Important topics covered:

• What is force?
• Balanced and Unbalanced Forces
• First law of motion
• Second law of Motion
• Third law of motion
• Inertia and Mass
• Mathematical Formulation of second law of motion
• Conservation of Momentum

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What is 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. We can’t see the force but can feel it.
• Force is vector quantity as it has both magnitude as well as direction.
• The SI unit of force is Newton.
• Opening and closing the door by push or pull is the example of force.

Effect of force:

• Force can make a stationary body to move.
• It can stop a moving body.
• By applying force we can change the direction of moving body.
• Speed of a body can be changed by action of force.
• The shape, size of a body can be changed by action of force.
• Examples: A ball at rest when kicked acquires motion, brake applied in moving vehicle stops it.

What are balanced and unbalanced forces?

Balanced force:

• When all the applied forces in different directions, nullify each other then it is said to be balanced forces.
• Body at rest remains at rest and moving object keeps moving.
• Shape or size may change.
• As in a rope game, the rope remains at rest as the magnitude of force applied on each ends are equal.

Unbalanced force:

• If the resultant of all the applied force becomes greater than zero then it is said to be unbalanced forces.
• Stationary object can be brought into motion.
• A moving object can acquire more speed on applying unbalanced force.
• It can decrease the speed of moving speed.
• It can stop a moving object.
• Unbalanced forces change the shape and size of an object.

Are there any other type of forces?

There are many forces which exist in nature:

• Gravitational forces
• Muscular force
• Frictional force
• Air resistance

What is motion?

• The change in position of an object with respect to time is said to be motion.
• Flying of bird, movement of train, running of child etc. are some examples of motion.
• Distance, displacement, speed, velocity etc. are the terms related to motion which we studied earlier in Motion class 9 notes.

Laws of motion:

Galileo’s observation on motion:

• Galileo mainly observed motion in inclined plane.
• The velocity of an object when rolled in an inclined plane its velocity increases.
• He first said that if an object is moving on a frictionless surface then it will continue to move forever at the same speed.
• There is no unbalanced force acting on any object.
• Practically, to attain the condition of zero unbalanced force acting on any object is impossible.
• There are many force (air resistance, Atmospheric pressure and many other small forces) that exist in nature and acts upon object.

Newton’s law of motion:

Newton after observing Galelio’s studies and the research and expanding it, he proposed three laws of motion. These laws of motion resulted in the foundation of classical mechanics. These laws explains the relationship between body and the force acting upon it.

What are the three laws of motion?

Newton gave us three laws of motion. They are as follows:

Newton’s first law of motion (law of inertia):

• According to Newton’s first law of motion, an object will either remain at rest or move in uniform motion on a straight line unless acted upon by an external force which can change its state of rest or motion.
• Every object in this universe resists the change in its state.

Inertia and Mass:

• Inertia: The tendency of an object to oppose the induced change in state of rest or motion is said to be
• We measure inertia of any object by its mass. Inertia is directly proportional to its mass.
• The inertia of heavy object is always more than the lighter one.
• Heavier objects show more resistance to the applied force.

Application of Newton’s First law of motion in everyday life:

• When a bus starts moving the person in the bus falls backward.
  This condition arises because when bus starts moving the legs also move with it but the rest part of the body has tendency to remain at rest.
• When driver of a bus applies brake suddenly then person standing in it falls in forward direction.
  This condition arises because the person standing in the moving bus is also in motion along the bus, but when brake is applied suddenly the legs in contact with the bus stops with the bus but rest part of the body has the tendency to be in motion.
• On a carom board if we hit the pile of coin, then only the pile present at bottom moves leaving rest of the coin of pile at its place.
  This happens because when striker hits the bottom coin, induce motion in it but rest of the coin of pile has tendency to remain at rest.
• Wet clothes when jerked before putting in sunlight makes it easy to dry.
  This happens because the droplets present in the cloth pores has tendency to remain at rest but when jerked the cloth acquires motion. This makes water droplets to move out of it so clothes easily dry out.

Newton’s Second law of motion:

• According to Newton’s second law of motion, the rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.
• Momentum: The product of mass and velocity is called momentum.
• It is a vector quantity and has direction same as the velocity of the object.
• Momentum is denoted by ‘p’.
• It’s SI unit is Kg metre/second.
• Thus equation of Momentum is “p = mv”, where m is mass of the object and v is associated velocity.
• Stationary body has zero momentum.
• 1 N force: When acceleration of 1m/s² is produced on 1kg object then it is said that 1 N force is applied.

Application of Newton’s  second law of motion:

• A cricketer when catches a ball moves his hand backwards in the direction of ball to decrease the velocity of the ball. If he would catch the ball without moving his hand it will require a greater force, This leads to drop of catches.

Mathematical formulation of Second law of motion:

Let the mass of any object be m and its initial velocity is u in a straight line. After time t with a constant acceleration a the object reaches to final velocity v.

• Initial momentum of the body: P₁ = m x u
• Final momentum of the body: P₂ = m x v
• Change in momentum; P₂ – P₁ = m(v-u)
• As per the second law of motion the rate of change of momentum is directly proportional to the applied force.
  F ∝ m(v – u)/t
  F ∝ ma since acceleration is rate of change of velocity (i.e (v – u)/t)
  F = K ma where K is the proportionality constant.
  1 unit force = K × (1 kg) × (1 m/s²), the value of K becomes 1.
  Thus, F = ma
• The SI unit of force is N (i.e. Kg m/s²).
• By the use of Newton’s Second law of motion we can find the force acting on any object.

Newton’s third law of Motion:

• To every action, there is an equal and opposite reaction.
• In other words, when a body exerts a force on another body, the second body instantly exerts a force of equal magnitude to the applied force back onto the first body. These forces are always opposite in direction and act on two different objects always.
• Force has same magnitude acting on each other but may or may not have equal acceleration.
• As, when a bullet is fired from a gun, Bullet moves with high speed but the gun moves a little back. This occurs due to a large difference in mass of the bullet as well as the gun.

Applications of Newton’s Third law:

• Helps in walking.
• It also helps in hitting a goli ball.
• Helps skydivers
• Newton’s third law has a great application in aerodynamics.

What is the law of conservation of momentum?

• According to the law of conservation of momentum, the sum of momenta of two objects before and after collision remains same given that no external unbalanced force acts upon them.
• Simply we can say that collision conserves the overall momentum of the objects.
• The momentum lost by one object is gained by the other.

Conservation of momentum formula:

• Initial momentum = Final momentum
• If m₁ & m₂ are the mass of any two object moving with initial velocity u₁ & u₂ and after collision the velocity became v₁ & v₂ respectively then conservation of momentum formula is given by:
  m₁ u₁ + m₂u₂ = m₁v₁ + m₂v₂

Conservation of momentum Example (class 9):

Q. How to find the Rate of Change of Momentum?

We can find the rate of change of momentum by simply applying Newton’s second law of motion. According to Newton’s second law of motion the rate of change of momentum is directly proportional to the applied force. 

Force and laws of motion examples:

Q. A Truck of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is reduced to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum.

Solution: Mass of the truck, m = 1200 kg 
Initial velocity (u) = 90 km/h = 25 m/s 
Final velocity (v) = 18 km/h = 5 m/s 
Time taken, t = 4 s 
According to the first equation of motion:
v = u + at
5 = 25 + a (4) 
a = – 5 m/s² 
Negative sign indicates that its a retarding motion i.e. velocity is decreasing. 
Change in momentum = mv – mu = m (v – u)
= 1200 (5 – 25) = – 24000 kg m s ^-1 
Force = Mass × Acceleration = 1200 × – 5 = – 6000 N 
Acceleration of the truck = – 5 m/s² 
Change in momentum of the truck = – 24000 kg m s ^-2

Q. why some of the leaves may get detached from a tree if we vigorously shake its branch?

Solution: When we shake its branches vigorously some leaves get detached because when the branches of a tree are shaken, it moves to and fro, but leaves have tendency to remain at rest. This is because the inertia of the leaves tend to resist the to and fro motion.

Q. How much momentum will a rod of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s^-2?

Solution:
Mass of the rod, m = 10 kg
Distance covered by the rod = 80 cm = 0.8 m
Acceleration (a) = 10 m/s2
Initial velocity of the rod, u = 0
Final velocity of the rod = v
According to the third equation of motion:
v² = u² + 2as
v²= 0 + 2 (10) 0.8
v= 4 m/s
Hence, the momentum with which the rod hits the floor is  = mv
= 40 kg m s-1

Q. A bike of mass 50 kg has a momentum of 1000 kg.m/s. Calculate the velocity of the bike.

Solution: Mass of the body, m = 50 kg
 Momentum p = 1000 kg.m/s
p = m x v
v= \(\frac{p}{m}\) = \(\frac{1000}{50}\) = 20 m/s
Hence, the velocity of bike = 20 m/s

Q. Why does a gunman get a jerk on firing a bullet?

Solution: When a bullet is fired from a gun, the force pushing the bullet forward is equal to the force sending the gun back but due to high mass of the gun, it moves only a little distance backwards giving a jerk to the gunman.