Class 9 Science Chapter 8 PDF

C hapter 8 FORCE AND LAWS OF MOTION In the previous chapter, we described the In our everyday life we observe that some motion of an object along a straight line in e...

C hapter 8 FORCE AND LAWS OF MOTION In the previous chapter, we described the In our everyday life we observe that some motion of an object along a straight line in effort is required to put a stationary object terms of its position, velocity and acceleration. into motion or to stop a moving object. We We saw that such a motion can be uniform ordinarily experience this as a muscular effort or non-uniform. We have not yet discovered and say that we must push or hit or pull on what causes the motion. Why does the speed an object to change its state of motion. The of an object change with time? Do all motions concept of force is based on this push, hit or require a cause? If so, what is the nature of pull. Let us now ponder about a ‘force’. What this cause? In this chapter we shall make an is it? In fact, no one has seen, tasted or felt a attempt to quench all such curiosities. force. However, we always see or feel the effect For many centuries, the problem of of a force. It can only be explained by motion and its causes had puzzled scientists describing what happens when a force is and philosophers. A ball on the ground, when applied to an object. Pushing, hitting and given a small hit, does not move forever. Such pulling of objects are all ways of bringing observations suggest that rest is the “natural objects in motion (Fig. 8.1). They move because state” of an object. This remained the belief we make a force act on them. until Galileo Galilei and Isaac Newton From your studies in earlier classes, you developed an entirely different approach to are also familiar with the fact that a force can understand motion. be used to change the magnitude of velocity of an object (that is, to make the object move faster or slower) or to change its direction of motion. We also know that a force can change the shape and size of objects (Fig. 8.2). (a) The trolley moves along the (b) The drawer is pulled. direction we push it. (a) (b) (c) The hockey stick hits the ball forward Fig. 8.2: (a) A spring expands on application of force; Fig. 8.1: Pushing, pulling, or hitting objects change (b) A spherical rubber ball becomes oblong their state of motion. as we apply force on it. Rationalised 2023-24 8.1 Balanced and Unbalanced box with a small force, the box does not move because of friction acting in a direction Forces opposite to the push [Fig. 8.4(a)]. This friction force arises between two surfaces in contact; Fig. 8.3 shows a wooden block on a horizontal in this case, between the bottom of the box table. Two strings X and Y are tied to the two and floor’s rough surface. It balances the opposite faces of the block as shown. If we pushing force and therefore the box does not apply a force by pulling the string X, the block move. In Fig. 8.4(b), the children push the box begins to move to the right. Similarly, if we harder but the box still does not move. This is pull the string Y, the block moves to the left. because the friction force still balances the But, if the block is pulled from both the sides pushing force. If the children push the box with equal forces, the block will not move. harder still, the pushing force becomes bigger Such forces are called balanced forces and than the friction force [Fig. 8.4(c)]. do not change the state of rest or of motion of There is an unbalanced force. So the box an object. Now, let us consider a situation in which two opposite forces of different starts moving. magnitudes pull the block. In this case, the What happens when we ride a bicycle? block would begin to move in the direction of When we stop pedalling, the bicycle begins the greater force. Thus, the two forces are to slow down. This is again because of the not balanced and the unbalanced force acts friction forces acting opposite to the direction in the direction the block moves. This of motion. In order to keep the bicycle moving, suggests that an unbalanced force acting on we have to start pedalling again. It thus an object brings it in motion. appears that an object maintains its motion under the continuous application of an unbalanced force. However, it is quite incorrect. An object moves with a uniform velocity when the forces (pushing force and frictional force) acting on the object are balanced and there is no net external force on it. If an unbalanced force is applied on the object, there will be a change either in its speed or in the direction of its motion. Thus, to accelerate the motion of an object, an Fig. 8.3: Two forces acting on a wooden block unbalanced force is required. And the change in its speed (or in the direction of motion) What happens when some children try to would continue as long as this unbalanced push a box on a rough floor? If they push the force is applied. However, if this force is (a) (b) (c) Fig. 8.4 88 SCIENCE Rationalised 2023-24 removed completely, the object would continue to move with the velocity it has acquired till then. 8.2 First Law of Motion By observing the motion of objects on an inclined plane Galileo deduced that objects move with a constant speed when no force acts on them. He observed that when a marble rolls down an inclined plane, its velocity increases [Fig. 8.5(a)]. In the next chapter, you will learn that the marble falls under the unbalanced force of gravity as it rolls down and attains a definite velocity by the time it reaches the bottom. Its velocity decreases when it climbs up as shown in Fig. 8.5(b). Fig. 8.5(c) shows a marble resting on an ideal frictionless plane inclined on both sides. Fig. 8.5: (a) the downward motion; (b) the upward Galileo argued that when the marble is motion of a marble on an inclined plane; released from left, it would roll down the slope and (c) on a double inclined plane. and go up on the opposite side to the same Newton further studied Galileo’s ideas on height from which it was released. If the force and motion and presented three inclinations of the planes on both sides are fundamental laws that govern the motion of equal then the marble will climb the same objects. These three laws are known as distance that it covered while rolling down. If Newton’s laws of motion. The first law of the angle of inclination of the right-side plane motion is stated as: were gradually decreased, then the marble An object remains in a state of rest or of would travel further distances till it reaches uniform motion in a straight line unless the original height. If the right-side plane were compelled to change that state by an ultimately made horizontal (that is, the slope applied force. is reduced to zero), the marble would continue In other words, all objects resist a change to travel forever trying to reach the same in their state of motion. In a qualitative way, height that it was released from. The the tendency of undisturbed objects to stay unbalanced forces on the marble in this case at rest or to keep moving with the same are zero. It thus suggests that an unbalanced velocity is called inertia. This is why, the first (external) force is required to change the law of motion is also known as the law motion of the marble but no net force is of inertia. needed to sustain the uniform motion of the Certain experiences that we come across marble. In practical situations it is difficult while travelling in a motorcar can be to achieve a zero unbalanced force. This is explained on the basis of the law of inertia. because of the presence of the frictional force We tend to remain at rest with respect to the acting opposite to the direction of motion. seat until the driver applies a braking force Thus, in practice the marble stops after to stop the motorcar. With the application of travelling some distance. The effect of the brakes, the car slows down but our body frictional force may be minimised by using a tends to continue in the same state of motion smooth marble and a smooth plane and because of its inertia. A sudden application of providing a lubricant on top of the planes. brakes may thus cause injury to us by impact FORCE AND LAWS OF MOTION 89 Rationalised 2023-24  or collision with the panels in front. Safety belts Galileo Galilei was born are worn to prevent such accidents. Safety belts on 15 February 1564 in Pisa, Italy. Galileo, right exert a force on our body to make the forward from his childhood, had motion slower. An opposite experience is interest in mathematics encountered when we are standing in a bus and natural philosophy. and the bus begins to move suddenly. Now But his father we tend to fall backwards. This is because the Vincenzo Galilei wanted sudden start of the bus brings motion to the him to become a medical bus as well as to our feet in contact with the doctor. Accordingly, floor of the bus. But the rest of our body Galileo Galilei Galileo enrolled himself (1564 – 1642) opposes this motion because of its inertia. for a medical degree at the When a motorcar makes a sharp turn at a University of Pisa in 1581 which he never high speed, we tend to get thrown to one side. completed because of his real interest in This can again be explained on the basis of mathematics. In 1586, he wrote his first the law of inertia. We tend to continue in our scientific book ‘The Little Balance [La straight-line motion. When an unbalanced Balancitta]’, in which he described Archimedes’ method of finding the relative force is applied by the engine to change the densities (or specific gravities) of substances direction of motion of the motorcar, we slip to using a balance. In 1589, in his series of one side of the seat due to the inertia of essays – De Motu, he presented his theories our body. about falling objects using an inclined plane The fact that a body will remain at rest to slow down the rate of descent. unless acted upon by an unbalanced force In 1592, he was appointed professor of can be illustrated through the mathematics at the University of Padua in following activities: the Republic of Venice. Here he continued his observations on the theory of motion and Activity ______________ 8.1 through his study of inclined planes and the pendulum, formulated the correct law for Make a pile of similar carom coins on uniformly accelerated objects that the a table, as shown in Fig. 8.6. distance the object moves is proportional to Attempt a sharp horizontal hit at the the square of the time taken. bottom of the pile using another carom Galileo was also a remarkable craftsman. coin or the striker. If the hit is strong He developed a series of telescopes whose enough, the bottom coin moves out optical performance was much better than quickly. Once the lowest coin is removed, the inertia of the other coins that of other telescopes available during those makes them ‘fall’ vertically on the days. Around 1640, he designed the first table. pendulum clock. In his book ‘Starry Messenger’ on his astronomical discoveries, Galileo claimed to have seen mountains on the moon, the milky way made up of tiny stars, and four small bodies orbiting Jupiter. In his books ‘Discourse on Floating Bodies’ and ‘Letters on the Sunspots’, he disclosed his observations of sunspots. Using his own telescopes and through his observations on Saturn and Venus, Galileo argued that all the planets must orbit the Sun Fig. 8.6: Only the carom coin at the bottom of a and not the earth, contrary to what was pile is removed when a fast moving carom believed at that time. coin (or striker) hits it. 90 SCIENCE Rationalised 2023-24  Activity ______________ 8.2 five-rupees coin if we use a one-rupee coin, we find that a lesser force is required to perform Set a five-rupee coin on a stiff card the activity. A force that is just enough to cause covering an empty glass tumbler a small cart to pick up a large velocity will standing on a table as shown in produce a negligible change in the motion of a Fig. 8.7. train. This is because, in comparison to the Give the card a sharp horizontal flick cart the train has a much lesser tendency to with a finger. If we do it fast then the card shoots away, allowing the coin to change its state of motion. Accordingly, we say fall vertically into the glass tumbler due that the train has more inertia than the cart. to its inertia. Clearly, heavier or more massive objects offer The inertia of the coin tries to larger inertia. Quantitatively, the inertia of an maintain its state of rest even when object is measured by its mass. We may thus the card flows off. relate inertia and mass as follows: Inertia is the natural tendency of an object to resist a change in its state of motion or of rest. The mass of an object is a measure of its inertia. Q uestions Fig. 8.7: When the card is flicked with the 1. Which of the following has more finger the coin placed over it falls in the tumbler. inertia: (a) a rubber ball and a stone of the same size? (b) a bicycle and a train? (c) a five- Activity ______________ 8.3 rupees coin and a one-rupee coin? Place a water-filled tumbler on a tray. 2. In the following example, try to Hold the tray and turn around as fast identify the number of times the as you can. velocity of the ball changes: We observe that the water spills. Why? “A football player kicks a football to another player of his team who Observe that a groove is provided in a kicks the football towards the saucer for placing the tea cup. It prevents goal. The goalkeeper of the the cup from toppling over in case of opposite team collects the football sudden jerks. and kicks it towards a player of his own team”. 8.3 Inertia and Mass Also identify the agent supplying the force in each case. All the examples and activities given so far 3. Explain why some of the leaves illustrate that there is a resistance offered by may get detached from a tree if an object to change its state of motion. If it is we vigorously shake its branch. at rest it tends to remain at rest; if it is moving 4. Why do you fall in the forward it tends to keep moving. This property of an direction when a moving bus object is called its inertia. Do all bodies have brakes to a stop and fall the same inertia? We know that it is easier to backwards when it accelerates push an empty box than a box full of books. from rest? Similarly, if we kick a football it flies away. But if we kick a stone of the same size with equal force, it hardly moves. We may, in fact, 8.4 Second Law of Motion get an injury in our foot while doing so! The first law of motion indicates that when an Similarly, in activity 8.2, instead of a unbalanced external force acts on an object, FORCE AND LAWS OF MOTION 91 Rationalised 2023-24 its velocity changes, that is, the object gets an on the time rate at which the momentum is acceleration. We would now like to study how changed. the acceleration of an object depends on the The second law of motion states that the force applied to it and how we measure a force. rate of change of momentum of an object is Let us recount some observations from our proportional to the applied unbalanced force everyday life. During the game of table tennis in the direction of force. if the ball hits a player it does not hurt him. On the other hand, when a fast moving cricket 8.4.1 MATHEMATICAL FORMULATION OF ball hits a spectator, it may hurt him. A truck SECOND LAW OF MOTION at rest does not require any attention when parked along a roadside. But a moving truck, Suppose an object of mass, m is moving along even at speeds as low as 5 m s–1, may kill a a straight line with an initial velocity, u. It is person standing in its path. A small mass, uniformly accelerated to velocity, v in time, t such as a bullet may kill a person when fired by the application of a constant force, F from a gun. These observations suggest that throughout the time, t. The initial and final the impact produced by the objects depends momentum of the object will be, p1 = mu and on their mass and velocity. Similarly, if an p2 = mv respectively. object is to be accelerated, we know that a The change in momentum ∝ p2 – p1 greater force is required to give a greater ∝ mv – mu velocity. In other words, there appears to exist ∝ m × (v – u). some quantity of importance that combines the object’s mass and its velocity. One such m × (v − u ) The rate of change of momentum ∝ property called momentum was introduced by t Newton. The momentum, p of an object is Or, the applied force, defined as the product of its mass, m and velocity, v. That is, m × (v − u ) F∝ p = mv (8.1) t Momentum has both direction and km × (v − u ) F= (8.2) magnitude. Its direction is the same as that t of velocity, v. The SI unit of momentum is = kma (8.3) kilogram-metre per second (kg m s-1). Since the application of an unbalanced force brings Here a [ = (v – u)/t ] is the acceleration, a change in the velocity of the object, it is which is the rate of change of velocity. The therefore clear that a force also produces a quantity, k is a constant of proportionality. change of momentum. The SI units of mass and acceleration are kg Let us consider a situation in which a car and m s-2 respectively. The unit of force is so with a dead battery is to be pushed along a chosen that the value of the constant, k straight road to give it a speed of 1 m s-1, which becomes one. For this, one unit of force is is sufficient to start its engine. If one or two defined as the amount that produces an persons give a sudden push (unbalanced force) acceleration of 1 m s-2 in an object of 1 kg to it, it hardly starts. But a continuous push mass. That is, over some time results in a gradual acceleration 1 unit of force = k × (1 kg) × (1 m s-2). of the car to this speed. It means that the change of momentum of the car is not only determined Thus, the value of k becomes 1. From Eq. (8.3) by the magnitude of the force but also by the F = ma (8.4) time during which the force is exerted. It may then also be concluded that the force necessary The unit of force is kg m s-2 or newton, to change the momentum of an object depends which has the symbol N. The second law of 92 SCIENCE Rationalised 2023-24 motion gives us a method to measure the force The first law of motion can be acting on an object as a product of its mass mathematically stated from the mathematical and acceleration. expression for the second law of motion. Eq. The second law of motion is often seen in (8.4) is action in our everyday life. Have you noticed that while catching a fast moving cricket ball, F = ma a fielder in the ground gradually pulls his m (v − u ) hands backwards with the moving ball? In or F = (8.5) t doing so, the fielder increases the time during or Ft = mv – mu which the high velocity of the moving ball decreases to zero. Thus, the acceleration of That is, when F = 0, v = u for whatever time, t the ball is decreased and therefore the impact is taken. This means that the object will of catching the fast moving ball (Fig. 8.8) is continue moving with uniform velocity, u also reduced. If the ball is stopped suddenly throughout the time, t. If u is zero then v will then its high velocity decreases to zero in a also be zero. That is, the object will remain very short interval of time. Thus, the rate of at rest. change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt Example 8.1 A constant force acts on an the palm of the fielder. In a high jump athletic object of mass 5 kg for a duration of event, the athletes are made to fall either on 2 s. It increases the object’s velocity a cushioned bed or on a sand bed. This is to from 3 m s –1 to 7 m s -1. Find the increase the time of the athlete’s fall to stop magnitude of the applied force. Now, if after making the jump. This decreases the rate the force was applied for a duration of of change of momentum and hence the force. 5 s, what would be the final velocity of Try to ponder how a karate player breaks a the object? slab of ice with a single blow. Solution: We have been given that u = 3 m s–1 and v = 7 m s-1, t = 2 s and m = 5 kg. From Eq. (8.5) we have, m (v − u ) F = t Substitution of values in this relation gives F = 5 kg (7 m s-1 – 3 m s-1)/2 s = 10 N. Now, if this force is applied for a duration of 5 s (t = 5 s), then the final velocity can be calculated by rewriting Eq. (8.5) as Ft v =u+ m On substituting the values of u, F, m and t, we get the final velocity, Fig. 8.8: A fielder pulls his hands gradually with the v = 13 m s-1. moving ball while holding a catch. FORCE AND LAWS OF MOTION 93 Rationalised 2023-24  Solution: Example 8.2 Which would require a greater force –– accelerating a 2 kg mass From Eq. (8.4) we have m1 = F/a1; and at 5 m s–2 or a 4 kg mass at 2 m s-2 ? m2 = F/a2. Here, a1 = 10 m s-2; a2 = 20 m s-2 and F = 5 N. Solution: Thus, m1 = 5 N/10 m s-2 = 0.50 kg; and From Eq. (8.4), we have F = ma. m2 = 5 N/20 m s-2 = 0.25 kg. Here we have m1 = 2 kg; a1 = 5 m s-2 If the two masses were tied together, and m2 = 4 kg; a2 = 2 m s-2. the total mass, m would be Thus, F1 = m1a1 = 2 kg × 5 m s-2 = 10 N; m = 0.50 kg + 0.25 kg = 0.75 kg. and F2 = m2a2 = 4 kg × 2 m s-2 = 8 N. The acceleration, a produced in the ⇒ F1 > F2. combined mass by the 5 N force would Thus, accelerating a 2 kg mass at be, a = F/m = 5 N/0.75 kg = 6.67 m s-2. 5 m s-2 would require a greater force. Example 8.5 The velocity-time graph of a Example 8.3 A motorcar is moving with a ball of mass 20 g moving along a velocity of 108 km/h and it takes 4 s to straight line on a long table is given in stop after the brakes are applied. Fig. 8.9. Calculate the force exerted by the brakes on the motorcar if its mass along with the passengers is 1000 kg. Solution: The initial velocity of the motorcar u = 108 km/h = 108 × 1000 m/(60 × 60 s) = 30 m s-1 and the final velocity of the motorcar v = 0 m s-1. The total mass of the motorcar along Fig. 8.9 with its passengers = 1000 kg and the time taken to stop the motorcar, t = 4 s. How much force does the table exert on From Eq. (8.5) we have the magnitude the ball to bring it to rest? of the force (F) applied by the brakes as m(v – u)/t. Solution: On substituting the values, we get The initial velocity of the ball is 20 cm s-1. F = 1000 kg × (0 – 30) m s-1/4 s Due to the frictional force exerted by the = – 7500 kg m s-2 or – 7500 N. table, the velocity of the ball decreases The negative sign tells us that the force down to zero in 10 s. Thus, u = 20 cm s–1; exerted by the brakes is opposite to the v = 0 cm s-1 and t = 10 s. Since the direction of motion of the motorcar. velocity-time graph is a straight line, it is clear that the ball moves with a constant acceleration. The acceleration a is Example 8.4 A force of 5 N gives a mass v −u m1, an acceleration of 10 m s–2 and a a = mass m2, an acceleration of 20 m s-2. t What acceleration would it give if both = (0 cm s-1 – 20 cm s-1)/10 s the masses were tied together? = –2 cm s-2 = –0.02 m s-2. 94 SCIENCE Rationalised 2023-24  The force exerted on the ball F is, F = ma = (20/1000) kg × (– 0.02 m s-2) = – 0.0004 N. The negative sign implies that the frictional force exerted by the table is Fig. 8.10: Action and reaction forces are equal and opposite to the direction of motion of opposite. the ball. Suppose you are standing at rest and intend to start walking on a road. You must 8.5 Third Law of Motion accelerate, and this requires a force in accordance with the second law of motion. The first two laws of motion tell us how an Which is this force? Is it the muscular effort applied force changes the motion and provide you exert on the road? Is it in the direction us with a method of determining the force. we intend to move? No, you push the road The third law of motion states that when one below backwards. The road exerts an equal object exerts a force on another object, the and opposite force on your feet to make you second object instantaneously exerts a force move forward. back on the first. These two forces are always It is important to note that even though equal in magnitude but opposite in direction. the action and reaction forces are always These forces act on different objects and never equal in magnitude, these forces may not on the same object. In the game of football produce accelerations of equal magnitudes. sometimes we, while looking at the football This is because each force acts on a different and trying to kick it with a greater force, object that may have a different mass. collide with a player of the opposite team. When a gun is fired, it exerts a forward Both feel hurt because each applies a force force on the bullet. The bullet exerts an equal to the other. In other words, there is a pair of and opposite force on the gun. This results in forces and not just one force. The two the recoil of the gun (Fig. 8.11). Since the gun opposing forces are also known as action and has a much greater mass than the bullet, the reaction forces. acceleration of the gun is much less than the Let us consider two spring balances acceleration of the bullet. The third law of connected together as shown in Fig. 8.10. The motion can also be illustrated when a sailor fixed end of balance B is attached with a rigid jumps out of a rowing boat. As the sailor support, like a wall. When a force is applied jumps forward, the force on the boat moves it through the free end of spring balance A, it is backwards (Fig. 8.12). observed that both the spring balances show the same readings on their scales. It means that the force exerted by spring balance A on balance B is equal but opposite in direction to the force exerted by the balance B on balance A. Any of these two forces can be called as action and the other as reaction. This gives us an alternative statement of the third law of motion i.e., to every action there is an equal and opposite reaction. However, it must be remembered that the action and reaction always act on two different objects, Fig. 8.11: A forward force on the bullet and recoil of the gun. simultaneously. FORCE AND LAWS OF MOTION 95 Rationalised 2023-24 Fig. 8.12: As the sailor jumps in forward direction, the boat moves backwards. Fig. 8.13 Activity ______________ 8.4 Request two children to stand on two Now, place two children on one cart and separate carts as shown in Fig. 8.13. one on another cart. The second law of motion Give them a bag full of sand or some can be seen, as this arrangement would show other heavy object. Ask them to play a different accelerations for the same force. game of catch with the bag. The cart shown in this activity can be Does each of them experience an constructed by using a 12 mm or 18 mm thick instantaneous force as a result of throwing the sand bag? plywood board of about 50 cm × 100 cm with You can paint a white line on two pairs of hard ball-bearing wheels (skate cartwheels to observe the motion of the wheels are good to use). Skateboards are not two carts when the children throw the as effective because it is difficult to maintain bag towards each other. straight-line motion. What you have learnt First law of motion: An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force. The natural tendency of objects to resist a change in their state of rest or of uniform motion is called inertia. The mass of an object is a measure of its inertia. Its SI unit is kilogram (kg). Force of friction always opposes motion of objects. Second law of motion: The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force. 96 SCIENCE Rationalised 2023-24  The SI unit of force is kg m s–2. This is also known as newton and represented by the symbol N. A force of one newton produces an acceleration of 1 m s –2 on an object of mass 1 kg. The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity. Its SI unit is kg m s–1. Third law of motion: To every action, there is an equal and opposite reaction and they act on two different bodies. Exercises 1. 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 2. When a carpet is beaten with a stick, dust comes out of it, Explain. 3. Why is it advised to tie any luggage kept on the roof of a bus with a rope? 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 (a) the batsman did not hit the ball hard enough. (b) velocity is proportional to the force exerted on the ball. (c) 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. 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 its acceleration. Find the force acting on it if its mass is 7 tonnes (Hint: 1 tonne = 1000 kg.) 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? 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 40000 N and the track offers a friction force of 5000 N, then calculate: (a) the net accelerating force and (b) the acceleration of the train. 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 FORCE AND LAWS OF MOTION 97 Rationalised 2023-24  stopped with a negative acceleration of 1.7 m s–2? 9. What is the momentum of an object of mass m, moving with a velocity v? (a) (mv)2 (b) mv2 (c) ½ mv2 (d) mv 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? 11. 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. 12. 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–1. Calculate the magnitude of change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick. 13. 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. 14. 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. 15. An object of mass 100 kg is accelerated uniformly from a velocity of 5 m s–1 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 on the object. 16. 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 98 SCIENCE Rationalised 2023-24  said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions. 17. 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. Additional Exercises A1. The following is the distance-time table of an object in motion: Time in seconds Distance in metres 0 0 1 1 2 8 3 27 4 64 5 125 6 216 7 343 (a) What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero? (b) What do you infer about the forces acting on the object? A2. 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.) A3. A hammer of mass 500 g, moving at 50 m s-1, 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? A4. 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. FORCE AND LAWS OF MOTION 99 Rationalised 2023-24