Ans. The sparks produced while sharpening a knife by rubbing it with the surface of a rotating grinding stone are tangential to the circumference of the grinding stone. The sparks m ove in straight lines on account of the property of inertia of direction. Q.17. Define momentum of an object. On what factors does it depend? What is its SI unit? Ans. Q.18. A ball thrown with a finite velocity on ground stops after covering some distance. Does it violate the first law of motion? Give reason. Ans. The stoppage of a ball after covering some distance on ground does not violate the first law of motion. In fact, the ball stops because a frictional force due to ground is opposing the motion of ball. Thus, it is supporting the first law of motion. Q.19. What is the effect of a force on the momentum of an object? Hence, define Newton's second law of motion. Ans. We know that an unbalanced force acting on an object causes change in its velocity. Therefore, we conclude that an unbalanced force acting on an object produces a change in its momentum. According to second law of motion, the rate of change of momentum of an object is directly proportional to the applied unbalanced force and in the direction of force. Q.20. What is the acceleration produced in an object on applying an unbalanced force on it? Hence define a unit of force. Ans. The acceleration produced in an object on applying an unbalanced force on it is given by the ratio of force applied (F) and the mass ( m ) of the object. Force F Acceleration produced a = Mass m or F= ma Hence, one unit of force is that force which produces unit acceleration when applied to a body of unit mass. Q.21. Define SI unit of force from second law of motion. Ans. According to second law of motion F = ma. If mass of an object m = 1 kg and a = 1 m s~ 2, then F= I kg x 1 m s~ 2 = 1 N. Hence, one newton force is the force which when acting on an object of mass 1 kg produces an acceleration of 1 m s~ 2 in it. Q.22. A force produces an acceleration of 5 m s -2 when applied on a body of mass 2 kg. Find the magnitude of force. How much acceleration will the same force produce when applied to a body of mass 4 k g? Q.23. A ship of mass 4 x 10 7 kg is pulled by a force of 6 x 10 5 N. Find the acceleration. If initially the ship was at rest, find its velocity after 10 minutes. As initial velocity of ship = 0 and time t = 10 minutes = 10 x 60 s = 600 s Final velocity of ship v = u + a t = x 600 = 9 m s -1 Q.24. Which would require a greater force accelerating a 3 kg mass at 6 m s -2 or a 4 kg mass at 4 ms- 2? Ans. In first case, m x = 3 kg and a, = 6 m s"~ 2, hence force needed F l = m ] a l =3 x 6 = 18 N In second case, m 2 = 4 kg and a 2 = 4 m s" 2, hence force needed F 2 = m 2 a 2 = 4 x 4 = 16 N => F, > F 2 Thus, a greater force is required for accelerating a 3 kg mass at 6 m s ~. 13

14 Q.25. A car is running at a rate of 72 km h _1 when suddenly brakes are applied so as to stop the car within 10 m. Find the force of brakes. (Assume total mass of car and passengers as 800 kg). Q.26. The velocity-time graph of a hard ball of mass 100 g moving along a straight line along a concrete track is given in Fig Calculate (i) the acceleration, (//') force exerted by the track to bring the ball to rest. Q.27. Show that second law of motion gives a measure of a force. Ans. Q.28. While catching a cricket ball, a player lowers his hands with the ball. Briefly explain, why? Ans. When the ball is caught by a fielder, momentum of ball is reduced to be zero. By lowering his hands with the ball, the player increases the time of catch i.e., time to stop the ball. Consequently for same change in momentum the rate of change of momentum i.e., the force exerted by ball on the player's hand will be less. Conse qquently, chances of pain or the player being hurt is very much reduced. Q.29. Automobiles are provided with shockers. Why? Ans. Automobiles e.g., car, bus, truck, motorbike etc. are provided strong spring systems known as shock absorbers or shockers. These gets compressed when the vehicle gets a jerk due to unevenness of road and then slowly regain their original size. Thus, they increase the time of jerk. Consequently, the driver and passengers experience a lesser force of jerk. In other words, shockers make t he journey smoother. Q.30. A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 m s" 1. How long does the body take to stop? Q.31. State Newton's third law of motion. Give one illustration too. Ans. Newton's third law of motion states that to every action there is an equal and opposite reaction. As an illustration consider a person hitting forcefully with his hand on a table. The person feels pain in his hand too, which is due to the reaction force exerted by the table on his hand. Q.32. A single isolated force is an impossibility. Justify the statement. Ans. In accordance with Newton's third law of motion we know that for every action force there must be a reaction force too. Thus, forces are present in pairs and a single isolated force is an impossibility. 14

15 Q.33. What do you mean by action and reaction forces? Ans. When one body applies force on second body, it is the action force. In turn, second body exerts an equal and opposite force on the first v body, which is the reaction force. Consider a ball /( moving with initial speed v colliding with a stationary ball B. During the collision force applied by A on ball B ( F, tg ) is the action force and the force exerted by B on ball A ) is the reaction force. Q.34. Show that walking of a man is an example of Newton's third law of motion. Ans. While walking a man presses the ground with his feat in backward direction. The ground in turn pushes the man in the forward direction. Thus, it is the reaction force due to ground which enables a man to walk. Q.35. It is difficult to walk on a sandy surface. Why? Ans. While walking we press the ground backward and are able to move forward due to reaction of ground on us. In case of sandy surface it is difficult to press the surface backward. As the action force is less, reaction force will also be correspondingly less and it will be difficult to walk on a sandy surface. Q.36. Apply Newton's third law of motion to the following problems i)rowing of a boat in a river, (ii) flight of a bird. Ans. (i) A boatman pushes the water backward with his oars. Water in turn exerts a force on boat in the forward direction, due to which boat is rowed in the forward direction. A bird pushes the air backward with its wings and is able to fly in forward direction due to reaction force exerted by air on the bird. Q.37. State the law of conservation of momentum. What is the special feature of this law? Ans. Q.38. On firing a bullet, the rifle always gives a backward kick. Why? Ans. When a bullet is fired from a rifle, the rifle exerts a force on the bullet. As a result, bullet comes out of the muzzle of rifle with a high velocity. In turn, the rifle experiences an equal force in the backward direction and it is this backward push due to which the rifle recoils. Q.39. Apply third law of motion to explain hammer-nail problem. Ans. When a carpenter hits the head of a nail with a hammer, the hammer exerts a force on the nail. Due to this force, the nail is driven into the wood. The nail also exerts an equal and opposite force on the hammer due to which its motion is stopped in the mid swing. (B-ll) Short Answer Type Questions (Three Marks Each) Q.l. What is inertia? What is its measure? In what three forms does it manifest? Ans. Inertia of a body is its inherent property to maintain its state of rest or of uniform motion along a straight line unless compelled by some external unbalanced force acting on it. Mass of a body is a measure of its inertia. Heavier the mass, greater is th e inertia of the body. Inertia may show itself in any of three forms, namely, (/') inertia of rest, (ii) inertia of motion, and (//7)inertia of direction. Q.2. What do you mean by inertia of rest? Give three examples to illustrate it. Ans. Inertia of rest is the inherent property of a body at rest due to which it cannot change its state of rest by itself. Following examples illustrate it: (i) A passenger standing in a bus falls backward when the driver suddenly accelerates the car from its rest position. (//') A bullet fired against a window glass pane passes through it making a clean hole in it. Rest of glass pane remains intact due to inertia of rest. (iii) We brush our shoes to remove dust particles, which fall below due to inertia of rest. Q.3. What is inertia of motion? Give three illustrations to explain the concept. Ans. The tendency of a moving object to maintain its state of uniform motion is called "inertia of motion". Following examples illustrate it: (i) A person jumping out from a running train or bus falls with his head in forward direction due to the inertia of motion. (ii) A circus performer jumps up from the back of a running horse, passes through a circular ring of lire and again regains his position on the horse back on account of the inertia of motion. ( i i i ) A ball thrown vertically upward by a child sitting in a running train comes back to his ha nds due to its inertia of motion. Q.4. Explain the concept of directional inertia by giving three examples. Ans. Directional inertia is the property of a body due to which it tends to maintain its direction of motion

16 along a given straight line. Following examples illustrate it: (i) When a motorcar takes a sharp turn at a high speed, passengers sitting in it get thrown to one side (opposite to that of turn) because they tend to continue in their straight line motion. (/;') When a particle being rotated along a circular path is let free, it moves along the tangent to the path due to its inertia of direction. ( i i i ) In a bicycle, rickshaw or motorbike mudguards provided with the wheels collect the mud from wheels on accounts of its property of directional inertia. Q.5. State and explain Newton's first law of motion. Ans. Statement : See point number 8 under the heading "Chapter At A Glance". Explanation :The law has two parts; (f ) a body tends to maintain its state of rest, and (ii) a body tends to maintain its state of uniform motion by itself. About first part we have no doubt as a book left on a table will remain there unless somebody disturbs its position. However, regarding second part we may have doubt because we see that a moving object comes to rest after covering some distance. However, this is an indirect evidence regarding correctness of first law of motion b ecause the moving object comes to rest only due to the action of frictional forces. If there is no friction, the object will continue its state of motion and will never come to rest e.g., the motion of stars. Q.6. Obtain definition of force from Newton's first law of motion. Ans. According to Newton's first law of motion, an object cannot change its state of rest or of uniform motion along a straight line by itself. To change its state of rest or motion an external unbalanced force is required. If external force is sufficiently large, it may change the state of rest or of uniform motion of the object. But if the external force is not appropriate, it may not be able to change the state of rest or motion of the object. Hence, we may define force as that extern al push or pull which changes or tries to change the state of rest or of uniform motion of an object along a given straight line. Q.7. Show, by drawing figures, how a force may change the size or shape of an object. Ans. Sometimes force applied on an object may change its size and shape too. We give two examples : Take a helical spring. Try to stretch it by applying forces at its ends outwards, the length of spring increases. However, if forces are applied inwards i.e., the spring is compressed and the length of the spring decreases. (ii) Take a spherical rubber ball and apply force on both sides by pressing with your hands. The ball becomes oblong. It shows that shape of ball has changed due to external force. Q.8. Briefly describe Galileo's experiment to show that objects move with a constant speed when no force acts on them. Ans. Consider a smooth double inclined plane OR as shown in Fig When a s mall glass marble (or steel b a l l ) is released from right from a point A (say at a height /;,), it would roll down the slope and go up on the opposite left side to a point B (say at a height h 7 ). Careful observations showed that value of h 0 and h ] are equal i.e., h 2 = hy If the inclinations of plane on both sides are equal (i.e., 9, = 9 0 ), the marble will climb the same distance that it covered while rolling down. If angle of inclination of left side of plane is decreased, the marble would travel longer distance till h 2 = hy If left side plane is made horizontal, the marble would continue to travel forever trying to reach the same