Introduction

- Looking at this fascinating, magnificent and immense cosmos-planets moving in an orderly manner, movement of machinery parts – all of them are acted upon by certain forces and are following certain laws. In order to understand this beauty, let us take a step, forward by understanding ‘Force and laws of motion’. Here, we shall study about force and its effects, Newton’s laws of motion and conservation of linear momentum.

**Force**

- Consider a box lying on the ground. A common observation is that we need some effort to move a stationary object, to stop a moving object, to change the direction of motion of a moving object or to change the shape of an object. We call this effort (push or pull) as force. You may push or pull an object gently or hard. This
**means that force has a magnitude**. You may push or pull an object in different directions. This means that force has a direction. So force is a vector quantity. We can say that force is an interaction between the object and the source (providing push or pull) which changes or tends to change.

- a) The state of rest or a uniform motion or
- b) The direction of motion of an object or
- c) Shape of the object.

In other words we can say that force is that cause which produces acceleration in the body on which it acts, or changes its direction of motion or shape.

**Balanced and Unbalanced Forces**

**Resultant Force :**It is the single force acting on a body which produces the same acceleration as produced by a number of forces acting simultaneously.**Balanced Forces :**Balanced forces are number of forces acting together as a body which do not bring about any change in its state of rest or of uniform motion in a straight line. In this case, resultant force is zero. Balanced forces do not produce any acceleration but they may bring about a change in shape of the body e.g. pressing a balloon from two sides.- Two opposite forces having same magnitude cannot change the speed of the moving object (as F = 0 and thus a = 0).
**Unbalanced Forces :**When a number of forces acting together on a body produce a change in its state of rest or of uniform motion in a straight line. They are known as**unbalanced forces**. Here, resultant force is not equal to zero so, there will be either a change in its speed or in the direction of motion. So, we require an unbalanced force to accelerate a body.

When the net force on the body ¹ 0, the body at rest starts moving in the direction of the net force.

If F1> F2, then F1 – F2> 0, the body accelerates in the direction of F1.

The effects of unbalanced forces are

(i) it can bring a stationary body in motion

(ii) it can produce acceleration in the body (+ve or –ve)

(iii) it can change the direction of motion of the body.

(iv) an object maintains its motion under the continuous application of unbalanced forces.

(v) it can change the shape of the body.

**Example of Balanced and Unbalanced Forces**

Consider a body kept on ground and being pulled to the right side with the help of a rope. Let us say that we apply a small force F and the body does not move. This is because we have two pairs of balanced forces acting on the body :

(i) Weight, mg acting vertically downward and force of reaction N of the ground acting on the body vertically upward. As N = mg, this is one pair of balanced forces, so body does it move in the vertical direction.

(ii) Applied force F and frictional force f. As F = f, this is the second pair of balanced forces so body doesn’t move in the horizontal direction.

If we increase force F, a stage reaches when the body begin to move. F becomes greater than f, second pair of forces becomes unbalanced and that is why motion is produced.

Galileo observed that as a ball is rolled down an inclined plane, its speed increases and when rolled up an inclined plane, its speed decrease. So, if it is rolled on a horizontal plane, the case is just in between the two situations described above. The result should also be in between, i.e., its speed should remain constant.

He also reached this conclusion in another way. Consider a marble resting a frictionless plane inclined on both sides when the marble is released from left, it rolls down the slope and goes up on the opposite side to the same height from which it was released. If the inclination of the planes on both sides are same. The marble climbs the same distance that it covered while rolling down. If the angle of inclination of right side plane is decreased, marble would travel further distance till it attains the same height. If this plane is ultimately made horizontal, the marble would continue moving trying to reach the same height. The unbalanced forces on the marble are zero. So, it suggests that an unbalanced (external) force is required to change the motions of the marble but no net force is required to maintain its uniform motion. Practically, it is difficult to get zero unbalanced force. This happens as frictional force is there on surface. If frictional force is completely absent, a body moving on a surface will continue to move.

Thus, if there is no unbalanced force on a body, the body will either remain at rest or will move with a uniform velocity, i.e., it remains unaccelerated. If there is a non-zero acceleration, it means that there is some unbalanced force acting on the body.

Newton 1st Laws of Motion

We found that,

- If a body is at rest, it remains at rest, if no unbalanced force acts on it.
- A body accelerates when an unbalanced force acts on it.

These facts form **Galileo’s law of inertia** or **Newton 1****st**** law of motion**. Galileo first suggested this idea and it was formulated into a law by Newton. Newton 1st law is stated as follows :

**Newton 1****st**** law of motion : A body at rest will remain at rest and a body in motion will remain in uniform motion unless acted upon by an unbalanced external force to change that state of rest or of uniform motion.**

To put it in simple words, if no unbalanced external force acts on a body at rest, it will remain at rest and if it is moving with uniform motion, it will continue to do so. Or, it will remain unaccelerated, if there is no net force on the body.

**Inertia :**A body does not change its state of rest or of uniform motion on its own. If it is at rest, it remains at rest. If it is moving, it continues to do so without any change in its speed or direction. Force is required to change its state of rest or motion. **This inability of a body to change its state of rest or uniform motion on its own is known as inertia**.

**Inertia and Mass **

- Consider two bodies of unequal masses, say a cricket and a tennis ball. On pushing the two balls equally hard, cricket ball will have a much smaller velocity as compared to that of tennis ball. Cricket ball has resisted the attempt to change its state more effectively than the tennis ball. Or a cricket ball has larger inertia than a tennis ball. In general,
**a heavier body has larger inertia than a lighter body**. This is valid for inertia of rest as well as for inertia of motion. Larger the mass, the larger is the inertia and vice-versa. Thus, mass is a measure of inertia.

**Types of Inertia **

(i) Inertia of rest

(ii) Inertia of motion

(iii) Inertia of direction

**Inertia of rest :**

** **It is the inability of a body by virtue of which it cannot move on its own. A body at rest remains at rest and cannot move on its own due to inertia of rest.

**Applications :**

** **(i) If we hit a carpet with a stick, carpet moves ahead and dust particles stay there due to inertia of rest and get removed.

(ii) The passengers in a car falls backwards when it starts suddenly. This happens because out feet are in constant contact with the floor of the car. They share the motion of the car but upper part of the body remains there due to inertia of rest and the passenger falls backward.

(iii) The rider falls backward when a horse starts suddenly due to inertia of rest.

(iv) When we shake the branches of a tree, the branch moves the fruits stay there due to inertia of rest and fall down.

**Inertia of Motion :**

It is the inability of a body in motion to stop on its own. A body in motion cannot come to rest on its own. A body in uniform motion neither gets accelerated nor get retarded on its own.

**Applications :**

** **(i) A person sitting in a moving car falls forward when it stop suddenly. This is because when the car stops, feet share the motion of car and come to rest but upper part of the body continues to move due to inertia of motion, so the person falls forward.

(ii) If a ball is thrown upward in a train moving with uniform velocity, it returns to the hands of thrower. This is because, during the upward and downward motion, the ball also moves along horizontal due to inertia of motion. So, it covers the same distance as the train and the ball returned to the hands of the thrower.

**Inertia of Direction :**

** **It is the inability of a body by virtue of which it cannot change its direction of motion on its own.

**Applications **

** **(i) The mud coming from the wheels of a moving car comes off tangentially.

(ii) When a vehicle takes a sharp turn at a high speed. The passengers get thrown to the other side due to inertia of direction. When the vehicle is moving in a straight path, the passengers share that motion. Due to the unbalanced force exerted by the engine, the car changes its direction but the passengers tend to maintain the original direction due to inertia of direction and thus they get thrown to one side.

**Example 1:**

On striking the coin at the bottom of a pole of carrom coins with a striker, that coin only moves away while the rest of the pile stays at its place.

**Solution :**

The force exerted on the lowest coin moves it, while the rest of the pile stays at its place due to inertia of rest.

**Example 2:**

Why does a person fall when he jumps out from a moving bus/train?

**Solution :**

The moment, the person’s feet touch the ground, they come to rest but upper part of his body continues to move due to inertia of motion.

**Linear Momentum :**

If two bodies of different masses moving with the same velocity are brought to rest in same time, the force required to stop the heavier body is more than that for the lighter body. Similarly, if two bodies of same mass are moving with different velocities, the force required to stops the faster moving body is more than that for the slow moving body. So, we understand that the force required to stop a moving body in a definite time depends on mass as well as velocity. Hence, the need for the term momentum.**Linear momentum** of a moving body is defined as the product of its mass and velocity and has the same direction as that of velocity. Normally, the word momentum is used for linear momentum (we are considering a body moving in a straight line) it is represented by letter p.

For a body of mass m moving with velocity v, linear momentum p is expressed as p = mv.

It is a vector quantity. It is in the direction of motion of the body (or the velocity of the body).

Its S.I. unit is kg ms–1 and C.G.S. unit is g cms–1.

Newton 2nd Law of Motion

- The rate of change of momentum of a moving body is directly proportional to the applied unbalanced external force and this change always takes place in the direction of the applied force.

Mathematical Formation of Newton 2nd Law of Motion

- Suppose

m = mass of body

u = initial velocity of body along a straight line.

v = final velocity of body along same straight line after time ‘t’.

F= magnitude of external unbalanced applied force (constant in magnitude).

t = time for which the force is applied.

Initial linear momentum, pi = mu

Final linear momentum pf = mv

Change in momentum = pf – pi

= mv – mu

= m(v – u)

So, rate of change in momentum

= ma (as acceleration, )

According to Newton’s 2^{nd}law of motion,

Rate of change in linear momentum force applied

i.e., ma F

or Fma

or F = kma …(i)

Where k is constant of proportionality. Its value depends on the units used for measuring the force. If we define F = 1 when m = 1 and a = 1

i.e., 1 unit force is that force which produces unit acceleration in a body of unit mass. Then, from equation (i).

Putting this value of k in equation (i), we get

F = ma …(ii)

This is the mathematical form of Newton’s 2^{nd}law of motion. It is also stated as

Force acting on a body is the product of mass of the body and its acceleration.

**Note : Remember, by force, we mean unbalanced external force. **

**Unit of Force**

** **The S.I. Unit of force is Newton and it is represented by N. One Newton force is that force which when acting on a body of mass 1 kg, produces in it an acceleration of 1 m/s^{2}, then from F = ma.

The CGS unit of force is dyne.

One dyne force is that force which when acting on a body of mass 1 g, produces in it an acceleration of 1 cm/s^{2} in its direction.

When, m = 1 g and a = 1 cm/s then from F = ma

1 dyne = 1 g × 1 cm/s = 1 g cm/s^{2}_{.}

Relation between S.I. and CGS Unit of Force

- 1 N = 1 kg m/s
^{2}

= 1 kg × 1 m/s^{2}

= 10^{3}g × 10^{2} cm/s^{2}

= 10^{5}g cm/s^{2}

= 10^{5} dyne

1 N = 10^{5} dyne.

Obtaining Newton 1^{st}law of Motion from 2^{nd}law of Motion

- From Newton 2
^{nd}law of motion, F = ma

or

If F = 0 then a = 0

(i) v = u i.e., if no force is applied on a body it continues to move with same velocity.

(ii) If u = 0, then v = u = 0 i.e., if a force is applied as a body lying at rest, it continues to be at rest.

Combining (i) and (ii), we get Newton’s 1st law of motion i.e., a body at rest will remain at rest and a body in motion will remain in uniform motion unless acted upon by an unbalanced internal force to change that state of rest or of uniform motion.

**Impulse :**

** **Impulse is defined as the change in linear momentum of the body produced by the force. It is measured as the product of the average force and time for which the force acts. It is a vector quantity whose direction is the direction of force.

F = ma

where pi = initial momentum = mu

and p_{f} = final momentum = mv

Ft = p_{f} – pi

Ft is called the impulse of force F in the time internal ‘t’.

Impulse, I = Ft

Impulse of a force acting as a body is equal to the change in linear momentum of the body produced by the force.

Consider a force having very large magnitude acting for a short duration of time e.g. a ball rebounding from a marble floor, it remains in contact with the floor for a short duration. The floor is exerting a large force in a short duration. Such a force is called as impulse force. F is very large and t is very small, their product (the impulse) remains finite. So, as impulsive force produces a finite change in momentum.

** **

Applications of Newton’s 2^{nd}Law of Motion

(i) **A cricketer withdraws his hands while catching a ball :**

Let u be the initial velocity of the ball of mass m when it reaches the cricketers hands. When he catches the ball, final velocity, v = 0

Ft = m(v – u)

m(v – u) is fixed.

If the cricketer withdraws his hands, t increases, so F decreases or the force of impart on his palm becomes small.

(ii) **Athletes takes a high jump on sand or cushioned bed :**

** **If an athlete jumps from a height on sand floor, his feet come to rest in a short time, so a very large force is exerted on his feet and he may hurt his feet. If he jumps on sand or cushioned bed, the time duration in which his feet come to rest increases, so the force exerted by his feet decreases and he is not hurt.

(iii) **A Karate player can break a number of bricks with a single blow of his hand:**

** **Karate player strikes the bricks very fast. Ft = m(v – u).

Very large force F is exerted (as t is very less) and u is very large and this is sufficient to break the bricks.

(iv) **Passengers in a moving car are advised to wear seat belts :**

** **On sudden application of brakes, passengers fall forward due to inertia of motion. The seat belt prevents them from falling forward suddenly i.e., t increases Ft = m(v – u). So F decreases and it prevents injury.

(v) **Shockers are provided in automobiles :**

** **Shockers decrease the rate of change of momentum by increasing the time interval, thereby the force during the jerk decreases. They also decreases the hardness of the shocks, as we pass over a rough road.

(vi) **China and glasswaves break, when they fall on a hand surface but they do not break when they fall on soft floor (like sand) or carpet :**

When china and glasswaves fall on a hard floor from a height. They come to rest in a short time so a large force is exerted on them and they break. But if they fall on sand or carpet, time duration in which they come to rest increases, so less force is exerted on them and they do not break.

**Example 3:**

A body of mass 1.5 kg is resting on a frictionless surface. Find its acceleration when it is acted upon by a force of 0.03 N.

**Solution :**

Here, m = 1.5 kg and F = 0.03 N

From the relation, F = ma

Acceleration,

**Example 4:**

A force acts for 0.1 s on a body of mass 2.4 kg initially at rest. The force then ceases to act and it moves through 4 m in the next two seconds. Calculate the magnitude of force.

**Solution :**

When force ceases to act, the body moves with the constant velocity. As it moves 4 m is 2s, its uniform velocity is 2 ms-1 body acquires a velocity 2 ms–1 is 0.1 s.

u = 0, v = 2ms–1, t = 0.1 s, m = 2.4 kg.

acceleration,

F = ma (Newton 2nd law)

= 2.4 × 20 = 48 N

**Example 5:**

A scooter is moving with a velocity of 72 km/h and it takes 4 second to stop after applying the brakes. Calculate the braking force on the scooter if its mass along with the rider is 300 kg.

**Solution :**

Initial velocity,

Time taken, t = 4s, final velocity, v = 0

Force,

Negative sign signifies that direction of force is opposite to the direction of motion.

**Example 6:**

A constant force acts on a body of mass 2.5 kg for 2s. It increases its velocity from 4 m/s to 8 m/s. Find the magnitude of applied force. Now if the same force were applied for 6 s, what would be the final velocity?

**Solution :**

v = u + at

v = 4 + at

**Example 7:**

A force of 10 N gives a mass m1 an acceleration of 4 m/s2, and a mass m2, an acceleration of 6 m/s2. What acceleration would it give if both the masses are tied together?

**Solution :**

F = m1a1 = m2a2

**Example 8:**

Which would require a greater force : accelerating a 3 kg mass at 6 m/s2 or a 5 kg mass at 3 m/s2 g

**Solution :**

F1 = m1a1 = 3 × 6 = 18 N

F2 = m2a2 = 5 × 3 = 1 5 N

Accelerating a 3 kg mass at 6 m/s2 would require a greater force.

**Example 9:**

Two balls A and B of masses m and 3m are in motion having velocities 3v and v respectively. Compare (i) their inertia (ii) their momentum (iii) force needed to stop them in same time.

**Solution :**

(i) 1 : 3 as mass is a measure of inertia.

(ii)

Newton 3rd law of Motion

- To every action, there is always an equal and opposite reaction and they act an different bodies. When a body exerts a force an another body, the second body instantaneously exerts a force on the first body. These two forces are always equal in magnitude but opposite is direction. These forces act on different bodies.

Consider two spring balances connected together as shown in the figure. The fixed end of spring balance A is connected with a wall. When the spring balance B is pulled with a force, it is found that reading on both the balances is same. It means that the force exerted by A on B is equal but opposite in direction to force exerted by B on A. If the force which B exerts on A is called the action then the force which A exerts on B is called the reaction.

**Note :**

- Action and reaction always act on different bodies.
- Action and reaction always occur at the same time. We cannot say that reaction occurs after action.
- Any force can be called action, the other force will be called reaction.
- 3rd law is valid irrespective of state of rest or motion of the body.
- Action and reaction may not produce acceleration of equal magnitude as each force acts on a different body as they may have a different mass.

**Applications of Newton’s 3****rd****law :**

** **(i) A boy walks because of the force exerted by ground on him.

To walk, a boy presses the ground in backward direction with foot and in return, the ground pushes his foot forward.

(ii) **Recoiling of a gun :**

** **When a bullet is fired from a gun, the gun exerts a forward force on the bullet. The bullet also exerts an equal and opposite force on the gun, which results in the recoil of the gun. Acceleration of the gun is much less than that of the bullet as the mass of gun is much larger than that of the bullet.

(iii) **When a man jumps out from a boat, the boat moves backward :**

** **When a man jumps out of the boat, the boat moves in the water in the opposite direction. By Newton’s 3rd law. The boat pushes you in the forward direction and you push the boat in the backward direction. So, you move towards the shore and the boat moves away from the shore.

**Example 10:**

Explain the moving of a boat.

**Solution :**

The boat man pushes the water backwards with mass (action). According to 3rdlaw, water exerts as equal and opposite force on the boat (reaction) because of which the boat moves forward.

** **

**Example 11:**

Why is it difficult to walk on sand or ice?

**Solution :**

When our foot pushes the sandy ground in backward direction. The sand gets pushed away and is not able to provide sufficient reaction (forward) and that is why we find it difficult to walk on sand or ice.

**Example 12:**

Why firemen find it difficult to hold a hose ejecting large amount of water at a very high velocity?

**Solution :**

Hose pipe moves backward due to backward reaction of water. So, firemen have to apply large force to keep the hose in position.

Significance of Newton laws

- The 1stlaw tells us about the natural state of motion of the body i.e., motion along a straight line with constant speed.
- The 2ndlaw tells us that if a body is not following its natural state of motion, there is a net unbalanced external force which is acting on the body.
- The 3rdlaw tells us about the nature of the force i.e., forces always exist in pairs.

**Note :**

The three laws are independent. If we derive 1st law from the 2nd, it doesn’t mean that 2nd law is the real law. The three laws are independent.

Conservation of Linear Momentum

Newton’s 1st law tells us that a particle remains at rest or moves with a constant velocity if the net force on it is zero. In this case, its linear momentumi.e., mass times velocity remains constant. This is an example of very important law called principle of conservation of linear momentum.

**Meanings of terms used :**

** **Consider two particles A and B. We call their group a system of particles. These particles belong to the system and any other particle is ‘external’ to it. The force exerted by A on B and that exerted by B on A are called **internal forces. **Any force on A or B by an external particle (other than A and B) is called an **external force**. Total linear momentum of the system is defined as the sum of linear momenta of A and B. If A and B on moving along same straight line, the momentum of the system is simply the arithmetic sum of their momenta i.e., m1v1 + m2v2. Where m1, m2 are their masses and v1 and v2 are their velocities. If they are in opposite direction, we take appropriate sign (+ or –, taking one direction as +ve, then other direction is –ve). These ideas may be extended to a system of more than two particles.

Principle of Conservation of Linear Momentum

** In an isolated system where there is no net external force on a system of particles, the total linear momentum of the system remains conserved.**

**Verification :**Consider an ideal collision between two bodies :

Consider two balls A and B moving in the same direction along a straight line with different velocities.

Let mA = mass of ball A

mB = mass of ball B

uA = initial velocity of ball A

uB = initial velocity of ball B

If uA> uB, the balls with collide. Let the collision last for time t.

Suppose, during collision,

FBA = Force exerted on B due to A.

FAB = Force exerted on A due to B.

Let us assume that no other external unbalanced force acts on the balls.

After collision,

Let vA = velocity of ball A after collision

vB = velocity of ball B after collision

Change in momentum of ball A = Momentum of A after collision – Momentum of A before collision

= mAvA – mAuA

Rate of change in momentum of ball

This is equal to the force exerted on A by B = FAB

(Newton’s 2nd law of motion)

or …..(i)

Similarly, …..(ii)

According to Newton 3rd law of motion,

FBA = –FAB

using equations (i) and (ii)

or mBvB – mBuB = –mAvA + mAuA

mAvA + mBvB = mAuA + mBuB …..(iii)

or total momentum after collision = total momentum before collision.

Equation (iii) shows that total momentum of the two balls remains unchanged. As a result of this ideal collision experiment, we say that the sum of momenta of the two objects before collision is equal to the sum of momenta of the two objects after collision, provided that there is no external unbalanced force acting on them. This is known as the laws of conservation of momentum. Alternatively, we can say that total momentum of the two objects is unchanged or conserved.

Application of law of Conservation of Linear Momentum

**Recoil Velocity of a Gun**

** **Let m1 = mass of the bullet

m2 = mass of the gun

v1 = velocity of the bullet

v2 = recoil of the gun

Before firing, total linear momentum of bullet and gun = 0 as both are at rest

After firing, total linear momentum of bullet and gun = m1v1 + m2v2

Applying the law of conservation of linear momentum as no external forces are involved,

m1v1 + m2v2 = 0

or m2v2 = –m1v1

or …(i)

This is the expression for recoil velocity of gun –ve sign signifies that v2 is in a direction opposite to v1. i.e., the gun recoils or moves backwards when the bullet moves forward. m2>> m, (gun is much heavier than the bullet)

so, v2<< v1 i.e., the recoil velocity of the gun is much smaller than the velocity of the bullet.

**Flight of rockets**

** **Before firing the rocket, the total momentum of the system = 0

On firing, the burnt gases rush out through the nozzle with great speed.

The rocket moves such that total momentum after firing equal to total momentum before firing.

or momentum of rocket + momentum of gases = 0

or momentum of rocket = – momentum of gases

(–ve sign signifies that rocket moves upward in the direction opposite to the direction of gases) with momentum equal to the momentum of escaping gases.

**Example 13:**

A 20 g bullet is shot from a gun of mass 10 kg with a velocity of 400 m/s. Calculate recoil velocity of the gun.

**Solution :**

m1 = 20 g = 20 × 10–3 kg = 2 × 10–2 kg, m2 = 10 kg

v1 = 400 m/s v2= ?

Total momentum of bullet and gun after firing

= Total momentum of bullet and gun before firing

m1v1 + m2v2 = 0

or

–ve sign signifies that the gun moves in a direction opposite to that of the bullet.

**Example 14:**

Two objects each of mass 2 kg are moving in the same straight line but in opposite directions towards each other. Velocity of each objects is 5 m/s. They stick to each other during collision. What is the velocity of the combined object after collision?

**Solution :**

m1 = m2 = 2 kg, u1 = 5 m/s, u2 = – 5 m/s

Total momentum before collision = m1u1 + m2u2

= 2(5) + 2(–5) = 0 ….(i)

Let the velocity of the combined object be v after collision.

Total momentum after collision = (m1 + m2)v …..(ii)

m1u1 + m2u2 = (m1 + m2)v according to conservation of linear momentum using equation (i) and (ii)

0 = (2 + 2)v

\ v = 0 m/s

**Example 15:**

An object of mass 1 kg is travelling in a straight line with a velocity of 10 m/s 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.

**Solution :**

m1 = 1 kg u1 = 10 m/s

m2 = 5 kg u2 = 0

Total momentum just before the impact = m1u1 + m2u2

= 1 × 10 + 5 × 0

10 kg m/s

Total momentum just after the impact = Total momentum just before the impact (according to principle of conservations of linear momentum)= 10 kg m/s

Let the velocity of the combined object be v

Then, total momentum after impact = (m1 + m2)v

= (1 + 5)v = 6 v

6v = 10 According to conservation of linear momentum

so,

**Example 16:**

The car A of mass 1000 kg travelling at 15 m/s collides with another car B of mass 1500 kg travelling at 25 m/s in the same direction. After collision, velocity of car B becomes 20 m/s. Calculate the velocity of car A after collision.

**Solution :**

Mass of car A, m1 = 1000 kg

initial velocity of car A, u1 = 15 m/s (Final velocity of car A = v1)

initial velocity of car B, u2 = 25 m/s (Final velocity of car B = v2)

mass of car B, m2 = 1500 kg

Total momentum after collision

= Total momentum before collision

m1v1 + m2v2 = m1u1 + m2u2

1000 v1 + 1500 × 20 = 1000 × 15 + 1500 × 25

1000 v1 + 30,000 = 15000 + 37500 = 52500

1000 v1 = 52500 – 30,000

m/s.

KEY POINTS |

**Force :**Force is an interaction between the object and the source (providing push or pull) which changes or tends to change

(a) the state of rest or of uniform motion of the object

(b) the direction of motion of the object

(c) shape or size of motion of the object

It is a vector quantity. Its S.I. unit is Newton (N).

**Resultant Force :**It is the single force acting as a body which produces the same effect i.e. the same acceleration as produced by a number of forces acting simultaneously.

**Balanced Forces :**Balanced forces are number of forces acting together on a body which do not bring about any change in its state of rest or of uniform motion in a straight line (or which produce no acceleration). Here, resultant force is zero.

**Unbalanced forces :**When a number of forces acting together on a body produce a change in its state of rest or of uniform motion in a straight line (or which produce a non-zero acceleration), they are known as unbalanced forces. Here, resultant force

**Inertia :**Is the natural tendency of an object to resist its state of rest or of uniform motion or its direction of motion.

**Inertia of rest :**Is the inability of body by virtue of which it cannot move on its own.

**Inertia of motion :**Is the inability of body in motion to stop on its own.

**Inertia of Direction :**Is the inability of body by virtue of which it cannot change its direction of motion on its own.

**Newton 1****st****Law of Motion :**A body at rest will remain at rest and a body in motion will remain is uniform motion unless acted upon by an unbalanced external force to change that state of rest or of uniform motion.

**Linear Momentum :**Linear momentum of a moving body is defined as the product of its mass and velocity and has the same direction as that of velocity. It is a vector quantity. Its S.I. unit is kg ms–1.

**Newton 2****nd****Law of Motion :**The rate of change of momentum of a moving body is directly proportional to the applied unbalanced external force and this change takes place in the direction of the applied force.

**Newton (N) (S.I. unit of force) :**One newton is that force which when acting on a body of mass 1 kg, produces is it an acceleration of 1 m/s2in its direction.

**Dyne (CGS unit of force) :**1 dyne is that force which when acting on a body of mass 1 g, produces in it an acceleration of 1 cm/s2in its direction.

**Relation between S.I. and CGS unit of force :**1 N = 105dyne.

**Impulse :**is defined as the change in linear momentum of the body produced by the force. It is measured as the product of the average force and time for which the force acts. It is a vector quantity. Its S.I. unit is N.S.

**Newton 3****rd****Law of Motion :**To every action, there is always an equal and opposite reaction and they act on different bodies.

**Principle of Conservation of Linear Momentum :**When there is no net external force as a system of particles, the total linear momentum of the system remains conserved.

EXERCISE |

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**Very Short Answer Type Questions :**- Which law tells us about the nature of force?
- Can balanced forces move a body at rest?
- Can balanced forces change the shape and size of a body?
- Can balance forces stop a moving body?
- What is the S.I. unit of momentum?
- On what factor does inertia of a body depend?
- Is momentum a scalar or vector?
- Name the physical quantity whose unit is kg ms–1.
- Which physical quantity corresponds to rate of change of momentum.
- Which principle is involved in the working of a jet plane?
- What is the other name for Newton 1stlaw of motion?

**Short Answer Type Question (2 marks)**

- Define force
- Name the various effects of force.
- Why does a person in a car tend to fall forward when it stops suddenly?
- Why does a person in a car tend to fall backward when it starts suddenly?
- What is one newton force?
- Define momentum of a body.
- A horse has to apply force continuously in order to move a cart with constant velocity. Explain.
- Water sprinkler used for watering lawns begin to rotate as soon as water is supplied. Explain its principle.
- A light feather is dropped from a height. It falls down with constant velocity. What is the net force on the feather?

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**Short Answer Type Questions (3 marks)**

- Derive the relation F = ma
- What is force? What is inertia? How is inertia measured?
- A truck of mass M is moved by a force F. It is then loaded with goods whose mass is equal to mass of the truck and driving force becomes , what will be the acceleration.
- Explain the use of seat belts in vehicles.
- State newton 3rdlaw of motion and principle of conservation of momentum.
- Why does a gun recoil on Firing? Obtain an expression for the recoil velocity of a gun.
- Why a cricket player loses his hands while catching a ball?
- A ball is thrown vertically upward with certain velocity. Its speed decreases continuously till it becomes zero. Then, it begins to fall downward and attains the same speed with which it was thrown (if air resistance is neglected). It means that the magnitude of initial and final momentum is same. Yet, it is not an example of conservation of momentum. Explain.
- A force acts for 0.2 sec on a body of mass 4 kg initially at rest. The force is then withdrawn and the body moves with a velocity of 2 ms–1. Find the magnitude of the force.
- A force produces an acceleration of 10 ms–2in a body of mass 400 g. What acceleration would be caused by the same force in a body of mass 4 kg?

**Long Answer Type Questions (5 Marks) **

- A force acts for 20 s on a stationary body of mass 200 kg after which the force ceases to act. It moves through a distance of 200 m in the next 5 sec. Calculate (i) the velocity acquired (ii) acceleration produced (iii) magnitude of the force.
- A car is moving with a uniform velocity of 60ms–1. It is stopped in 4s by applying a force of 1500 N through its brakes. Calculate (i) the change in momentum of the car (ii) retardation produced (iii) mass of the car.
- State Newton 1slaw of motion. Hence, define force and inertia.
- State and explain Newton’s 3rd law of motion. How will you verify it experimentally?
- Give at least four applications of Newton’s 2ndlaw of motion.

**Multiple Choice Questions :**

- A passenger in a moving train throws a ball up which falls behind him. Motion of the train is

(a) uniform (b) accelerated

(c) along circular track (d) retarded

- Rocket works on the principle of conservation of

(a) energy (b) velocity

(c) mass (d) momentum

- When an object undergoes acceleration

(a) its momentum increases (b) its speed increases

(c) an unbalanced force always acts on it (d) all of the above

- A passenger throws a ball up in a train moving with uniform velocity. The ball will

(a) fall on his left (b) fall behind him

(c) fall ahead of him (d) return back to him

- If soldiers have an option of using rifles of different heights but with bullets of fixed weight, they would prefer

(a) light guns as they can be carried easily

(b) light guns as they have move recoil

(c)heavy guns as they have less recoil

(d)heavy guns as they can be hold firmly.

WORKSHEET – 1

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- Match the column

** ** Column I Column II

(p) Catching a moving ball (i) force changes speed and direction of

body

(q) Compressing a spring (ii) force tries to move a body at rest

(r) Pushing a wall (iii) force changes shape and size of a body

(s) Kicking a moving football (iv) force stops a moving body

- Is force required to be move a body uniformly along a circle?
- What is measure of inertia of a body in linear motion?
- Two equal and opposite forces act on a stationary body. Will the body move?
- Two equal and opposite forces acts on a moving object. How is its motion affected?

WORKSHEET – 2

- What is the momentum of a boy of mass 40 kg working with a velocity of 2 m/s?
- Calculate the force required to produce an acceleration of 3 m/s2in a body of mass 10 kg. What would be the acceleration if the force were doubled?
- A car is moving with a velocity of 90 km/h and it takes 5 second to stop after the brakes were applied. Calculate the braking force on the car if its mass along with the passengers is 1000 kg.
- A force produces an acceleration of 1.5 m/s2 in a disk. Three such disks are tied together and the same force is applied on the combination. What will be the acceleration?
- When a horizontal force P acts on a cart of mass 20 kg, it moves with a uniform velocity on a horizontal floor. When a force of 1.2 P acts on the cart, it moves with an acceleration of 0.05 m/s2. Find the value of P?

WORKSHEET – 3

- The law that defines force and inertia is

(a) Newton 1st law

(b) Newton 2nd law

(c) Newton 3rd law

(d) None of the above

- Newton 2ndlaw of motion gives us

(a) Definition of inertia

(b) Definition of force

(c) Measure of force

(d) None o the above

- Newton’s 3rdof motion talks about

(a) Natural state of motion of the body

(b) Definition of force

(c) Measure of force

(d) Nature of force

- Swimming is based on

(a) Newton 1st law

(b) Newton 2nd law

(c) Newton 3rd law

(d) None of the above

- Comment on the statement ‘The sum of action and reaction on a body zero’. Is it true for false?

WORKSHEET – 4

- A man of mass 60 kg running with a velocity of 18 km/h jumps into a car of mass 1 quintal standing on the rails. Find the velocity with which the car starts travelling along the rails.
- A truck of mass 2500 kg moving at 15 m/s collides with a car of mass 1000 kg moving at 5 m/s in the opposite direction. Find the velocity with which they move together.
- A girl of mass 50 kg jumps out of a rolling boat of mass 300 kg to the bank with a horizontal velocity of 3 m/s With what velocity does the boat begin to move backwards?
- Principle of conservation of linear momentum is deduced from

(a) Newton 1st law

(b) Newton 2nd law

(c) Newton 3rd law

(d) None of the above

- Recoil velocity of a gun is

(a) equal to velocity of bullet

(b) much smaller than velocity of bullet

(c) much greater than velocity of bullet

(d) cannot say

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