Chapter 9 - Force And Laws Of Motion Page no :- 118
Solution
1
Mass
is a measure of the inertia of a body. The greater the mass of a body; the
greater is its inertia.
(a)
Mass of a stone is more than the mass of a rubber ball of same size. Hence,
inertia of a stone is greater than that of a rubber ball of same size.
(b)
Mass of a train is more than the mass of a bicycle. Hence, inertia of a train
is greater than that of a bicycle.
(c) Mass of a five rupee coin is more than that of a
one-rupee coin. Hence, inertia of a five rupee coin is greater than that of a
one-rupee coin.
Concept Insight: More mass means more inertia.
Concept Insight: More mass means more inertia.
Solution 2
The velocity of the ball changes four times.
(i) As a football player kicks the football, its speed
changes from zero to a certain value. As a result, the velocity of the ball
gets changed. In this case, the force is applied by the kick of the player.
(ii) When the ball reaches another player, he kicks the ball
towards the goal post. As a result, the direction of the ball and its speed
both get changed. Therefore, its velocity also changes. In this case, the force
is applied by the kick of the player.
(iii) When the goalkeeper collects the ball, the ball comes
to rest, i.e. its speed reduces to zero from a certain value. Thus, the
velocity of the ball changes. In this case, the force is applied by the hands
of the goalkeeper.
(iv) The goalkeeper then kicks the stationary ball towards
his team player, i.e., the speed of the ball increases from zero to a certain
value. Hence, its velocity changes once again. In this case, the force is applied
by the kick of the goalkeeper.
Concept Insight:- Velocity
is a vector quantity. It has both magnitude and direction.
Solution
3
Some leaves of a tree may get detached when we shake its
branch vigorously. This is because when the branch of the tree is shaken, it
moves to and fro, but due to inertia its leaves tend to remain at rest. Due to
this reason, the leaves fall down from the tree.
Concept Insight:- Inertia resists change in state of motion.
Solution
4
When a moving bus brakes to a stop,
we fall in the forward direction because though the lower part of our body
comes to a stop when the bus stops but the upper part of the body continues to
be in motion in the forward direction due to its inertia, thus making us fall
in the forward direction.
When a bus accelerates from rest,
we fall backwards because though the lower part of our body starts moving with
the bus but the upper part of the body tries to remain at rest due to its
inertia, thus making us fall in the backward direction.
Concept Insight:- Inertia resists any change in the state of
motion of a body.
Chapter 9 - Force And Laws Of Motion Page
no :- 126
Solution
1
A horse pushes the ground in the backward direction.
According to Newton's third law of motion, a reaction force is exerted by the
ground on the horse in the forward direction. As a result, the horse moves
forward along with the cart.
Concept Insight:- Action and reaction forces
act on two different bodies and that too in opposite directions.
Solution
2
Due to the backward reaction of the water ejecting from the
hose pipe.
When a fireman holds a hose, which is ejecting large amounts
of water at a high velocity, then a reaction force is exerted on him by the
ejecting water in the backward direction. This is because of Newton's third law
of motion. As a result of the backward force, the hose pipe tends to go
backward and slips from the hands of fireman which makes it difficult for the
fireman to hold the hose pipe.
Concept
Insight:- Action and reaction
forces act on two different bodies and that too in opposite directions.
Solution 3
Mass of the rifle, m1 =
4 kg
Mass of the bullet, m2 = 50 g = 0.05 kg
Recoil
velocity of the rifle = v1
Bullet is fired with an initial
velocity, v2 = 35 m/s
Initially, the rifle is at rest.
Thus, its initial velocity, v = 0
Total
initial momentum (before firing) of the rifle and bullet system = (m1 +
m2)v =0
Total final
momentum (after firing) of the rifle and bullet system
= m1v1 +
m2v2
= 4(v1) + 0.05
× 35
= 4v1 + 1.75
According to the law of conservation of momentum:
Concept Insight:- Total momentum after the firing = Total momentum before the firing
4v1 + 1.75 = 0
4v1 = − 1.75
The
negative sign indicates that the rifle recoils backwards with a velocity of
0.4375 m/s.
Chapter 9 - Force And Laws Of Motion Page
no :- 127
Solution
1
Mass of first object, m1 =
100 g = 0.1 kg
Mass of
second object, m2 = 200 g = 0.2 kg
Velocity of
first object before collision, v1 = 2 m/s
Velocity of
second object before collision, v2 = 1 m/s
Velocity of
first object after collision, v3 = 1.67 m/s
Velocity of
second object after collision = v4
According
to the law of conservation of momentum:
Concept Insight:-
Total momentum before collision = Total momentum after collision
Hence, the
velocity of the second object becomes 1.165 m/s after the collision.
Chapter 9 - Force And Laws Of Motion Page
no :- 128
Solution
1
Yes. Even when an object experiences a net zero external
unbalanced force, it is possible that the object is travelling with a non-zero
velocity. This is possible only when the object has been moving with a constant
velocity in a particular direction. Then, there is no net unbalanced force
applied on the body. The object will keep moving with the same non-zero
velocity.
Concept Insight:- To change the state of motion, a net non-zero external
unbalanced force must be applied on the object.
Solution
2
Inertia of an object tends to resist any change in its state
of rest or state of motion. When a carpet is beaten with a stick, then the
carpet comes to motion. But, the dust particles try to retain their state of
rest. Hence, the dust particles come out of the carpet.
Concept
Insight:- Inertia resists
change in state of motion.
Solution 3
When the bus suddenly accelerates from rest and moves
forward, it acquires a state of motion. However, the luggage kept on the roof,
owing to its inertia, tends to remain in its state of rest and hence may fall
down from the roof of the bus.
Similarly, when the moving bus stops suddenly, then due to
its inertia of motion, the luggage kept on the roof of the bus tends to remain
in motion and hence may fall down from the roof of the bus.
Hence, it is advised to tie the luggage kept on the roof of a
bus with a rope so that it does not fall down when the bus starts or stops
suddenly.
Concept
Insight:- Inertia resists
change in state of motion
Solution 4
(c) There is a force on the ball opposing the motion.
A batsman hits a cricket ball, which then rolls on a level
ground. After covering a short distance, the ball comes to rest because there
is frictional force on the ball opposing its motion.
Frictional force always acts in the direction opposite to the
direction of motion. Hence, this force is responsible for stopping the cricket
ball.
Solution
5
Initial velocity, u = 0 (since
the truck is initially at rest)
Distance
travelled, s = 400 m
Time
taken, t = 20 s
Acceleration,
a=?
According
to the second equation of motion:
Given:
1 tonne = 1000 kg
Therefore,
7 tonnes = 7000 kg
Mass
of truck, m = 7000 kg
From
Newton's second law of motion:
Concept Insight:- Force, F = Mass × Acceleration
F
= ma = 7000×2 = 14000 N
Hence, the acceleration of the truck is 2 m/s2 and
the force acting on the truck is 14000 N.
Solution 6
Initial velocity of the stone, u = 20 m/s
Final velocity of the stone, v =
0 (finally the stone comes to rest)
Distance covered by the stone, s
= 50 m
According to the third equation
of motion:
v2 = u2 +
2as
where, a = acceleration
(0)2 = (20)2 +
2 × a × 50
0 = 400 + 100 a
-400 = 100 a
a
= - 4 m/s2Concept Insight:- The negative sign indicates that acceleration is acting against the motion of the stone.
Mass
of the stone, m = 1 kg
From Newton's second law of motion:
Force, F = Mass
Acceleration
F = ma
F = 1 × (- 4) = -4 N
Hence, the force of friction between the stone and the ice is -4 N.
From Newton's second law of motion:
Force, F = Mass
Acceleration F = ma
F = 1 × (- 4) = -4 N
Hence, the force of friction between the stone and the ice is -4 N.
Solution 7
(a) Force exerted by the engine,
F = 40000 N
Frictional
force offered by the track, Ff = 5000 N
Hence,
net accelerating force, Fa = F - Ff = 40000 -
5000 = 35000 N
(b)
Let acceleration of the train be a.
Net
accelerating force on the wagons, Fa = 35000 N
Mass
of the wagons, M = Mass of a wagon × Number of wagons = 2000 x 5 =
10000 kg
From Newton's second law of motion:
Concept Insight:- Force = Mass x Acceleration
Fa =
Ma
Hence,
the acceleration of the train is 3.5 m/s2.
Mass of the four
wagons behind the first wagon = 4 2000 = 8000 kg
Acceleration of
the wagons = 3.5 m/s2
Thus, force of
wagon 1 on remaining four wagons behind it = 8000 3.5 = 28000 N
Hence, the force
exerted by wagon 1 on wagon 2 is 28000 N.
Solution
8
Mass of the automobile vehicle,
m = 1500 kg
Final
velocity, v = 0 (finally the automobile stops)
Acceleration
of the automobile, a = -1.7 ms-2
From
Newton's second law of motion:
Force
= Mass × Acceleration = 1500 × (-1.7) = -2550 N
Hence, the force between the automobile and the road
is -2550 N, in the direction opposite to the motion of the automobile.
Solution 9
(d) mv
Mass
of the object = m
Velocity
= v
Concept Insight:- Momentum = Mass × Velocity
Momentum = mv
Solution 10
Force applied, P = 200 N
Force of friction, F = ?
As the wooden cabinet is to move across the floor with a
constant velocity, no force (f) is spent in accelerating the cabinet, i.e.,
f = P-F = 0
or, F = P = 200 N
Concept Insight:- For a non-accelerated motion, no net force is required.
Solution 11
Mass of first object, m1 = 1.5 kg
Mass of second object, m2 = 1.5 kg
Velocity first object before collision, v1 =
2.5 m/s
Velocity of second object before collision, v2 =
-2.5 m/s
(Negative sign arises because mass m2 is
moving in an opposite direction)
After collision, the two objects stick together.
Total mass of the combined object = m1 + m2
Velocity of the combined object = v
According to the law of conservation of momentum:
Concept
Insight:- Total momentum before collision =
Total momentum after collision
m1 v1 + m2 v2 =
(m1 + m2) v
1.5(2.5) + 1.5 (-2.5) = (1.5 + 1.5) v
3.75 - 3.75 = 3 v
v = 0
Hence, the velocity of the combined object after collision is
0 m/s.
Chapter 9 - Force And Laws Of Motion Page
no :- 129
Solution
1
When we push a massive truck parked along the roadside, it
does not move. The justification given by the student that the two opposite and
equal forces cancel each other is totally wrong. This is because force of
action and reaction never act on one body. There is no question of their
cancellation. The truck does not move because the push applied is far less than
the force of friction between the truck and the road.
Concept
Insight:- Action and reaction forces act on different
objects.
Solution
2
Mass
of the hockey ball, m = 200 g = 0.2 kg
Hockey ball travels with velocity, v1 =
10 m/s
Initial momentum = mv1
After being struck by the stick, the hockey ball travels in
the opposite direction with velocity, v2 = -5 m/s
Final momentum = mv2
Concept Insight:- Change in momentum = Final
momentum - Initial momentum
Change in momentum = mv2 - mv1 = m
(v2 - v1) = 0.2
[-5-10] = 0.2 (-15) = -3 kg ms-1
Hence, the change in momentum of the hockey ball is -3 kg ms-1.
Solution
3
Mass
of the bullet, m = 10 g = 0.01 kg
It is given
that the bullet is travelling with a velocity of 150 m/s.
Thus, when
the bullet enters the block, its velocity = Initial velocity, u = 150 m/s
Final
velocity, v = 0 (since the bullet finally comes to rest)
Time taken
to come to rest, t = 0.03 s
According
to the first equation of motion,
v = u + at
where , a
is the acceleration of the bullet
0 = 150 +
(a × 0.03)
Concept
Insight:- Negative
sign indicates that the velocity of the bullet is decreasing.
According
to the third equation of motion:
v2 =
u2 + 2 as
0 = (150)2 +
2×(-5000)×s
0 = 22500 + 2×(-5000)×s
0=22500 -
10000 s
10000 s =
22500
Hence, the distance of
penetration of the bullet into the block is 2.25 m.
From
Newton's second law of motion:
Concept Insight:- Force,
F = Mass Acceleration
Mass of the
bullet, m = 0.01 kg
Acceleration
of the bullet, a = -5000 m/s2
F = ma =
0.01×(-5000) = -50 N
Hence, the
magnitude of force exerted by the wooden block on the bullet is 50 N.
Solution
4
Mass of the object, m1 = 1 kg
Velocity of
the object before collision, v1 = 10 m/s
Mass of the
stationary wooden block, m2 = 5 kg
Velocity of
the wooden block before collision, v2 = 0 m/s
Total
momentum before collision = m1v1+m2v2 = (1×10)+(5×0) = 10 kg m s-1
According
to the law of conservation of momentum, the total momentum just after the
impact will be the same as the total momentum just before the impact.
i.e., the
total momentum just after the impact will be 10 kg m s-1.
It is given
that after collision, the object and the wooden block stick together.
Total mass
of the combined system = m1 + m2
Velocity of
the combined system = v
According
to the law of conservation of momentum:
Concept Insight:- Total
momentum before collision = Total momentum after collision
m1v1+m2v2 =
(m1+m2)v
(1×10)+(5×0)
= (1+5)v
10+0 = 6v
10 = 6v
v = 1.67 m/s
Hence,
velocity of the combined object after collision will be 1.67 m/s.
Solution
5
The suggestion made by Kiran that
the insect suffered a greater change in momentum as compared to the change in
momentum of the motor car is wrong. The suggestion made by Akhtar that the
motor car exerted a larger force on the insect because of large velocity of
motor car is also wrong. The explanation put forward by Rahul is correct. On
collision of insect with motor car, both experience the same force as action
and reaction are always equal and opposite. Further, changes in their momenta
are also the same. Only the signs of changes in momenta are opposite, i.e.,
change in momenta of the two occur in opposite directions, though magnitude of
change in momentum of each is the same.
Solution
6
Mass of the dumbbell, m = 10 kg
Distance covered by the dumbbell, s = 80
cm = 0.8 m
Acceleration in the downward direction, a =
10 m/s2
Initial velocity of the dumbbell, u = 0
Final velocity of the dumbbell (when it was about to hit the
floor) = v
Concept
Insight Choose the
equation of motion wisely out of the three, to minimize the number of steps in
calculations.
According to the third equation of motion:
v2 = u2 +
2as
v2 = 0 + 2 (10) 0.8
v = 4 m/s
Hence, the momentum with which the dumbbell hits the floor
= mv = 10×4 = 40 kg m s-1
Momentum transferred to the floor is 40 kg m/s.
Chapter - Page no :-
Solution
1
Chapter 9 - Force And Laws Of Motion Page
no :- 130
Solution
1
(a) A
careful observation of the distance-time table shows that
It is known
that
(i) for
motion with uniform velocity (zero acceleration)
(ii) for
motion with uniform acceleration
In the
present case, . Therefore, we conclude in
this case that acceleration must be increasing uniformly with time.
. Therefore, we conclude in
this case that acceleration must be increasing uniformly with time.
(b) As F =
ma, therefore, F 
a. Hence, the force must
also be increasing uniformly with time.
a. Hence, the force must
also be increasing uniformly with time.
Solution
2
Here, mass of motorcar, m = 1200 kg
Let each person exert a push F on the motorcar.
Total push of two persons = F + F = 2F
As this push gives a uniform velocity to the motorcar along a
level road, it must be a measure of the force of friction (f) between the
motorcar and the road,
i.e., f = 2F.
When three person push, total force applied = F + F + F = 3F
Force that produces acceleration (a=0.2 m/s2),
i.e., ma = 3F-f = 3F-2F = F
or, F = ma = 1200 × 0.2 = 240 N
Solution
3
Thus, the
force of the nail on the hammer is 2500 N. Negative sign indicates the opposing
force.
Solution
4
Change in
momentum = mv-mu = m(v-u) = 1200×(5-25)= -24000 kg m/s
Force
required , F = ma = 1200×(-5) = -6000 N
Magnitude
of force required = 6000 N
Negative
sign shows that force is opposing the motion.
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