Newton’s Second Law of the Motion: Class 11 CBSE Physics

Newton’s Second Law of Motion: Class 11 CBSE Physics is the most important among his three laws of motion, so class 11 students are required to pay more attention to study it because the first law and third law are the application of the second law of motion. The mathematical representation of Newton’s second law of motion is F = ma, where F is an applied force that causes a body in motion,m is the mass and a is the acceleration produced by the force, Newton’s second law of the motion tells us the relationship between acceleration and the mass which are proportional to each other.

Newton’s Second Law of the Motion: Class 11 CBSE Physics

Verification: Before we study the second law of motion, let’s know the momentum, which is the product of mass and velocity,P =mv, where P is the momentum,m is the mass and v is the velocity

According to Newton’s Second law of the motion

Rate of the change in momentum = Force Applied

Let there is a small change in momentum is Δp in small time Δt

Δp/Δt = F

(P_f –P_i)/t =F

Where P_f is the final momentum and P_i is the initial momentum

(mv -mu)/t = F

m(v -u)/t = F

According to first equation of the motion.a =(v-u)/t

F=ma (m is constant)

Note: Although mass is constant but there may be a situation where mass also can vary, like in the case of rocket propulsion,so the point to be noted here that newton’s second law states the rate in change of the momentum is the force in which either mass, velocity or both are responsible for a change in the momentum.

Newton’s second law of motion in the case when mass varies: The mass of an object varies when its velocity is equivalent to the velocity of light. According to Einstein, the mass of an object increases with the speed of light, we shall study it later.

Differential Form of the Newton’s Second Law of Motion:

As we know Δp/Δt = F

If there is infinetesimal change in momentum i.e dp in infinitesimal time dt

Then the Force is

F = dp/dt

If the mass also varies with the speed

F = d/dt(mv)

According to product rule of derivatives

F = m dv/dt +v dm/dt

The above equation is the ultimate equation of Newton’s second law of motion.

If the mass is constant

So, dm/dt =0

F = mdv/dt

F = ma

For evaluating a and F,let’s consider the equation F=ma,when m is constant

F should be replaced by the net force F_net

F_net= ma

Example: An object of the mass m is dragged by a force F which is directed by an angle θ from the horizontal,then find the acceleration produced by the force.

Solution:

The forces acting on the object are

Normal reaction N

Gravitational force mg

Two-component of the force(F) , vertical component Fsinθ and horizontal component Fcosθ

Since body will move along the plane

∴ N +Fsinθ= mg

Vertical component and N both will be canceled by mg

Therefore net force is

F_net= Fcosθ

Fcosθ = ma

a = Fcosθ/m

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Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
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Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
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Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

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Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
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NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equations	Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt	Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals	Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds	Chapter 12- Electricity
Chapter 5-Periodic classification of elements	Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process	Chapter 14-Sources of Energy
Chapter 7-Control and Coordination	Chapter 15-Environment
Chapter 8- How do organisms reproduce?	Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

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Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
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