## Force And Laws Of Motion

In the previous chapter, we learned about the unidirectional motion of an object in terms of speed, velocity, distance and acceleration in a given time interval without discussing about the cause of that motion. In this chapter, we will study about that cause and the dynamics of the motion.

We will learn how the system varies with time and what causes are responsible for that variation. To understand the dynamics we will also learn about the laws which govern motion in our everyday life.

## Force And Laws Of Motion Force in Nature

Consider some situations which occurs in our day-to-day life, like a boy kicking a ball or a girl squeezing a lemon or a mother kneading a flour dough . In all these situations, we see that the objects interact with each other either by pushing or by pulling which further changes the position, speed or shape of the object.

Through these examples, we can come up with a definition of force. Force is the interaction of objects by pushing or pulling which tends to change the shape or the state of motion of that object.

Following effects can be bring out when a force is applied on an object:

- A stationery object will start moving once after a force is applied.

**Example:**paddling the bicycle. - Force is required to stop the moving object.

**Example:**apply brake to a running car. - Speed of a moving body can be changed.

**Example:**Press accelerator to increase the speed of a car and apply brake to decrease or stop its speed. - Direction of moving object can be changed after applying force.

**Example:**Change the direction of steering a car. - Among all these force can even change the shape and size of an object.

**Example:**Hammering a stone will break it into several pieces. Force is a vector quantity i.e., it can be completely defined by both direction and magnitude.

## Force And Laws Of Motion Balanced and Unbalanced Forces

Force can be defined as an agent, which can produce acceleration in a body on which it acts, or produce a change in its size or shape, or both.

**Balanced Forces:**When more than one force is applied on an object in such a way that the forces does not bring any change in its state of rest or motion, then the forces are said to be balanced forces. Balanced forces may bring out the change in the shape on the object. If the resultant of applied forces is equal to zero, it is called balanced force. Balanced forces do not cause any change of state of an object. Balanced forces are equal in magnitude and opposite in direction. Balanced forces can change the shape and size of the object.**Unbalanced Forces:**When more than one force is applied on an object in such a way that the forces bring out a change in its state of rest or motion, then the forces are said to be unbalanced forces. If the resultant of applied forces are greater than zero, the forces are called unbalanced forces (Fig. 2.2). An object in rest can be moved because of applying balanced forces. Forces can be broadly classified into two types:- Contact Force
- Field Force or Non-contact force

**Contact Force**

The force exerted by an object over the other object which is in contact with the former can be defined as contact force.

**Example:** Pulling a cart

Some important contact forces are:

**Normal force:**If contact forces between the bodies are perpendicular to the surfaces in contact, the forces are known as contact forces.

For example: A wooden block kept on table is in equilibrium. Block applies a downward force on a table due to its weight and table pushes the block upwards. Thus both table and block apply a normal force on each other.**Frictional force:**When we try to slide the heavy box on a rough floor by pushing it, a force acts parallel to the surface in contact with the floor and opposes the pushing force. This parallel force is called the frictional force.

**Example:**

In the above example, the truck is being pushed from opposite sides in such a way that it does not move i.e., equal force is applied from both the sides. Such forces are called balanced forces where net force is zero.

**Non-contact Force**

The force exerted by an object over the other object when they are not physically in contact with each other is called non-contact force or action at a distance.

**Examples:**

**Gravitational pull:**It is the downward force acting on an object due to gravitational pull of earth. If the object is not in contact with the earth the earth pulls it. If we release a stone or ball or apple from height it will fall on the ground.**Magnetic force or Electrostatic force:**It is known that a magnet can pull an iron piece from distance. Also when we rub a comb with hair and bring it near bits of paper, it attracts them from distance.

In the above example, the truck moves in the direction of the force applied because there is no equal opposite force acting on it.

The outcome of such unbalanced forces are as following:

- Stop a moving object suddenly
- Increase the speed of a moving object
- Decrease the speed of a moving object
- Move a static object
- Change the shape and size of an object

## Force And Laws Of Motion Galileo’s Experiments

Galileo after a series of experiments concluded that a body continues to move with uniform velocity if no force acts on it. He observes when a marble rolls down a smooth incline plane, its velocity increases. Its velocity decreases when it climbs up.

He also said that if a marble, kept on one side of the smooth plane inclined at both sides, released from rest, it will roll down the slope and go up on the opposite side to the same height above bottom line, from which it is released.

If the angle of inclination of the right side plane were gradually decreased the marble would travel further distances till it reach the original height. If the right side of the plane is made horizontal the marble will continue to travel forever trying to reach the same height that it was released from.

Thus, it suggests that an unbalanced force (gravity) is required to change the motion of the marble, but not net force is needed to sustain the uniform motion of marble.

Newton further studied the Galileo’s experiment and postulated the three fundamental laws of motion which laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. They are summarized as following:

**First law:**When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a net force.**Second law:**In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object: F = ma.**Third law:**When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

According to Galileo, there is no need of force to continue the motion of an object. If an object is moving, it will be in the same state until and unless an external force is applied to stop it.

**Example:** A boy riding a cycle applies brake. The cycle does not stop immediately In fact, speed gets reduced slowly and steadily.

As per the above discussion, we form the Galileo’s law of inertia which states that

- If a body is at rest, it remain continues to at rest unless a force is applied to it.
- If a body is moving, it will continue to move with the same speed in the same direction unless a force is applied to it.

We come across certain experiences while traveling in a car which can be explained on the basis of the law of inertia. For example, we tend to remain at rest with respect to the seat until the drives applies a brakes to stop the car. With the application of braking force, the car slows down but our body tends to remain in the same state of motion because of its inertia.

## Force And Laws Of Motion Newton’s First Law of Motion

‘If an object is in a state of rest, it will remain in the state of rest and if it is in the state of motion, it will remain moving in the same direction with the same speed unless an external force is applied on it.’

## Force And Laws Of Motion Master Your Test

**Question 1. Describe Newton’s First law.**

**Answer:** If an object is in a state of rest, it will remain in the state of rest and if it is in state of motion, it will remain moving in the same direction with the same speed unless an external force is applied on it.

**Question 2. What did Galileo conclude through his series of experiments?**

**Answer:** Galileo concluded that the natural state of the body is to oppose change in its state of rest or motion.

**Question 3. Why a groove is provided in the saucer to hold the cup?**

**Answer:** A groove is provided in a saucer for placing the tea cup because it prevents the cup from toppling over in case of any sudden jerks.

## Force And Laws Of Motion Track Your Learning Question And Answers

**Question 1. Choose the correct statement.**

- The object will move at constant speed when the net force is zero.
- Law of inertia is Newton’s second law of motion.
- All objects do not resist a change in their state of motion.
- All object maintains its state of motion under the continuous application of an unbalanced force.

**Answer.** 1. The object will move at constant speed when the net force is zero.

**Question 2. Newton’s laws of motion laid the foundation for ___________.**

**Answer.** classical mechanics

**Question 3. Newton gave five laws of motion. (True/False)**

**Answer.** False

**Question 4. Seatbelts are required in the cars because of law of inertia. (True/False)**

**Answer.** True

## Force And Laws Of Motion Inertia and Mass

Inertia is derived from the Latin word inert which means unchangeable. Inertia is defined as the inability to an object to change its current state. The object with heavy weight has more inertia than the lighter one. Therefore it can be said that ‘The larger the mass, larger is the inertia, and vice versa’. In other words if the mass of the body is more, it is difficult to move the body from rest or if it is moving then it is difficult to stop it.

Therefore, mass is the measure of inertia. The S.I. unit is Kilogram (kg).

**Example 1:**

Passengers travelling in a bus are running with the same speed as that of the bus and also in the same direction. When driver applies brake, lower part of the body stops but upper part of body doesn’t, hence tends to fall forward, when brakes are applied to a running bus.

**Example 2:** It is easy to hit an empty box than a box filled with stones. The force applied while hitting both boxes is same. Empty box will move from its original place while box filled with stone doesn’t move from its place, in fact can cause injury to foot because inertia of box filled with stone is greater than inertia of empty box.

**Types of Inertia**

**Inertia of Rest**

A body being at rest will remain at rest until and unless an external force is applied to change its state of rest. This property of body is called inertia of rest.

**Example:** Passengers sitting in a bus fall backward as soon as the driver starts the bus. This is because the lower part of the passenger is in close contact with the bus. The lower part moves as the bus starts but the upper part of the body doesn’t move immediately, therefore it experiences jerk. This is due to the inertia of rest.

**Inertia of Motion**

An object which is in a state of motion and continues to be in a state of motion with the same speed in the same direction in a straight line unless an external force is applied to it to change its state. This property is known as inertia of motion.

When a boy jumps from the moving train, he falls down. This is because when the boy was inside the train, his whole body was in a state of motion with the running train. When he jumps from the train, on to a platform, lower part comes to rest while the upper part is still in the state of motion.

This results to the boy falling in the direction of motion of the train. To avoid falling down, the boy should continue to run on the platform in the same direction of motion of the train for some distance.

**Example:** An athlete runs for some distance before taking a long jump. The reason behind doing this is that running changes the state of body from rest to motion which makes it easier for him to do long jump.

**Inertia of Direction**

An object moving in a straight line will continue to move in the same direction until and unless some external force compels it to change the direction of motion.

Momentum: The momentum of a body is defined as the product of its mass and velocity.

Thus, momentum = mass × velocity

Or, p = m × v

Where, p = momentum

m = mass of the body

v = velocity of the body

The SI unit of momentum is kilograms meter per second (kg.m/s)

Note: The force required to stop a moving body is directly proportional to its ass and velocity.

**Change in momentum:** It is defined as the difference between final momentum and initial momentum. Suppose initial momentum is mu, and final momentum is mv, then

Change in momentum = mv – mu

**Rate of change of momentum:** The rate at which momentum is changing is known as rate of change of momentum.

Rate of change of momentum = \(\frac{m v-m u}{t}\)

Or, = \(\frac{m(v-u)}{t}\)

## Force And Laws Of Motion Conservation of Momentum

Conservation of momentum states that the momentum of a system is constant if there are no external forces acting on the system (Fig. 2.11). It is embodied in Newton’s first law.

Suppose we have two interacting objects 1 and 2 of different masses. The forces between them are equal and opposite. According to Newton’s second law, force is the time rate of change of the momentum, therefore the rate of change of momentum P1 of object 1 is equal to minus the rate of change of momentum P2 of an object 2,

\(\frac{d P_1}{d t}=-\frac{d P_2}{d t}\) (1)

Now, if the rate of change is always equal and opposite, it follows that the total change in the momentum of an object 1 is equal and opposite of the total change in the momentum of object 2. It means that if we sum up the two momenta, the result is zero,

\(\frac{d\left(P_1+P_2\right)}{d t}=0\) (2)

However, the statement that the rate of change of this sum is zero is equivalent to stating that the quantity P1 + P2 is constant. This sum is called the total momentum of a system, and in general it is the sum of individual momenta of each particle in the system.

Example: As shown in the above figure, consider two balls of different masses m_{1 }and m_{2} that are moving towards each other. Velocity of both balls are v_{1} and v_{2}. After collision both balls exert some force. Let t be the time taken for collision to last. Ball with mass m_{1} exerts force F_{12} on second ball. Ball with mass m_{2} will exert a force F_{21} on first ball.

Velocity of both balls after collision will be va1 and vb1, Momentum before collision = m_{1} v_{1}

Rate of change of Momentum during collision for ball A F vab = m_{1} (v_{a1} – v_{1})/t.

Rate of change of momentum during collision for Ball B F vba = m_{2} (v_{b1} – v_{2})/t.

According to Newton’s third law, Fab = −Fba

m1(v_{a1} – v_{1})/t = –m_{2} (v_{b1} – v_{2})/t

m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{a1} + m_{2} v_{b1}

Total momentum before collision = m_{1} v_{1} + m_{2} v_{2}

Total momentum after collision = m_{1} v_{a1} + m_{2 }v_{b1}

## Force And Laws Of Motion Track Your Learning Question And Answers

**Question 1. For every action there is an equal and opposite ______.**

**Answer.** Reaction

**Question 2. The product of mass and velocity of a moving body is known as ______.**

**Answer.** Momentum

**Question 3. Conservation of momentum states that the momentum of a system is constant if there are no ______ acting on the system.**

**Answer.** external forces

**Question 4. Rate of change of momentum is equal to**

- ma
- mv
- pv
- ut

**Answer.** 1. ma

## Force And Laws Of Motion Fill in the Blanks

**Question 1. For a body of 2 kg moving under gravity, force is ______.**

**Answer.** Zero

**Question 2. When a stationary car starts suddenly, the passengers fall ______.**

**Answer.** Backwards

**Question 3. A water tanker filled up to half of its tank capacity is running with uniform speed when the brakes are applied suddenly. The water of its tank will move ______.**

**Answer.** Forward

**Question 4. Aforce of ______ is needed to stop a car of mass 1200 kg moving with an acceleration of 2 ms–2 .**

**Answer.** 2400N

**Question 5. Momentum of a system of particles does not change until ______ is applied.**

**Answer.** Force

**Question 6. When bomb explodes into fragments, these fragments must move in a ______ direction.**

**Answer.** Opposite

**Question 7. For the measurement of small forces, we can use a ______.**

**Answer.** Force gauge

**Question 8. For a body undergoing uniform motion, force is ______.**

**Answer.** Zero

**Question 9. A jet plane works on the principle of ______.**

**Answer.** Third law of motion

**Question 10. ______ law of motion is called universal law of motion.**

**Answer.** First

## Force And Laws Of Motion Match the Columns

**Question 1. Choose the correct unit.**

- A-1, B-2, C-3, D-4
- A-4, B-3, C-2, D-1
- A-2, B-1, C-3, D-4
- A-2, B-3, C-1, D-4

**Answer.** 3. A-2, B-1, C-3, D-4

**Question 2. Choose the correct equation.**

- A-1, B-2, C-3, D-4
- A-4, B-3, C-2, D-1
- A-2, B-1, C-3, D-4
- A-2, B-3, C-1, D-4

**Answer.** 1. A-1, B-2, C-3, D-4

**Question 3. Choose the correct code related to Newton’s law of motion.**

- A-1, B-2, C-3, D-4
- A-4, B-3, C-2, D-1
- A-2, B-1, C-3, D-4
- A-3, B-2, C-1, D-4

**Answer.** 4. A-3, B-2, C-1, D-4

**Question 4. Choose the correct code.**

- A-1, B-2, C-3, D-4
- A-4, B-3, C-2, D-1
- A-2, B-1, C-3, D-4
- A-2, B-4, C-3, D-1

**Answer.** 4. A-2, B-4, C-3, D-1

## Force And Laws Of Motion Assertion Reasoning

Direction: For the following questions the options will remain the following:

- Both A and R are correct and R is the correct explanation of A.
- Both A and R are correct but R is not a logical explanation of A.
- A is correct but R is incorrect.
- R is correct but A is incorrect.

**Assertion:**Force and acceleration graph is a straight line when force is needed to produce a given acceleration in an object is directly proportional to the mass of the object.

**Reason:**As force increases, acceleration also increases.**Assertion:**On shaking the branch of a tree, fruits fall down.

**Reason:**Branch comes in motion while fruits remain in the state of rest due to inertia.**Assertion:**When a passenger jumps from the running train, he falls down.

**Reason:**Upper part of body comes to rest while lower part is still in motion.

## Force And Laws Of Motion Comprehension Passage

Galileo Galilei was born on 15 February, 1564 in Italy. He had interest in mathematics and natural philosophy. In the year 1586, he wrote his first scientific book named as ‘The little Balance’. This book has the description about Archimedes method of finding the relative densities of substances using a balance.

In 1589, in his series of essays ‘De Motu’ he wrote about falling objects using an inclined plane to slow down the rate of descent.

In 1592, he got appointed as a professor of mathematics at the university of Padua in the Republic of venice. Here, he did research on motion. With the study of inclined planes and pendulum, he derived the law for uniformly accelerated objects which states that distance travelled by the object is directly proportional to the square of its time taken.

**Question 1. Galileo was born in the year ______.**

- 1560
- 1562
- 1564
- 1566

**Answer.** 3. 1564

**Question 2. What was the name of his first scientific book?**

- The secret
- The little Balance
- The magic
- De Motu

**Answer.** 2. The little Balance

**Question 3. In which year Galileo became a professor in University of Padua?**

- 1562
- 1592
- 1597
- 1599

**Answer.** 2. 1592

**Question 4. What research he did in the university of Padua?**

- Motion
- Speed
- Velocity
- Acceleration

**Answer.** 1. Motion

**Question 5. Where was Galileo born?**

- India
- America
- Europe
- Italy

**Answer.** 4. Italy

## Force And Laws Of Motion Integer Type Questions

**Question 1. A boy pushes a wall in the north direction with a force of 15 N. What force is exerted by the wall on the boy?**

**Answer.** 15 N

**Question 2. How much force is required to produce an acceleration of 2 m/s in an object of mass 0.8 kg?**

**Answer.** 1.6 N

**Question 3. A cricket ball of mass 100 g moving with a speed of 30 m/s is brought to rest by a player in 0.03 s. Find the average force.**

**Answer.** 1500 N

**Question 4. An object of mass 20 kg moves with an acceleration of 2 m/s ^{2}. Find the change in momentum.**

**Answer.**40 N

**Question 5. Which object will require more force? One object of 2 kg mass is moving with acceleration of 5 m/s ^{2}. Another object has acceleration of 2 m/s^{2} and the weight is 4 kg.**

**Answer.**The object of 2 kg mass moving with acceleration 5 m/s

^{2}will require more force.