Newton’s Second Law of Motion, Applications, Formula, Example

Newton’s Second Law: Newton’s Second Law of Motion, formulated by Sir Isaac Newton, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation F = ma represents this law in math. In this equation, F stands for the force acting on the object, m is the object’s mass, and a is the object’s acceleration. This fundamental principle underpins our understanding of how objects respond to external forces, guiding everything from everyday motion to space exploration, and offering universal insights into the behavior of matter in the universe.

What is Newton’s Second Law of Motion?

Newton’s second law of motion states that the acceleration of the body depends upon two variables, that is, the net force applied and the mass of the object.  The acceleration of the object is directly proportional to the net force acting on the body and inversely proportional to the mass of the object. So it can be written as-

a = F/ m (This equation shows that acceleration is inversely proportional to the mass of the body)

F = ma( This equation shows that acceleration is directly proportional to the net force acting on the body)

Newton’s Second Law Formula

Newton’s Second Law of Motion, expressed as the mathematical formula F = ma, is a fundamental principle in classical mechanics. This formula establishes a direct relationship between force (F), mass (m), and acceleration (a) for an object subjected to a net force. As a cornerstone of physics, Newton’s Second Law formula plays a pivotal role in explaining object motion under external forces, enabling applications in diverse scientific and engineering fields, from comprehending planetary motion to designing vehicles and structures.

Mathematical Formula of Second Law of Motion

Suppose a body of mass(m) is moving in a straight line with its initial velocity(u). It is uniformly accelerated to velocity(v) in time(t) by the application of a constant force(F) throughout the time(t).

The initial and final momentum of the body becomes,

p1 = mu

p2 = mv

Therefore, Change in Momentum ∝ p2 – p1

∝ mv – mu

∝ m × (v – u)

Velocity is equal to displacement upon the time taken

Then, the rate of change of momentum ∝ m×( v − u )/t

The applied force will be, F ∝ m×(v- u)/t

F = k m(v-u)/t

F = k ma 

Here, a = (v-u)/t is the acceleration.

F = Net force applied

m = mass of the body

k = proportionality constant

SI Unit of Force

The SI units of mass and acceleration are kg and m/s² respectively.

1 unit of force = k × (1 kg) × (1 m/s²).

F = ma

The SI unit of force is kg m/s² or newton, which has the symbol N.

Application of Second Law of Motion

Some of the applications of the Second law of motion are-

• Pushing of Car and Truck.
• Pushing of Shopping cart.
• Kicking a ball.
• Two people walking.
• Rocket Launch.
• Car Crash.

Exercise based on Newton’s Second Law

Q1. A truck is moving with a velocity of 30m/s and it takes 5s to stop after the brakes are applied. Calculate the force exerted by the brakes on the truck if its mass along with the passengers is 1500 kg.

Solution: According to the question,

The initial velocity of the motorcar, u = 30m/s

The final velocity of the motorcar, v = 0 m s-1
On substituting the values, we get F = 1500 kg × (0 – 30) m s-1/5 s

= – 9000 kg m/s² or – 9000 N.

The negative sign tells us that the force exerted by the brakes is opposite to the direction of motion of the motorcar.

Q2.If there is a block of mass 4kg, and a force of 30 N is acting on it in the positive x-direction, and a force of 50 N in the negative x-direction, then what would be its acceleration?

Solution: Net Force = 30N – 50N

Net Force = -20N

Acceleration = -20/4 = -5m/s²

The negative acceleration indicates that the block is slowing and its acceleration vector is moving in an opposite direction directed opposite to the direction of motion.

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