What is second law of of motion ? - Future Study Point

# What is second law of of motion ?

Newton’s second law of motion is originated from the lap of Newton’s first law of motion, law of inertia. The law of inertia is the resistivity of a thing to change in itself. Inertia is proportional to the mass of a thing. If we apply a force on an object, the object will resist the change in itself. If the change is supposed as a change in the velocity of the object since the object has mass also, therefore, the change will be in its momentum. According to the second law of motion, the force is directly proportional to the rate of change in momentum and concluded to the fact that the acceleration produced on the object is inversely proportional to the mass.

The second law of motion is one of the law among Newton’s three laws of motion, the second law of motion is the relationship between mass and acceleration. The second law states that the force is proportional to the rate of change of momentum, mass is always constant, so we can also say the force is proportional to the acceleration so ultimately we get the relation F = ma where F is force, m is mass and a is the acceleration.

If mass changes with the change in velocity then how will you explain the second law of motion? Do you know why does the moon revolves around the earth and not the earth does the same around the moon? Where does your energy go out when you push a truck and truck doesn’t move. How does the earth spin around its own axis? All your answers are hidden in Newton’s second law of motion.

## What is second law of of motion ?

Observe two stones one is heavier than the other one, throw them one by one, of course, you can through the lighter object up to more distance as compared to a heavier object. To understand this we have to go through the Newton’s second law of motion.

Suppose an object with mass m moves with velocity u and due to an external force applied on it its velocity changes to v in time t.

∵The momentum (p) = mass × velocity

Initial momentum = mu and final momentum = mv

Change in momentum = mv – mu

The time is taken t to achieve the momentum mv from mu

The rate of change in momentum =(mv -mu)/t

According to Newton’s second law of motion, the force(F) is directly proportional to the rate of change of momentum.

F∝ (mv -mu)/t

F∝ m(v -u)/t

Since (v -u)/t = a

F ∝ ma

F = kma

k is the constant of proportionality.

Evaluation of k- As we know 1N force is defined as the force which accelerates an object of mass 1kg by 1 m/s². So,if F = 1N, m =1kg and a = 1m/s²

from the above equation f = kma, 1N = kg.m/s²

k = F/ma = 1N/(1kg× 1m/s²) = 1NKg-1m-1

Therefore substituting the value of k =1, the equation become

F = ma

This is the equation of the second law of motion, which tells us answers of all the above questions mentioned in the first paragraph of this post.

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The second law of motion states about an external force applied on an object of mass which results to accelerate the object from u to v, here mass is constant, then what do you think in the case where mass is not constant, as an example a vehicle moves from the position(u) to position (v), at the expense of fuel inside it, definitely its mass also changes. Actually Newton’s second law tells about change in momentum means the change in the product of mass and velocity (mv ) and not about the individual changes in velocity or mass. Therefore with the loss of fuel how much velocity of vehicle increases, we should have to consider that.

If we push a truck by applying a muscular force but the truck doesn’t move as it is requiring significant changes in the momentum of the truck (mv–mu) , the force applied by us generates energy which is absorbed by truck in the form of potential energy and rest of energy transferred to the environment as an example heat and sweats generated by our body.

Newton’s second law of motion F = ma tells us if we apply the same force on two objects one is lighter and another one heavier then the lighter object will be accelerated more as compared with the heavier object, as an example stones of 4 kg and 2 kg are thrown by a force of 5 N.Let the accelerations produced by the force 5N on them are a1 and  a2 .

a1  = F/m = 5/2 =2.5 m/s²,a2  = 5/4 =1.25 m/s²

Thus the lighter object i.e of 2 kg will be accelerated more and hence transported to more distance.

The fact explained above is also applicable in the case of moon revolves around the earth and not the earth around the moon.

The moon and the earth attract each other by the same gravitational force, moon revolves around the earth but the earth does not revolve around the moon because the mass of the moon is lesser than the earth, the moon is accelerated relative to the earth, it is that’s why moon revolves around the earth.

The cause of the earth spin around its own axis is, newton’s rotational version of the second law of motion τ = I. α where I is inertia= mr²( r radius of the earth) and α is angular momentum, τ is torque. The torque τ is responsible for the spinning of the earth around its own axis.

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