In the previous chapter, we described the

motion of an object along a straight line in

terms of its position, velocity and acceleration.

We saw that such a motion can be uniform

or non-uniform. We have not yet discovered

what causes the motion. Why does the speed

of an object change with time? Do all motions

require a cause? If so, what is the nature of

this cause? In this chapter we shall make an

attempt to quench all such curiosities.

For many centuries, the problem of

motion and its causes had puzzled scientists

and philosophers. A ball on the ground, when

given a small hit, does not move forever. Such

observations suggest that r

est is the “natural

state” of an object. This remained the belief

until Galileo Galilei and Isaac Newton

developed an entirely different approach to

understand motion.

In our everyday life we observe that some

effort is required to put a stationary object

into motion or to stop a moving object. We

ordinarily experience this as a muscular effort

and say that we must push or hit or pull on

an object to change its state of motion. The

concept of force is based on this push, hit or

pull. Let us now ponder about a ‘force’. What

is it? In fact, no one has seen, tasted or felt a

force. However, we always see or feel the effect

of a force. It can only be explained by

describing what happens when a force is

applied to an object. Pushing, hitting and

pulling of objects are all ways of bringing

objects in motion (Fig. 8.1). They move because

we make a force act on them.

From your studies in earlier classes, you

are also familiar with the fact that a force can

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

direction we push it.

(b) The drawer is pulled.

Fig. 8.1: Pushing, pulling, or hitting objects change

their state of motion.

(a)

(b)

Fig. 8.2: (a)

A spring expands on application of force;

(b) A spherical rubber ball becomes oblong

as we apply force on it.

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hapter

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SCIENCE88

box with a small force, the box does not move

because of friction acting in a direction

opposite to the push [Fig. 8.4(a)]. This friction

force arises between two surfaces in contact;

in this case, between the bottom of the box

and floor’s rough surface. It balances the

pushing force and therefore the box does not

move. In Fig. 8.4(b), the children push the box

harder but the box still does not move. This is

because the friction force still balances the

pushing force. If the children push the box

harder still, the pushing force becomes bigger

than the friction force [Fig. 8.4(c)].

There is an unbalanced force. So the box

starts moving.

What happens when we ride a bicycle?

When we stop pedalling, the bicycle begins

to slow down. This is again because of the

friction forces acting opposite to the direction

of motion. In order to keep the bicycle moving,

we have to start pedalling again. It thus

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

unbalanced force is required. And the change

in its speed (or in the direction of motion)

would continue as long as this unbalanced

force is applied. However, if this force is

8.1 Balanced and Unbalanced

Forces

Fig. 8.3 shows a wooden block on a horizontal

table. Two strings X and Y are tied to the two

opposite faces of the block as shown. If we

apply a force by pulling the string X, the block

begins to move to the right. Similarly, if we

pull the string Y, the block moves to the left.

But, if the block is pulled from both the sides

with equal forces, the block will not move.

Such forces are called balanced forces and

do not change the state of rest or of motion of

an object. Now, let us consider a situation in

which two opposite forces of different

magnitudes pull the block. In this case, the

block would begin to move in the direction of

the greater force. Thus, the two forces are

not balanced and the unbalanced force acts

in the direction the block moves. This

suggests that an unbalanced force acting on

an object brings it in motion.

Fig. 8.3: Two forces acting on a wooden block

What happens when some children try to

push a box on a rough floor? If they push the

(a) (b)

(c)

Fig. 8.4

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FORCE AND LAWS OF MOTION 89

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.

Galileo argued that when the marble is

released from left, it would roll down the slope

and go up on the opposite side to the same

height from which it was released. If the

inclinations of the planes on both sides are

equal then the marble will climb the same

distance that it covered while rolling down. If

the angle of inclination of the right-side plane

were gradually decreased, then the marble

would travel further distances till it reaches

the original height. If the right-side plane were

ultimately made horizontal (that is, the slope

is reduced to zero), the marble would continue

to travel forever trying to reach the same

height that it was released from. The

unbalanced forces on the marble in this case

are zero. It thus suggests that an unbalanced

(external) force is required to change the

motion of the marble but no net force is

needed to sustain the uniform motion of the

marble. In practical situations it is difficult

to achieve a zero unbalanced force. This is

because of the presence of the frictional force

acting opposite to the direction of motion.

Thus, in practice the marble stops after

travelling some distance. The effect of the

frictional force may be minimised by using a

smooth marble and a smooth plane and

providing a lubricant on top of the planes.

Fig. 8.5: (a) the downward motion; (b) the upward

motion of a marble on an inclined plane;

and (c) on a double inclined plane.

Newton further studied Galileo’s ideas on

force and motion and presented three

fundamental laws that govern the motion of

objects. These three laws are known as

Newton’s laws of motion. The first law of

motion is stated as:

An object remains in a state of rest or of

uniform motion in a straight line unless

compelled to change that state by an

applied force.

In other words, all objects resist a change

in their state of motion. In a qualitative way,

the tendency of undisturbed objects to stay

at rest or to keep moving with the same

velocity is called inertia. This is why, the first

law of motion is also known as the law

of inertia.

Certain experiences that we come across

while travelling in a motorcar can be

explained on the basis of the law of inertia.

We tend to remain at rest with respect to the

seat until the driver applies a braking force

to stop the motorcar. With the application of

brakes, the car slows down but our body

tends to continue in the same state of motion

because of its inertia. A sudden application of

brakes may thus cause injury to us by impact

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or collision with the panels in front. Safety belts

are worn to prevent such accidents. Safety belts

exert a force on our body to make the forward

motion slower. An opposite experience is

encountered when we are standing in a bus

and the bus begins to move suddenly. Now

we tend to fall backwards. This is because the

sudden start of the bus brings motion to the

bus as well as to our feet in contact with the

floor of the bus. But the rest of our body

opposes this motion because of its inertia.

When a motorcar makes a sharp turn at a

high speed, we tend to get thrown to one side.

This can again be explained on the basis of

the law of inertia. We tend to continue in our

straight-line motion. When an unbalanced

force is applied by the engine to change the

direction of motion of the motorcar, we slip to

one side of the seat due to the inertia of

our body.

The fact that a body will remain at rest

unless acted upon by an unbalanced force

can be illustrated through the

following activities:

Activity ______________ 8.1

• Make a pile of similar carom coins on

a table, as shown in Fig. 8.6.

• Attempt a sharp horizontal hit at the

bottom of the pile using another carom

coin or the striker. If the hit is strong

enough, the bottom coin moves out

quickly. Once the lowest coin is

removed, the inertia of the other coins

makes them ‘fall’ vertically on the

table.

Galileo Galilei was born

on 15 February 1564 in

Pisa, Italy. Galileo, right

from his childhood, had

interest in mathematics

and natural philosophy.

But his father

Vincenzo Galilei wanted

him to become a medical

doctor. Accordingly,

Galileo enrolled himself

for a medical degree at the

University of Pisa in 1581 which he never

completed because of his real interest in

mathematics. In 1586, he wrote his first

scientific book ‘The Little Balance [La

Balancitta]’, in which he described

Archimedes’ method of finding the relative

densities (or specific gravities) of substances

using a balance. In 1589, in his series of

essays – De Motu, he presented his theories

about falling objects using an inclined plane

to slow down the rate of descent.

In 1592, he was appointed professor of

mathematics at the University of Padua in

the Republic of Venice. Here he continued his

observations on the theory of motion and

through his study of inclined planes and the

pendulum, formulated the correct law for

uniformly accelerated objects that the

distance the object moves is proportional to

the squar

e of the time taken.

Galileo was also a remarkable craftsman.

He developed a series of telescopes whose

optical performance was much better than

that of other telescopes available during those

days. Around 1640, he designed the first

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

and not the earth, contrary to what was

believed at that time.

Galileo Galilei

(1564 – 1642)

Fig. 8.6: Only the carom coin at the bottom of a

pile is removed when a fast moving carom

coin (or striker) hits it.

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FORCE AND LAWS OF MOTION 91

five-rupees coin if we use a one-rupee coin, we

find that a lesser force is required to perform

the activity. A force that is just enough to cause

a small cart to pick up a large velocity will

produce a negligible change in the motion of a

train. This is because, in comparison to the

cart the train has a much lesser tendency to

change its state of motion. Accordingly, we say

that the train has more inertia than the cart.

Clearly, heavier or more massive objects offer

larger inertia. Quantitatively, the inertia of an

object is measured by its mass. We may thus

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.

uestions

1. Which of the following has more

inertia: (a) a rubber ball and a

stone of the same size? (b) a

bicycle and a train? (c) a five-

rupees coin and a one-rupee coin?

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.

3. Explain why some of the leaves

may get detached from a tree if

we vigorously shake its branch.

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?

8.4 Second Law of Motion

The first law of motion indicates that when an

unbalanced external force acts on an object,

Activity ______________ 8.2

• Set a five-rupee coin on a stiff card

covering an empty glass tumbler

standing on a table as shown in

Fig. 8.7.

• Give the card a sharp horizontal flick

with a finger. If we do it fast then the

card shoots away, allowing the coin to

fall vertically into the glass tumbler due

to its inertia.

• The inertia of the coin tries to

maintain its state of rest even when

the card flows off.

Fig. 8.7: When the card is flicked with the

finger the coin placed over it falls in the

tumbler.

Activity ______________ 8.3

• Place a water-filled tumbler on a tray.

• Hold the tray and turn around as fast

as you can.

• We observe that the water spills. Why?

Observe that a groove is provided in a

saucer for placing the tea cup. It prevents

the cup from toppling over in case of

sudden jerks.

8.3 Inertia and Mass

All the examples and activities given so far

illustrate that there is a resistance offered by

an object to change its state of motion. If it is

at rest it tends to remain at rest; if it is moving

it tends to keep moving. This property of an

object is called its inertia. Do all bodies have

the same inertia? We know that it is easier to

push an empty box than a box full of books.

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,

get an injury in our foot while doing so!

Similarly, in activity 8.2, instead of a

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its velocity changes, that is, the object gets an

acceleration. We would now like to study how

the acceleration of an object depends on the

force applied to it and how we measure a force.

Let us recount some observations from our

everyday life. During the game of table tennis

if the ball hits a player it does not hurt him.

On the other hand, when a fast moving cricket

ball hits a spectator, it may hurt him. A truck

at rest does not require any attention when

parked along a roadside. But a moving truck,

even at speeds as low as 5 m s

–1

, may kill a

person standing in its path. A small mass,

such as a bullet may kill a person when fired

from a gun. These observations suggest that

the impact produced by the objects depends

on their mass and velocity. Similarly, if an

object is to be accelerated, we know that a

greater force is required to give a greater

velocity. In other words, there appears to exist

some quantity of importance that combines

the object’s mass and its velocity. One such

property called momentum was introduced by

Newton. The momentum, p of an object is

defined as the product of its mass, m and

velocity, v. That is,

p = mv (8.1)

Momentum has both direction and

magnitude. Its direction is the same as that

of velocity, v. The SI unit of momentum is

kilogram-metre per second (kg m s

-1

). Since

the application of an unbalanced force brings

a change in the velocity of the object, it is

therefore clear that a force also pr

oduces a

change of momentum.

Let us consider a situation in which a car

with a dead battery is to be pushed along a

straight road to give it a speed of 1 m s

-1

, which

is sufficient to start its engine. If one or two

persons give a sudden push (unbalanced force)

to it, it hardly starts. But a continuous push

over some time results in a gradual acceleration

of the car to this speed. It means that the change

of momentum of the car is not only determined

by the magnitude of the force but also by the

time during which the force is exerted. It may

then also be concluded that the force necessary

to change the momentum of an object depends

on the time rate at which the momentum is

changed.

The second law of motion states that the

rate of change of momentum of an object is

proportional to the applied unbalanced force

in the direction of force.

8.4.1 MATHEMATICAL FORMULATION OF

SECOND LAW OF MOTION

Suppose an object of mass, m is moving along

a straight line with an initial velocity, u. It is

uniformly accelerated to velocity, v in time, t

by the application of a constant force, F

throughout the time, t. The initial and final

momentum of the object will be, p

= mu and

= mv respectively.

The change in momentum ∝ p

– p

∝ mv – mu

∝ m × (v – u).

The rate of change of momentum ∝

( )

× −

m v u

Or, the applied force,

∝

( )

× −

m v u

( )

× −

km v u

(8.2)

= kma (8.3)

Here a [ = (v – u)/t ] is the acceleration,

which is the rate of change of velocity. The

quantity, k is a constant of proportionality.

The SI units of mass and acceleration are kg

and m s

-2

respectively. The unit of force is so

chosen that the value of the constant, k

becomes one. For this, one unit of force is

defined as the amount that produces an

acceleration of 1 m s

-2

in an object of 1 kg

mass. That is,

1 unit of force =

k × (1 kg) × (1 m s

-2

Thus, the value of k becomes 1. From Eq. (8.3)

F = ma (8.4)

The unit of force is kg m s

-2

or newton,

which has the symbol N. The second law of

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FORCE AND LAWS OF MOTION 93

motion gives us a method to measure the force

acting on an object as a product of its mass

and acceleration.

The second law of motion is often seen in

action in our everyday life. Have you noticed

that while catching a fast moving cricket ball,

a fielder in the ground gradually pulls his

hands backwards with the moving ball? In

doing so, the fielder increases the time during

which the high velocity of the moving ball

decreases to zero. Thus, the acceleration of

the ball is decreased and therefore the impact

of catching the fast moving ball (Fig. 8.8) is

also reduced. If the ball is stopped suddenly

then its high velocity decreases to zero in a

very short interval of time. Thus, the rate of

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

the palm of the fielder. In a high jump athletic

event, the athletes are made to fall either on

a cushioned bed or on a sand bed. This is to

increase the time of the athlete’s fall to stop

after making the jump. This decreases the rate

of change of momentum and hence the force.

Try to ponder how a karate player breaks a

slab of ice with a single blow.

The first law of motion can be

mathematically stated from the mathematical

expression for the second law of motion. Eq.

(8.4) is

F = ma

or F

( )

−

m v u

(8.5)

or Ft = mv – mu

That is, when F = 0, v = u for whatever time, t

is taken. This means that the object will

continue moving with uniform velocity, u

throughout the time, t. If u is zero then v will

also be zero. That is, the object will remain

at rest.

Example

8.1 A constant force acts on an

object of mass 5 kg for a duration of

2 s. It increases the object’s velocity

from 3 m s

–1

to 7 m s

-1

. Find the

magnitude of the applied force. Now, if

the force was applied for a duration of

5 s, what would be the final velocity of

the object?

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

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

= +

v u

On substituting the values of u, F, m and

t, we get the final velocity,

v = 13 m s

-1

Fig. 8.8: A fielder pulls his hands gradually with the

moving ball while holding a catch.

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Example 8.2

Which would require a

greater force –– accelerating a 2 kg mass

at 5 m s

–2

or a 4 kg mass at 2 m s

-2

Solution:

From Eq. (8.4), we have F = ma.

Here we have m

= 2 kg; a

= 5 m s

-2

and m

= 4 kg; a

= 2 m s

-2

Thus, F

= m

= 2 kg × 5 m s

-2

= 10 N;

and F

= m

= 4 kg × 2 m s

-2

= 8 N.

⇒ F

> F

Thus, accelerating a 2 kg mass at

5 m s

-2

would require a greater for

ce.

Example 8.3 A motorcar is moving with a

velocity of 108 km/h and it takes 4 s to

stop after the brakes are applied.

Calculate the for

ce 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

with its passengers = 1000 kg and the

time taken to stop the motorcar, t = 4 s.

From Eq. (8.5) we have the magnitude

of the force (F) applied by the brakes as

m(v – u)/t.

On substituting the values, we get

F = 1000 kg × (0 – 30) m s

-1

/4 s

= – 7500 kg m s

-2

or – 7500 N.

The negative sign tells us that the force

exerted by the brakes is opposite to the

direction of motion of the motorcar.

Example 8.4 A force of 5 N gives a mass

, an acceleration of 10 m s

–2

and a

mass m

an acceleration of 20 m s

-2

What acceleration would it give if both

the masses wer

e tied together?

Solution:

From Eq. (8.4) we have m

= F/a

; and

= F/a

. Here, a

= 10 m s

-2

;

= 20 m s

-2

and F = 5 N.

Thus, m

= 5 N/10 m s

-2

= 0.50 kg; and

= 5 N/20 m s

-2

= 0.25 kg.

If the two masses were tied together,

the total mass, m would be

m = 0.50 kg + 0.25 kg = 0.75 kg.

The acceleration, a produced in the

combined mass by the 5 N force would

be, a = F/m = 5 N/0.75 kg = 6.67 m s

-2

Example

8.5 The velocity-time graph of a

ball of mass 20 g moving along a

straight line on a long table is given in

Fig. 8.9.

Fig. 8.9

How much force does the table exert on

the ball to bring it to rest?

Solution:

The initial velocity of the ball is 20 cm s

-1

Due to the frictional force exerted by the

table, the velocity of the ball decreases

down to zero in 10 s. Thus, u = 20 cm s

–

;

v = 0 cm s

-1

and t = 10 s. Since the

velocity-time graph is a straight line, it is

clear that the ball moves with a constant

acceleration. The acceleration a is

−

v u

= (0 cm s

-1

– 20 cm s

-1

)/10 s

= –2 cm s

-2

= –0.02 m s

-2

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FORCE AND LAWS OF MOTION 95

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

opposite to the direction of motion of

the ball.

8.5 Third Law of Motion

The first two laws of motion tell us how an

applied force changes the motion and provide

us with a method of determining the force.

The third law of motion states that when one

object exerts a force on another object, the

second object instantaneously exerts a force

back on the first. These two forces are always

equal in magnitude but opposite in direction.

These forces act on different objects and never

on the same object. In the game of football

sometimes we, while looking at the football

and trying to kick it with a greater force,

collide with a player of the opposite team.

Both feel hurt because each applies a force

to the other. In other wor

ds, there is a pair of

forces and not just one force. The two

opposing forces are also known as action and

reaction forces.

Let us consider two spring balances

connected together as shown in Fig. 8.10. The

fixed end of balance B is attached with a rigid

support, like a wall. When a force is applied

through the free end of spring balance A, it is

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,

simultaneously.

Fig. 8.10: Action and reaction forces are equal and

opposite.

Suppose you are standing at rest and

intend to start walking on a road. You must

accelerate, and this requires a force in

accordance with the second law of motion.

Which is this force? Is it the muscular effort

you exert on the road? Is it in the direction

we intend to move? No, you push the road

below backwards. The road exerts an equal

and opposite force on your feet to make you

move forward.

It is important to note that even though

the action and reaction forces are always

equal in magnitude, these forces may not

produce accelerations of equal magnitudes.

This is because each force acts on a different

object that may have a different mass.

When a gun is fired, it exerts a forward

force on the bullet. The bullet exerts an equal

and opposite force on the gun. This results in

the recoil of the gun (Fig. 8.11). Since the gun

has a much greater mass than the bullet, the

acceleration of the gun is much less than the

acceleration of the bullet. The third law of

motion can also be illustrated when a sailor

jumps out of a rowing boat. As the sailor

jumps forward, the force on the boat moves it

backwards (Fig. 8.12).

Fig. 8.11: A forward force on the bullet and recoil

of the gun.

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SCIENCE96

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.

Activity ______________ 8.4

• Request two children to stand on two

separate carts as shown in Fig. 8.13.

• Give them a bag full of sand or some

other heavy object. Ask them to play a

game of catch with the bag.

• Does each of them experience an

instantaneous force as a result of

throwing the sand bag?

• You can paint a white line on

cartwheels to observe the motion of the

two carts when the children throw the

bag towards each other.

Fig. 8.12: As the sailor jumps in forward direction,

the boat moves backwards.

Fig. 8.13

Now, place two children on one cart and

one on another cart. The second law of motion

can be seen, as this arrangement would show

different accelerations for the same force.

The cart shown in this activity can be

constructed by using a 12 mm or 18 mm thick

plywood board of about 50 cm × 100 cm with

two pairs of hard ball-bearing wheels (skate

wheels are good to use). Skateboards are not

as effective because it is difficult to maintain

straight-line motion.

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FORCE AND LAWS OF MOTION 97

• 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.

(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

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SCIENCE98

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)

(b) mv

(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

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FORCE AND LAWS OF MOTION 99

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.

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