CHAPTER 9: FORCE AND LAWS OF MOTION

Force:-
• Force is the physical cause which changes or try to change the position of an object.
• In other words, we can say that push or pull acting on the body to accelerate it is called force.
• Force is vector quantity as it has both magnitude as well as direction.

Example :- to open a door, either we push or pull it. A drawer is pulled to open and pushed to close.
Units of force: -
In S.I system, force is measured in newton represented by letter “N”
In C.G.S [ Centimetre Gram Second] system its values are represented in dynes.
Newton: -
The force applied is said to be one newton [1N] if it produces acceleration of 1m/sec² and in a body of mass
1kg.
Dyne: -
The force applied is said to be one dyne if it produces acceleration of 1cm/sec²⁻ in a body of mass 1 gram.
1N =105 Dyne
Effect of Force :-
• Force can move a stationary body or object.
• Force can stop a moving body.
• Force can change the direction of a moving object.
• Force can change the speed of a moving body.
• Force can change the shape and size of an object.
Net force: The resultant of all the forces acting on a body is known as net force.

Types of forces:-
Forces are mainly of two types based on the net force/ resultant force acting on an object: -
• Balanced forces
• Unbalanced forces
Balanced Forces :-
If the resultant of applied forces is equal to zero, it is called balanced forces.
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Balanced forces do not cause any change of state of an object.
Balanced forces are equal in magnitude and opposite in direction.

Unbalanced Forces :-
If the resultant of applied forces is greater than zero, the forces are called unbalanced forces.
Unbalanced forces can do the following :-
• Move a stationary object
• Increase the speed of a moving object
• Decrease the speed of a moving object
• Stop a moving object
• Change the shape and size of an object

Laws of Motion :-
Galileo Galilei:- Galileo first of all said that object move with a constant speed when no forces act on them.
This means if an object is moving on a frictionless path and no other force is acting upon it, the object would
be moving forever. That is, there is no unbalanced force working on the object.
Galileo’s Observation
• He observed the motion of objects on an inclined plane.
• When marble is rolled down an inclined plane its velocity increases.
Galileo’s Arguments
• When marble is rolled down from the left – It will go up on the opposite side up to the same
height at which it is dropped down.

• If the inclination of planes is equal – The marble would travel equal distances while
climbing up as travelled while rolling down.
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 • If we decrease the angle of inclination of the right plane – The marble would travel further
until it reaches its original height.

If the right-side plane is made flat – Marble would travel forever to achieve the same height.

Galileo's Inference
• We need an unbalanced force to change the motion of the marble but no force is required
when the marble is moving uniformly.
• In other words, objects move at a constant speed if no force acts upon them.
Newton’s Laws of Motion :-
Newton studied the ideas of Galileo and gave the three laws of motion. These laws are known as Newton’s
laws of motion.
The tendency of objects to remain in the state of rest or to keep moving uniformly or to keep moving in
one direction is called Inertia.
Mass and Inertia :-
Inertia of an object is measured by its mass [how much matter is present in that object].
Inertia is directly proportional to the mass. This means inertia increases with increase in and decreases with
decrease in mass. A heavy object will have more inertia than the lighter one, thus it is difficult to push or pull
a heavy box over the ground than the lighter one.
There are three types of inertia:
Inertia of rest: The inability of a body to change by itself its state of rest is called inertia of rest.
Inertia of direction: The inability of a body to change by itself its direction of motion.
Inertia of motion: The inability of the body to change by itself its state of motion is called inertia of motion.
Newton’s First Law of Motion (Law of Inertia):-
An object remains in the state of rest or in uniform motion along a straight line, until it is compelled to change
the state by applying external force.
Explanation: - If any object is in the state of rest, then it will remain in rest until a external force is applied
to change its state. Similarly, an object will remain in motion until any external force is applied over it to
change its state. This means all objects resist to in changing their state. The state of any object can be changed
by applying external forces only.

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Examples of Inertia
• We fall back when a vehicle starts moving in the forward direction because our body is in
the rest state and it opposes the motion of the vehicle.

• We fall forward when brakes are applied in a car because our body is opposite the change
of state of motion to rest.

Momentum :-
Momentum is the power of motion of an object.
The product of velocity and mass is called the momentum. Momentum is denoted by ‘p’.
Therefore,
• Momentum of the object = Mass x Velocity Or, p = m×v
• Where, p= momentum, m = mass of the object and v= velocity of the object.
Momentum and Mass and Velocity :-
Since momentum is the product of mass and velocity (p = m × v) of an object. This means momentum is
directly proportional to mass and velocity. Momentum increases with increase of either mass or velocity of an
object.
This means if a lighter and a heavier object is moving with same velocity, then heavier object will have more
momentum than the lighter one.
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 If a small object is moving with great velocity, it has tremendous momentum. And because of momentum, it
can harm an object more severely.
For example :- a small bullet having a little mass even kills a person when it is fired from a gun.
Usually, road accidents prove more fatal because of high speed than in slower speed. This happens because
vehicles running with high speed have greater momentum compared to a vehicle running with slower speed.
Momentum of an object which is in the state of rest :-
• Let an object with mass ‘m’ is in the rest.
• Since, object is in rest, therefore, its velocity, v= 0
• Now, we know that
• Momentum = mass × velocity Or p = m × 0 = 0
Thus, the momentum of an object in the rest i.e., non – moving, is equal to zero.
Newton’s Second Law of Motion: -
According to Newton’s second law of motion, the rate of change of linear momentum of a body is directly
proportional to the external force applied on the body, and this change takes place always in the direction of
the applied force.
Now, the rate of change of linear momentum of a body can be obtained by dividing “change in linear
momentum’ of the body by the ‘time taken’ for this change. Thus, according to Newton’s second law of
motion,

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Mathematical formulation of Newton’s second law of motion:-
• m = mass of body.
• u = initial velocity of the body along a straight line,
• F = an external force applied on the body, which is constant in magnitude,
• t = time for which the force is applied
• v = Final velocity of the body along the same straight line, after t second.
According to the Newton’s Second Law of motion force is directly proportional to the rate of change of
momentum.

• The rate of change of momentum of an object is proportional to the applied force. So, Newton's second
law of motion can be expressed as

• Suppose an object of mass, mm is moving along a straight line with an initial velocity, uu. It is
uniformly accelerated to velocity, vv in time, tt by the application of a constant force, FF throughout
the time, tt.
• The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively.
• Now change in momentum would be

• Now force applied is proportional to rate of change of momentum. So,

where, a =(v-u)/t is the acceleration which is the rate of change of velocity. The quantity,k is a
constant of proportionality
• The unit of force is chosen in such a way that the value of the constant, k becomes one.
• For this, one unit of force is defined as the amount that produces an acceleration of 1 ms-2 in an
object of 1 kg mass. That is,
1 unit of force = k × (1 kg) × (1 m s-2). Thus, the value of k becomes 1.
• From Eq. 2
F = ma (3)
• The unit of force is kgms-2 or Newton, which has the symbol N.
• The second law of motion gives us a method to measure the force acting on an object as a product of
its mass and acceleration.
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This equation is the form of Newton’s Second Law of Motion. According to this equation, Newton’s Second
Law of Motion can also be stated as follow:

The acceleration produced by a moving body is directly proportional to the force applied over it and inversely
proportional to the mass of the object.

From the above relation it is clear that

Acceleration increases with increase in force and vice versa.

Acceleration decreases with increase in mass and vice versa.

That’s why a small vehicle requires less force to attain more acceleration while a heavy vehicle requires more
force to get the same acceleration.

Newton’s Second Law of Motion in everyday life:

a. A fielder pulls his hand backward; while catching a cricket ball coming with a great speed, to reduce
the momentum of the ball with a little delay. According to Newton’s Second Law of Motion; rate of
change of momentum is directly proportional to the force applied in the direction. While catching a
cricket ball the momentum of ball is reduced to zero when it is stopped after coming in the hands of
fielder. If the ball is stopped suddenly, its momentum will be reduced to zero instantly. The rate of
change in momentum is very quick and as a result, the player’s hand may get injured. Therefore, by
pulling the hand backward a fielder gives more time to the change of momentum to become zero. This
prevents the hands of fielder from getting hurt.
b. For athletes of long and high jump sand bed or cushioned bed is provided to allow a delayed change
of momentum to zero because of jumping of athlete. When an athlete falls on the ground after
performing a high or long jump, the momentum because of the velocity and mass of the athlete is
reduced to zero. If the momentum of an athlete will be reduced to zero instantly, the force because of
momentum may hurt the player. By providing a cushioned bed, the reduction of the momentum of the
athlete to zero is delayed. This prevents the athlete from getting hurt.
c. Seat belts in car - Seat belts in the vehicles prevent the passenger from getting thrown in the direction
of motion. In case of emergency, such as accidents or sudden braking, passengers may be thrown in
the direction of motion of vehicle and may get fatal injuries. The stretchable seat belts increase the
time of the rate of momentum to be reduced to zero. The delayed reduction of momentum to zero
prevents passengers from such fatal injury.

Newton’s third law:

Newton’s Third Law of Motion states that there is always reaction for every action in opposite direction and
of equal magnitude.
Explanation: Whenever a force is applied over a body, that body also applies same force of equal magnitude
and in opposite direction.
Example:
Walking of a person: A person is able to walk because of the Newton’s Third Law of Motion. During
walking, a person pushes the ground in backward direction and in the reaction the ground also pushes the
person with equal magnitude of force but in opposite direction. This enables him to move in forward direction
against the push.
a. Recoil of gun: When bullet is fired from a gun, the bullet also pushes the gun in opposite direction,
with equal magnitude of force. This results in gunman feeling a backward push from the butt of gun.
b. Propulsion of a boat in forward direction: Sailor pushes water with oar in backward direction;
resulting water pushing the oar in forward direction. Consequently, the boat is pushed in forward
direction. Force applied by oar and water are of equal magnitude but in opposite directions.

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Law of Conservation of Momentum: The sum of momenta of two objects remains same even after
collision.
In other words, the sum of momenta of two objects before collision and sum of momenta of two objects after
collision are equal.
Mathematical Formulation of Conservation of Momentum:
Suppose that, two objects A and B are moving along a straight line in same direction and the velocity of A is
greater than the velocity of B.
Let the initial velocity of A=u1
Let the initial velocity of B= u2
Let the mass of A= m1
Let the mass of B=m2
Let both the objects collide after some time and collision lasts for ' t' second.
Let the velocity of A after collision= v1
Let the velocity of B after collision= v2

We know that, Momentum = Mass × Velocity

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Above equation says that total momentum of object A and B before collision is equal to the total momentum
of object A and B after collision. This means there is no loss of momentum, i.e. momentum is conserved.
This situation is considered assuming there is no external force acting upon the object.
This is the Law of Conservation of Momentum, which states that in a closed system the total momentum is
constant.
In the condition of collision, the velocity of the object which is moving faster is decreased and the velocity
of the object which is moving slower is increased after collision. The magnitude of loss of momentum of
faster object is equal to the magnitude of gain of momentum by slower object after collision.
Conservation of Momentum – Practical Application
• Bullet and Gun – When bullet is fired from a gun, gun recoils in the opposite direction of bullet. The
momentum of bullet is equal to momentum of gun. Since, the bullet is has very small mass compared
to the gun, hence velocity of bullet is very high compared to the recoil of gun. In the case of firing of
bullet, law of conservation of momentum is applied as usual.
• In the collision of atoms, the conservation of momentum is applied.
• In the game of snooker, when a ball is hit by stick, the conservation of momentum is applied.
• When the mouth of an inflated balloon is let open, it starts flying, because of conservation of
momentum.
• When a cricket ball is hit by bat, the Law of Conservation of Momentum is applied.
• When the coins of carom board are hit by striker, the Law of Conservation of Momentum is applied.
• Newton’s cradle is one of the best examples of conservation of momentum.

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