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/s2. SI unit of force is kgm/s

2

But 1 kgm/s2 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/s2 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 m1 and m2 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

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.

B] Questions given on page number 126-127 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. I t 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 collis ion), u0

= 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 di rection 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. I t 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

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 o f 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 ' - m a = 7000 x 2 = 14000 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 v2 - 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 40000 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 [ = + 40000 N and the forced of friction

acting on train due to track F ^ = - 5000 N

(Force F0 is negative because force of friction always opposes the motion)

.-. Net accelerating force acting on the train F = ± F2 = 40000 - 5000 = 35000 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. I t means it w i l l 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 = 28000 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( -1 . 7 ) = -2 5 5 0 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 ?

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 { = m2 = 1.5 kg

As the objects are moving with equal speeds in mutually opposite directions along a s traight line, hence

ul = + 2.5 m s^1 but u7 = - 2.5 m s~'.

As the two objects stick together due to collision, their final velocity will be the same. Let V| = v2 = v

(say)

Using conservation law of momentum, we have

It means that after collision both the balls w i l l 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 o f 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, i t 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 i n 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 = 1 0 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 i n 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.

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. A n 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 - 100 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

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 ?

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

Time in seconds Distance in metres

0 0

1 1

2 8

3 27

4 64

5 125

6 2 1 6

7 343

Q.A.I. The following is the distance-time table of an object in motion :

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 o f force suggests that the force is opposing the motion o f 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 i n 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 o f a body to maintain its state of rest or of uniform motion along a straight line by

itself.

Q.5. What is a measure of inertia ? Ans. The mass of a n 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 i n a car a t 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 =

3 x 2 = 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 ?

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 o f motion.

Q.41. Which law of motion is involved i n 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.

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 i n Fig.

9.01, so that the block does not move from its rest

position. Obviously, it means that net effect of F ] and F2

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. 9.02. 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 o f 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 i n 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 o f motion. However, the mango tends

to maintain its state o f 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 = 0 + 0.015 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 m s -

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, m2 = 4 kg and a2 = 4 m s"2, hence force needed F2 = m2a2 = 4 x 4 = 16 N => F , > F 2

Thus, a greater force is required for accelerating a 3 kg mass at 6 m s ~.

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. 9.03. 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.

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 a n

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 , t g ) 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 i n backward direction. The ground in turn pushes the man in the forward

direction. Thus, i t 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 ab le 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.

(i i i) 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 u p 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

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.

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 i n Fig. 9.07. When a s ma l l glass marble (or

steel b a l l ) is released from right from a point A (say a t a height /;,), it would roll down the slope and go

up on the opposite left side to a point B (say at a height h7). Careful observations showed that value of h0

and h ] are equal i.e., h2 = h y If the inclinations of plane on both sides are equal ( i .e., 9, = 90), 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 h2 = h y If left side plane is made

horizontal, the marble would continue to travel forever trying to reach the same

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.

height, from which it was released. The unbalanced force on Q

the marble in this case is zero. It shows that objects move with

a constant speed when no force acts on them.

Q.9. Show by giving examples that momentum of an object depends upon its mass as well as velocity.

Ans. Momentum of a body is the product of its mass and velocity. It means that momentum of a body is (i)

directly proportional to its mass, and (ii) directly proportional to its velocity. To explain, its consider

following examples :

It is easier to catch a tennis ball than a cricket ball moving with same speed because mass of tennis ball is

less than that of a cricket ball. It shows that momentum depends on the mass of an object.

A person may play with a bullet in his hand. However, the same bullet may even kill that person when fired

from a rifle. It shows that the momentum depends on the velocity of the mo ving object.

Q.10. A car with a dead battery, is to be pushed for some time so as to start it. Why ? What does this example

signify ?

Ans. If we want to start a car with a dead battery, then we have to push it along a straight road to give it a

certain minimum speed (of about 1 m s~'). When one or two persons give it a sudden push, they are unable to

give desired speed to the car and it does not start. However, a continuous push over sometime results in a

gradual acceleration of the car to this minimum speed and car starts.

The example signifies that effect of a force depends on (i) magnitude of the force, and (ii) time for which the

force is applied.

Q.ll. Obtain first law of motion from the mathematical expression for the second law of motion.

Ans. According to second law of motion, we have F = ma.

If there is no external unbalanced force (i.e., F = 0) then acceleration a of the object will be zero (because

mass of an object can never be zero). Thus, we conclude that in the absence of an external unbalanced force

on object will be in a state of unaccelerated motion i.e., v = u. It means that the object will continue moving

with uniform velocity u throughout.

If however, a = 0, then v = 0. It means that a body at rest will remain at rest in the absence of an unbalanced

force.

Thus, we have obtained mathematical statement of first law of motion from the statement of second law of

motion.

Q.l2. Show that first law of motion is a special case of second law of motion when force acting is zero.

Ans.

Q. 13. State and briefly explain Newton's second law of motion.

Ans. Second law of motion states t h a t the rate o f change of mo me n t u m of an object is directly

proportronal to the external unbalanced force applied on it and takes place in the direction of applied force.

Let an object of mass m was initially moving with a velocity u . I t means its initial momentum - mu.If on

applying a constant force F for time / the velocity of the object changes to v then final momentum of given

object = mv.

Q.14. Glass and china ware are wrapped in straw or paper before packing. Briefly explain Why ?

Ans. Glass and China wares are wrapped individually in straw or paper before packin g. If during loading or

unloading in transit packing gets some jerk then straw or paper, being compressible, increase the time of

jerk. As a result for given change in momentum the force of jerk will be less and chances of breakage of

glass and china wares will be reduced.

Q.15. A person is prone to more serious injuries when falling from a certain height on a hard concrete floor than

on a sandy surface. Explain why.

Ans. When a person falls from a height on a hard concrete floor, he immediately comes in re st position. It

means change in momentum is taking place in an extremely short time and consequently, force exerted by

the floor on the man to destroy its momentum is extremely large. Hence, chances of more injuries. When a

person falls on a sandy surface, the surface gets compressed downward and it increases the time. As a result

for same change in momentum force exerted by sandy surface on the person is less and chances of being hurt

are less.

Q.16. In a high jump athletic event, the athletes are made to fall either on a cushioned bed or on a sand bed. Why

?

Ans. Q.17. Briefly explain how an expert karate player breaks a slab of ice with a single blow. Ans. The karate player

brings his arms downward from a height and then suddenly strikes on the ice slab in the middle. As time

involved is extremely small, for given change in momentum the force exerted is extremely large.

Consequently, the ice slab may break even with a single blow.

Q.18. A car starting from rest gains a speed of 60 km/h after covering a distance of 60 m. The mass of the car is

432 kg. Assuming that the opposing force due to air resistance and friction on the car is 200 N, calculate the total

force supplied by the engine of car.

Ans.

F= ma = 432X125/24 =1000 N

However, as an opposing force of 200 N due to air resistance and friction is also to be overcome by the car

engine, hence total force supplied by the engine of car = 1000 + 200 = 1200 N

Q.19. An auto driver moving with a speed of 36 km/h sees a child standing in the middle of the road. He applies

brakes and brings his vehicle to rest in 2.5 s just in time to save the child. If the mass of the auto and the driver be

320 kg, then calculate the force of brakes.

The negative sign means that brakes are exerting the force so as to oppose the motion.

Q.20. A constant force of friction of 50 N is acting on a body of mass 200 kg moving initially with a speed of 15 m

s-1

. How long does the body take to stop ? What distance will it cover before coming to rest ?

Ans. Here frictional force F = -50 N [-ve sign, because force is opposing the motion] mass m = 200 kg,

initial speed u = 15 m s"1, final speed v = 0 From the relation F = ma, we have

Now using the relation v = u + at, we have

and the total distance covered by the body before coming to rest will be

Q.21. Two bodies of masses 4 kg and 5 kg are acted upon by the same force. If the acceleration of the lighter body

is 3 m s~2, then find the acceleration produced in heavier body. What will be the acceleration if that very force is

applied on both bodies tied together ?

Q.22. A bullet of mass 25 g moving with a speed of 200 m s"1 is stopped within 5 cm of the target. What is the

average resistance force offered by the target ?

Q.23. Describe an experimental arrangement to prove that action and reaction forces are equal and

opposite.

Ans. Take two spring balances A and B and connect them together. The fixed end of balance B is attached

with a rigid support (say a wall). Apply some force at the free end of spring balance A, as shown in Fig. 9.08.

We observe that reading of both the spring balances A and B is exactly same.

It means that the force exerted by spring balance A on balance B (the action force) is exactly equal in

magnitude but opposite in direction to the force exerted by the balance B on balance A (the reaction force).

Q.24. State the law of conservation of momentum. Give two illustrations in its support.

Ans. For statement of law of conservation of momentum —

Following illustrations provide experimental evidence for the laws of conservation of momentum : ( f ) When

a man jumps from a boat to the shore, the boat slightly moves away from the shore. Initially man and boat,

together, had zero momentum. When man jumps from the boat, total momentum will be zero only if the boat

moves in a direction opposite to the direction of motion of man.

( i f ) When a gun is fired, the bullet comes out of the muzzle and carries a forward momentum. The gun, in

turn, is imparted an equal momentum in the reverse direction so as to conserve the total momentum of gun -

bullet system. Consequently, the gun recoils backward.

Q.25. Find an expression for the recoil velocity of a gun, when it fires a bullet ?

Q.26. What do you mean by the force of friction ? How can it be minimised ?

Ans. Frictional force is a force which always opposes motion of a body over a given surface. When -ever a

body actually moves over a surface or even tends to move over the surface, frictional force appears in a

direction opposite to the motion. And this opposite force tries to oppose the motion of body.

Effect of frictional force may be minimised by making the sliding body and the plane smooth and by

providing a lubricant on top of the planes.

Q.27. An object A of mass 2 kg moving with a velocity of 3 m s_1

collides head on with object B of mass 1 kg

moving in the opposite direction with a velocity of 4 m s_1

. After collision both bodies stuck together and move

with a common velocity. Find this velocity.

Ans. Here for object A m ] = 2 kg and «, = + 3 m s~' and for object B m2 = 1 kg and s , = -4 ms "1

[w, is

taken as -ve because direction of motion of B is opposite to A ]

If after collision the two objects move together with a velocity v, then in accordance with the law of

conservation of momentum,

Q.28. An explosion breaks a stone at rest into two pieces. One piece of mass 2 kg goes towards east with a speed of

10 m s_1

. The other piece flies off with a speed of 20 m s~'. What is the mass of other piece and in what direction

should it go ?

Ans. Here total initial momentum of stone, being in rest, is = 0.

Now after explosion /», = 2 kg, v, = 10 in s"1 (due east), v2 = 20 m s

-1. If mass of second piece be m2,

then from the conservation law of momentum, we have

Q.29. A bullet of mass 20 g is fired into a stationary block weighing 3 kg. After the impact the block and bullet

move together with a velocity of 15 cm s '. What was the velocity of the bullet when it just collided with the block ?

Ans. Here mass of bullet m, = 2 0 g = ^ kg = 0.020 kg, initial velocity of bullet = (say), mass of

block m-, = 3 kg, initial velocity of block = 0.

After collision common velocity of block and bullet v = 15 cm s~' = 0.15 m s_1

From conservation law of

momentum, we have

Q.30. A 30 kg shell is flying at 48 m s

_1. Suddenly, it explodes and one of its part of 18 kg conies to rest, while the

remaining part flies off. Find the velocity of the latter.

Ans. Here mass of shell m = 30 kg, initial velocity of shell u = 48 m s-'

Total initial momentum = mu = 30 x 48. ...(;) On explosion, mass of one part w , = 18 kg, hence, mass of other

part m2 = 30 - 18 = 12 kg. As first part comes to rest v, = 0.

Let velocity of other part be v2

Then, total final momentum = m ] v ] + w2v, = 1 8 x 0 + 1 2 x v 7 = 12v2 ....(ii)

Applying conservation law of momentum, we have

total final momentum = total initial momentum 12v2 = 30 x 48

(C) Long Answer Type Questions (Five Marks Each) Q.1. (a) State Newton's laws of motion.

Which law gives the definition of force ?

Which law shows that forces are always produced in pairs ?

Which law gives the measurement of force ?

(e) Which law is known as law of inertia ?

Ans. (a) For statement of Newton's laws of motion—see points 8, 16 and 21, respectively under the heading

"Chapter At A Glance".

The first law of motion gives the definition of force.

Third law of motion shows that forces are produced in pairs, (cl) Second law of motion gives a measurement

of force.

(e) First law o f motion is known as the law of inertia.

Q2. Mathematically show that during collision of two balls total momentum of the system remains unchanged.

Hence, state the law of conservation of momentum.

Q.3. Prove that the law of conservation of momentum is a logical conclusion based on Newton's laws

of motion.

Ans. The answer is same as that of Long Answer Type Question 3.

Q.5. A machine gun of mass 10 kg fires 20 g bullets at the rate of 10 bullets per second with a speed of 500 m s '.

What force is required to hold the gun in position ?