4.3newtons 1st Law and 2nd Law

4.
3 Newton’s Laws Of Motion

Newton’s Laws of motion were first proposed by Sir Isaac Newton in the late 17th century.
Newton’s laws of motion are three laws that describe the relationship between the motion of an
object and the forces acting on it. These laws are:
1. Newton’s first law of motion
2. Newton’s second law of motion
3. Newton’s third law of motion .
4.3.1 Newton’s First Law Of Motion

According to Newton’s first law of motion,
“A body in the state of rest stays at rest and a body in the state of uniform motion stays at
uniform motion until and unless a net external force is applied.”
Simply, we can say that an object which is at rest will continue to stay at rest and an object which
is in uniform motion continues to stay in uniform motion until an external force is applied. The
first law of motion is also called as Law of Inertia.
There are two conditions on which Newton’s first law of motion depends on. These conditions
are:
 For Objects at Rest: If an object is at rest, i.e. there, velocity and acceleration are zero.
The object will remain at rest until an external force is applied.
 For Objects in Motion: If an object is in a state of uniform motion, i.e. it has an initial
velocity. The object will remain in a state of uniform motion until an external force is
applied.
The net force on an object is defined as the vector sum of all external forces exerted on the
object.
External forces come from the object’s environment.
Internal forces, which are forces that occur between objects within a system, cancel each other
out in terms of the motion of the system as a whole. Therefore, internal forces do not contribute
to changes in the object’s state of motion, and Newton’s first law focuses on the effects of
external forces that can cause changes in motion.
Inertia and mass

Inertia is the natural tendency of an object to resist a change in its state of rest or in its state of
uniform motion. It is the fundamental property of any object. We can observe inertia in our daily
life as, when a bus starts from rest we tend to lean backward, this is because of the Inertia of rest.
Although inertia is the tendency of an object to continue its motion in the absence of a force,
mass is a measure of the object’s resistance to changes in its motion due to a force. This kind of
mass is often called inertial mass because it’s associated with inertia. The greater the mass, the
greater the inertia. They are related concepts, with mass influencing the amount of inertia an
object possesses. Mass is a scalar quantity and its SI unit is kilogram(Kg).
Newton’s First Law of Motion Example in Daily Life

In our daily life, we came across various examples which support Newton’s First Law of Motion.
Some of the examples which support this law are,
 Brakes applied by a vehicle abruptly. When the brakes of a vehicle are applied quickly,
the passenger will be thrown forward due to the presence of inertia. Inertia tries to keep
the passenger moving.
 A book lying on the table remains at rest as long as no net force acts on it.
 A ball rolling on the ground.
 Athlete taking a short run before long/high jump.
 A marathon runner continues to run several meters beyond the finish line due to inertia.
Applications of Newton’s First Law of Motion

1. Seatbelts: Designed to restrain passengers during sudden stops, preventing them from
moving forward due to their inertia.
2. Airbags: Deploy to provide a cushioning effect during sudden deceleration, reducing the
impact force on occupants.
3. Sports: Understanding inertia helps athletes optimize movements, like a pitcher using
their body’s inertia to throw a baseball.
4. Machinery Design: Engineers use the principles of inertia to design efficient and safe
machinery, ensuring parts move smoothly or stop when intended.
5. Earth’s Rotation: The rotation of the Earth exemplifies Newton’s first law, as objects on
its surface are moving with the Earth’s rotational velocity unless acted upon by external
forces.
6. Astronomy: Celestial bodies in the universe follow Newton’s first law, moving unless
influenced by gravitational or other forces.
4.3.2 Newton’s second law of motion

Newton’s first law explains what happens to an object that has no net force acting on it: The
object either remains at rest or continues moving in a straight line with constant speed. Newton’s
second law answers the question of what happens to an object that does have a net force acting
on it.
According to Newton’s second law of motion,
“The acceleration of an object is directly proportional to the net force applied to it and inversely
proportional to its mass.”
Newton’s second law of motion can also be stated as ”For a constant mass, the rate of change of
momentum is directly proportional to the force applied.”
Newton’s second law of motion is mathematically expressed as;
F = ma,
Where’s ( F ) is the force applied to an object, ( m ) is its mass, and ( a ) is the resulting
acceleration.
The SI unit of force is the newton, symbolized by the letter “N.”
1N=1kg.m/s²
Examples:
1. A body of weight 100 N is suspended with the help of strings as shown in figure. The
tensions T1 and T2 will be
Solution:
Resolution of forces along horizontal direction gives;

T₁ cos 30° T₂ cos 45°
T₁
√3 =T₂ √2
2 2
T₂=
√3 T ₁
2
Resolution of forces along vertical direction gives;
T₁ sin 30⁰ + T₂ sin 45⁰= 100N
1 3
√
√2
T 1 × + T 1 × =100 N
2 2 2
T1(1+√3)=200N
T1=73.2N
T2=89.65N
2. Two forces of 15 N and 25 N are applied to an object in the same direction. What is the
net force acting on the object?
Solution:
When forces are applied in the same direction, you can find the net force by simply adding
them.
F net= 15N+25N=40N
3. Two masses of 𝑚1 = 2𝑘𝑔 and 𝑚2 = 8𝑘𝑔 are connected by a mass less string. They are
Supported on a frictionless horizontal surface. A horizontal force of 𝐹 = 40𝑁 is applied to
the mass, 𝑚2, as shown. Calculate the tension in the string between the two masse.
Solution:
In the y-direction, the net force in each mass is zero, i.e., the weights and the normal forces are
equal but opposite, and hence. ∑ 𝐹𝑦 = 0
On the other hand, the horizontal forces acting on the masses are:
Mass, m1: ∑ 𝐹𝑥 = 𝑇 = 𝑚1𝑎𝑥….. (a)
Mass, m2: ∑ 𝐹𝑥 = 𝐹 – 𝑇 = 𝑚2𝑎𝑥…… (b)
Substituting Eq. (a) into (b), we get ∑ 𝐹𝑥 = 𝐹 – 𝑚1𝑎𝑥 = 𝑚2𝑎𝑥,
So that the acceleration of the masses is
Fx 40 N
ax= = =4 m/ s ²
m 1+ m2 10 Kg
Then, substituting the value of the calculated acceleration into Eq. (a), we find the tension, T, in
the string to be:
𝑇 = 𝑚1𝑎𝑥 = (2𝑘𝑔)(4𝑚/s²)=8N
Gravitational force and weight

All objects are attracted to the Earth. The attractive force exerted by the Earth on an object is
called the gravitational force, F𝑔. This force is directed toward the center of the Earth, and its
magnitude is called the weight of the object. We know that a freely falling object experiences an
acceleration 𝑔⃗ acting toward the center of the Earth. Applying Newton’s second law ∑ 𝐹⃗ = 𝑚𝑎⃗
to a freely falling object of mass 𝑚, with 𝑎⃗ = 𝑔⃗ and ∑ 𝐹⃗ = 𝐹⃗g, gives
Fg= mg
 The weight of an object can vary depending on its geographical location. Weight is the
force exerted on an object due to gravity, and gravity varies with location. The
acceleration due to gravity ((g)) is not constant everywhere on Earth.
 At different geographical locations, the value of (g) can be affected by factors such as
altitude, latitude, and local geological features. Generally, (g) is slightly greater at the
poles than at the equator due to the Earth’s rotation. Altitude also plays a role; at higher
altitudes, gravity is slightly weaker than at sea level.
 However, it’s important to note that the mass of an object remains constant regardless of
its location. Weight depends on both mass and the local gravitational acceleration and is
given by the equation (W = mg), where (W) is weight, (m) is mass, and (g) is the
acceleration due to gravity.

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4.

3 Newton’s Laws Of Motion

4.3.1 Newton’s First Law Of Motion

Inertia and mass

Newton’s First Law of Motion Example in Daily Life

Applications of Newton’s First Law of Motion

4.3.2 Newton’s second law of motion

Resolution of forces along horizontal direction gives;

Gravitational force and weight

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