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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