# LAKHMIR SINGH AND MANJIT KAUR Solutions for Class 9 Physics Chapter 2 - Force and laws of motion

## Chapter 2 - Force and laws of motion 55

The product of mass and velocity of a body is called momentum.

Momentum is the measure of quantity of motion of a body

The SI unit of momentum is kilogram meters per second(kg.m/s)

Momentum is a vector quantity and is dirceted along the direction of velocity.

The total momentum of the bullet and the gun before firing would be zero because velocities of both of them will be zero.

Momentum has its SI unit as kilogram meters per second(kg.m/s)

Momentum of a body of mass 'm' and velocity 'v' will be

p = m x v

Balanced forces cannot produce motion in a body but can its shape.

Frictional force slows down a moving bicycle when we stop pedaling it.

The given statement is false.

Force of gravity causes this change in speed.

Inertia is the property of bodies to resist a change in their state of rest or motion

Newton's first law of motion is also known as Galileo's law of inertia.

Object B has more inertia. Since mass is a measure of inertia of a body and object B has greater mass, so it will have greater inertia.

Isaac Newton gave the laws of motion.

Force is a vector quantity.

The speed of the running bull should be multiplied with its mass to get its momentum.

a) Mass

b) forward

c) backward

d) inertia

e) friction; air

Since the speed of tennis ball and cricket ball is same, the momentum of cricket ball will be higher due to its mass being greater than mass of tennis ball. So, less force is required to stop a tennis ball than to stop a cricket ball.

p = m x v

This equation signifies that momentum of a body is the product of its mass and its velocity.

Here, p is momentum of the body

m is the mass of the body

v is the velocity of the body.

A karate player can break a pile of tiles with a single blow because he strikes the pile with his hand very fast. In doing so, the large momentum of his hand is reduced to zero in a very short time. This exerts a large force on the pile of tiles which is sufficient to break them apart.

Mass of the toy car, m = 200 g = 0.2 kg

Speed, v = 5 m/s

Momentum, p = m x v = 0.2 x 5 = 1 kg.m/s

Mass of car = 1500 kg

Velocity v_{1} = 36 km/hr = 10 m/s

Momentum p_{1} = 1500 x 10 = 15000 kg.m/s

Velocity v_{2} = 72 km/hr = 20 m/s

Momentum p_{2} = 1500 x 20 = 30000 kg.m/s

Change in momentum = p_{2}-p_{1}= 30000 - 15000 = 15000 kg.m/s

Mass of the body, m = 25 kg

Momentum p = 125 kg.m/s

p = m x v

_{}= _{}= 5 m/s

Velocity of the body is 5 m/s

a) Mass of elephant = 2000kg

Velocity = 5 m/s

Momentum = 2000 x 5 = 10000 kg.m/s

b) Mass of bullet = 0.02 kg

Velocity = 400 m/s

Momentum = 0.02 x 400 = 8 kg.m/s

## Chapter 2 - Force and laws of motion 56

Balanced forces can change the shape of the object. For example, when a balloon is pressed between hands, then balanced forces (equal and opposite forces) act on the balloon due to which the shape of the balloon changes.

Inertia of motion is the property of a body due to which it resists a change in its state of uniform motion. For eg., if there is no air resistance and no friction to oppose the motion of a moving bicycle, it will go on moving forever.

Newton's first law of motion states that a body at rest will remain at rest, and a body in motion will continue in motion in a straight line with a uniform speed unless it is compelled by an external force to change its state of rest or of uniform motion. For example, a book lying on a table remains on the table unless we lift it with the force of our hands. And, on a frictionless surface, a moving car continues to be in the state of motion until brakes are applied on it.

Inertia of a body depends on its mass. A cricket ball has more inertia than a rubber ball of the same size because it has more mass than the rubber ball.

When a bus starts suddenly, its passengers tend to fall backwards because due to their inertia, the passengers tend to remain in a state of rest even when the bus starts moving.

When a bus stops suddenly, its passengers tend to fall forward because due to their inertia, the passengers tend to remain in a state of motion even though the bus has come to rest.

When a hanging carpet is beaten with a stick, the carpet moves to and fro with the force of the stick while the dust particles remain in their state of rest on account of their inertia and thus dust particles separate out from the carpet.

When a tree is shaken, the tree moves to and fro while the fruits and leaves remain in their state of rest on account of their inertia and thus fruits and leaves separate from the tree and fall from the tree.

It is dangerous to jump out of a moving bus because the jumping man, who is moving with the high speed of the bus would tend to remain in state of motion due to inertia even on falling to the ground and get hurt due to resistance offered by the ground.

Mass of car, m = 10 kg

Momentum = m x v

a) Velocity, v = 5 m/s

Momentum = 10 x 5 = 50 kg.m/s

b) Velocity, v = 20 cm/s = 0.2 m/s

Momentum = 10 x 0.2 = 2 kg.m/s

c) Velocity, v = 36km/hr = 10 m/s

Momentum = 10 x 10 = 100 kg.m/s

a) Momentum is the physical quantity which is the measure of the quantity of motion of a moving body. It depends on mass and velocity of the body.

b) Mass of body = 5 kg

Velocity v_{1} = 20 m/s

Momentum p_{1} = 20 x 5 = 100 kg.m/s

Velocity v_{2} = 0.2 m/s

Momentum p_{2} = 5 x 0.2 = 1 kg.m/s

Change in momentum = p_{2}- p_{1}= 1-100 = -99 kg.m/s (Negative sign shows that momentum decreases)

a) Force is an influence which tends to set a stationary body in motion or stop a moving body; or which tends to change the speed and direction of a moving body; or which tends to change the shape and size of a body.

b) Various effects of force are

i) A force can move a stationary body.

ii) A force can stop a moving body.

iii) A force can change the speed of a moving body.

iv) A force can change the direction of a moving body.

v) A force can change the shape and size of a body.

a) Kicking a stationary football.

b) Applying brakes to a moving bicycle.

c) Pressing an accelerator to speed up a moving car.

d) A moving cricket ball hit by a bat.

e) Flattening of dough by a rolling pin to make chapatis.

a) If the resultant of all the forces acting on a body is zero, the forces are called balanced forces. These forces do not change the state of rest or of uniform motion of a body but can change the shape of the body. For example, when a balloon is pressed between hands, then balanced forces (equal and opposite forces) act on the balloon due to which the shape of the balloon changes.

If the resultant of all the forces acting on a body is not zero, the forces are called unbalanced forces. These forces change the state of rest or of uniform motion of a body. For eg., if we push a toy car lying on the ground, it starts moving due to the unbalanced force exerted by our hands.

b) When we press a rubber ball between our hands, balanced forces acts on it and hence its shape changes.

a) When a bus takes a sharp turn, the passengers tend to fall sideways because of their inertia or their tendency to continue moving in a straight line.

b) Road accidents at high speeds are much worse than road accidents at low speeds because the momentum of vehicles at high speeds is very high and causes a lot of damage to the vehicles and injuries to the passengers during collision.

## Chapter 2 - Force and laws of motion 57

The wall will receive equal momentum from both the balls because both balls have equal mass and velocity.

In this case, the bicycle has been compelled to change its state of motion by the external force of air resistance and friction. If there were no air resistance and no friction to oppose the motion of the bicycle, then according to the first law of motion, the bicycle would go on moving forever.

Mass of ball = 500 g = 0.5 kg

Initial velocity = 10 m/s

i) Initial momentum = 0.5 x 10 = 5 kg.m/s

ii) Velocity at the highest point = 0 m/s

Momentum at the highest point = 0.5 x 0 = 0 kg.m/s

The two forces acting on the car are force of friction and air resistance. Force of friction contributes more to slow down and stop the car.

a) X are unbalanced force.

b) Y are balanced forces.

## Chapter 2 - Force and laws of motion 74

Force corresponds to the rate of change of momentum.

The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.

The SI unit of force is newton(N)

A newton force is
defined as that force which when acting on a body of mass of 1 kg produces an
acceleration of 1m/s^{2} in it.

Force acting on a body is directly proportional to the acceleration produced in the body.

_{}

Acceleration remains same since

_{}

Now if force is doubled i.e. 2F and mass is doubled i.e. 2m

Then acceleration _{}

Newton is the SI unit of force.

Jet airplanes work on the principle of conservation of momentum.

Rockets work on the principle of conservation of momentum.

True, because rocket does not require air for obtaining uplift or for burning its fuel.

Mass, m = 1 kg

Acceleration, a =
1m/s^{2}

Force F = m x a = 1 x 1= 1N

Force F =5 N

Mass m = 10 kg

Acceleration _{} = _{} = 0.5 m/s^{2}

The force exerted by the floor on her = the downward force exerted by the girl =250 N

This is due to Newton's third law of motion which states that to every action there is an equal and opposite reaction.

Less mass of the small car makes it easier to accelerate a small car than a large car because acceleration is inversely proportional to mass of the car

_{}

a) Equal; opposite

b) Vector; kg.m/s

c) Acceleration; rate; momentum

d) Magnitude; directions

e) Momentum; force

Force is directly proportional to the product of 'mass' of the body and the 'acceleration' produced in the body by the action of force.

F = m x a

where F is the force applied on the body

m is the mass of the body

a is the acceleration produced in the body

To take boat away from the bank of a river, the boatman pushes the bank with the oar. The bank exerts an equal and opposite force on the boat which makes the boat move forward away from the bank.

Gunman gets a jerk on firing a bullet because when a bullet is fired from a gun, the force sending the bullet forward is equal to the force sending the gun backwards but due to high mass of the gun, it moves only a little distance backwards giving a jerk to the gunman.

To make the cart move, the horse bends forward and pushes the ground with its feet. When the forward reaction to the backward push of the horse on the ground is greater than the opposing frictional forces of the wheels, the cart moves.

## Chapter 2 - Force and laws of motion 75

A rockets works on the principle of action and reaction. In a rocket, the hot gases produced by the rapid burning of fuel rush out of a jet at the bottom of the rocket at a very high speed. The equal and opposite reaction force of the downward going gases pushes the rocket upward with a great speed.

Action and reaction act on two different bodies. Action and reaction are equal in magnitude but they act in opposite directions and there is simultaneous action and reaction.

When a man jumps out from a boat, the boat moves backwards due to the fact that to step out of the boat, the man presses the boat with his foot in the backward direction. The push of the man on the boat is action. The boat exerts an equal force on the man in the forward direction and since the boat is not fixed and is floating, it moves backwards due to the action force exerted by the man.

It becomes very difficult to walk on a slippery road because of the fact that on a slippery road, the friction is much less, and we cannot exert a backward action force on slippery ground which would produce a forward reaction force on us.

To start his run, a runner bends forward and pushes the ground with his feet in the backward direction. In turn ground exerts a reaction force on the runner in the forward direction which makes him run.

Mass of bullet, m_{1} = 60g = 0.06 kg

Velocity of bullet v_{1} = 500 m/s

Mass of gun m_{2} = 5 kg

Recoil velocity v_{2}

According to the law of conservation of momentum

m_{1} x v_{1} = m_{2} x v_{2}

0.06 x 500 = 5 x v_{2}

v_{2} = _{} = 6 m/s

Mass of bullet, m_{1} = 10g = 0.01
kg

Velocity of bullet v_{1}
= 200 m/s

Mass of block with
the bullet as bullet gets embedded in it, m_{2} = 2+0.01 = 2.01 kg

Recoil velocity v_{2}

According to the law of conservation of momentum

m_{1} x v_{1} = m_{2}
x v_{2}

0.01 x 200 = 2.01 x v_{2}

v_{2} = _{} = 0.99 m/s

Mass of the body = 2kg

Initial velocity u = 0

Final velocity v = 30 m/s

Time t = 1 s

Acceleration a = _{}= _{} = 30 m/s^{2}

Force = m x a =2 x 30 = 60 N

Mass of the body = 5 kg

Initial velocity u = 10 m/s

Final velocity v = 35 m/s

Time t = 25 s

Acceleration a = _{}= _{} = 1 m/s^{2}

Force = m x a =5 x 1 = 5 N

Mass of the car = 2400 kg

Initial velocity u = 20 m/s

Final velocity v = 0 m/s

Time t = 10 s

Retardation a = _{}= _{} = -2 m/s^{2}

Force = m x a =2400 x -2 = - 4800 N

Mass of the body = 20 kg

Initial velocity u = 0 m/s

Final velocity v = 100 m/s

Force F = 100 N

Acceleration a = _{}= _{} = 5 m/s^{2}

Time t = _{}= _{}= 20 s

Mass of the body = 2.5 kg

Initial velocity u = 20 m/s

Final velocity v = 0 m/s

Force F = 10 N

Acceleration a = _{}= _{} = 4 m/s^{2}

Since v < u, so
acceleration will have a negative sign a = -4 m/s^{2}

Time t = _{}= _{}= 5 s

Mass of the body = 10 kg

Initial velocity u = 4 m/s

Final velocity v = 8 m/s

Time t = 2 s

a) Momentum before force acts p_{1}= m x u = 10 x 4 = 40 kg.m/s

b) Momentum after force acts p_{2} = m x v = 10 x 8 = 80 kg.m/s

c) Gain in momentum for 2 s = p_{2}-p_{1} =40 kg.m/s

Gain in momentum per second = _{} = 20 kg.m/s

d) Acceleration a = _{}= _{} = 2 m/s^{2}

Force = m x a = 10 x 2 =20 N

Mass of the gun m_{1} = 3 kg

Mass of bullet m_{2} = 30 g = 0.03 kg

Velocity of bullet v_{2} =100 m/s

i) According to the law of conservation of momentum

m_{1} x v_{1} = m_{2} x v_{2}

3 x v_{1}= 0.03 x 100

Recoil velocity v_{1} = _{} = 1 m/s

ii) Initial velocity of the gun u = 0 m/s

Final velocity of the gun v = 1 m/s

Time t = 0.003 s

Acceleration a = _{}= _{} = _{} m/s^{2}

^{ }Force = m x a =3 x_{} = 1000 N

a) Law of conservation of momentum

b) Newton's second law of motion

c) Newton's third law of motion

d) Newton's first law of motion

a) A player moves his hands backwards while catching a fast ball because a fast moving ball has a large momentum and in stopping this ball, its momentum has to be reduced to zero. Now, when a cricket player moves back his hands on catching the fast ball, then the time taken to reduce the momentum of the ball is increased. So, the rate of change of momentum of ball is decreased and hence a small force is exerted on the hands of the player and the hands of the player do not get hurt.

b) Mass of ball = 150 g = 0.15 kg

Initial velocity u = 30 m/s

Final velocity v = 0 m/s

Time t = 0.05 s

Acceleration a =_{}=_{}= - 6000 m/s^{2}

Force = m x a = 0.15 x 6000 = 90 N

a) According to Newton's third law of motion: Whenever one body exerts a force on another body, the second body exerts an equal and opposite force on the first body. In other words, to every action, there is an equal and opposite reaction. Two examples to illustrate this law-

When a man jumps out from a boat, the boat moves backwards. This is due to the fact that to step out of the boat, the man presses the boat with his foot in the backward direction. The push of the man on the boat is action. The boat exerts an equal force in the forward direction and since the boat is not fixed and is floating, it moves backwards due to the action force exerted by the man.

Gunman gets a jerk on firing a bullet from his gun. This is because when a bullet is fired from a gun, the force sending the bullet forward is equal to the force sending the gun backwards but due to high mass of the gun, it moves only a little distance backwards giving a jerk to the gunman.

b) When a fireman directs a powerful stream of water on a fire, the hose pipe tends to go backward due to the reaction force of the water rushing through it in the forward direction at a great speed.

## Chapter -

## Chapter 2 - Force and laws of motion 76

a) According to the law of conservation of momentum: When two (or more) bodies act upon one another, their total momentum remains constant (or conserved) provided no external forces are acting. It means that when one body gains momentum, then some other body loses an equal amount of momentum i.e. momentum is neither created nor destroyed.

b)

a. Rocket taking off from the ground

The chemicals inside the rocket burn and produce very high velocity blast of hot gases. These gases pass out through the tail nozzle of the rocket in the downward direction with tremendous speed and the rocket moves up to balance the momentum of the gases. The gases have a very high velocity ang hence a very large momentum. An equal momentum is imparted to the rocket in the opposite direction, so that it goes up with a high velocity.

b. Flying of jet aeroplane

In jet aeroplanes, a large volume of gases produced by the combustion of fuel is allowed to escape through a jet in backward direction. Due to high velocity, the backward rushing gases have a large momentum. They impart an equal and opposite momentum to the jet aeroplane due to which it moves forward with a great speed.

a) If of a balloon filled with compressed air and its mouth untied is released with its mouth in the downward direction, the balloon moves in the upward direction because the air present in the balloon rushes out in the downward direction. The equal and opposite reaction of downward going air pushes the balloon upwards.

b) Mass of the unloaded truck, m_{1}= 2000 kg

Acceleration a_{1} = 0.5 m/s^{2}

Mass of loaded truck, m_{2} = 2000+ 2000 = 4000 kg

Acceleration a_{2}

m_{1} x a_{1} = m_{2} x a_{2}

a_{2} = _{}= 0.25 m/s^{2}

## Chapter 2 - Force and laws of motion 77

Car seat-belts are somewhat stretchable so as to increase the time taken by the passengers to fall forward. Due to this, the rate of change of momentum of passengers is reduced and hence less stopping force acts on them. So the passengers do not get hurt.

The paratroopers roll on landing to increase the time taken to reduce the momentum of their body. Thus, the rate of change of momentum is reduced and hence less force is exerted on their legs and they do not get hurt.

An aircraft needs air because air moving under the wings of aircraft is strong enough to hold it up and air is also required to burn the fuel in aircraft engines. Since there is no air on moon, an aircraft cannot fly on moon.

It is possible for a small animal to fall from a considerable height without being injured because a small animal has small mass, so the momentum produced is less. When the small animal falls to the ground with less momentum, less opposing force of ground acts on it and hence no injury is caused to it

Mass of the boy, m_{1}= 50 kg

Speed of boy, u_{1} = 5 m/s

Mass of trolley m_{2} = 20 kg

Speed of trolley u_{2} =1.5 m/s

Combined mass of boy and trolley, m = 20+ 50 = 70 kg

Combined velocity v

Acc. to the law of conservation of momentum

m_{1}u_{1} + m_{2}u_{2} = mv

50 x 5 + 20 x 1.5 = 70 x v

v = _{}= 4 m/s

Mass of the boat m_{b} = 300 kg

Velocity of boat v_{b}

Mass of girl m_{g} = 50 kg

Velocity of girl v_{g} = 3 m/s

Acc. to the law of conservation of momentum

m_{b}v_{b}=m_{g}v_{g}

300 x v_{b} = 50 x 3

v_{b} = _{} = 0.5 m/s

Mass of first truck, m_{1}= 500 kg

Speed of first truck, u_{1} = 4 m/s

Mass of second truck, m_{2} = 1500 kg

Speed of second truck, u_{2} =2 m/s

Combined mass of both trucks, m = 1500 + 500 = 2000 kg

Combined velocity v

Acc. to the law of conservation of momentum

m_{1}u_{1} + m_{2}u_{2} = mv

500 x 4 + 1500 x 2 = 2000 x v

v = _{}= 2.5 m/s

Mass of the ball x, m_{1}= 1 kg

Speed of ball x, u_{1} = 2 m/s

Mass of ball y, m_{2} = 1 kg

Speed of ball y, u_{2} =0 m/s (at rest)

Velocity of ball x after collision, v_{1} = 0 m/s

Velocity of ball y after collision, v_{2}

Acc. to the law of conservation of momentum

m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

1 x 2 + 1 x 0 = 1 x 0 + 1 x v_{2}

v_{2} = _{}= 2 m/s

Mass of car A, m_{1}= 2000 kg

Speed of car A, v_{1} = 10 m/s

Mass of car B, m_{2} = 500 kg

Speed of car B, v_{2}

Acc to law of conservation of momentum

m_{1}v_{1} = m_{2}v_{2}

2000 x 10 = 500 x v_{2}

v_{2} = _{} = 40 m/s

Mass of the man, m_{1}= 80 kg

Speed of man, v_{1}

Mass of bullet m_{2} = 20 g = 0.02 kg

Speed of bullet v_{2 }= 400 m/s

Acc to law of conservation of momentum

m_{1}v_{1} = m_{2}v_{2}

80 x v_{1} = 0.02 x 400

v_{1} = _{} = 0.1 m/s

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