Effect of Force on Motion: Newton's Second Law- inews71

In the football ground, we always see that a player kicks a stationary football and directs it to distant places creating motion. At the time of the kick, when the player touches the ball, only at that instant, force is applied on the ball. The stationary ball goes into motion due to this force. We can apply force also for a long time instead of just for a moment. By pushing a stationary go-cart for a long time and we can release it after setting it into motion. It can move for a while until it ceases its motion due to friction. The direction of velocity can also be changed by the application of force. When a bowler throws a cricket ball towards the batsman, then the batsman can direct the ball totally in a different direction by hitting the ball with his bat. In the three examples described above, we see that velocity is changed by the application of force on an object for a short or a long time. In the previous chapter, we have seen that the rate of change of velocity is acceleration. Therefore we can say when force is applied on an object, acceleration is produced. The relation between the force applied on a body and the acceleration is Newton's second law. 

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Newton's second law: The rate of change of momentum of a body is proportional to the applied force acting on it and the change of momentum also takes place in the direction in which the force acts. 

If a body is moving with an initial velocity u and the velocity is changed (by increasing or decreasing) from u to v after a time t. 

Therefore, change of momentum: 

mv-mu

So, the rate of change of momentum: 

mv-mut=m(v-u)t=ma

Since we considered that there is no change of mass, so we can write like this. Further, we know that acceleration is: 

a=(v-u)t

Therefore if the applied force is F, then we can write Newton's second law of motion as: 

            F or ma 

But we don't want to express the law in proportional form, rather we want to write it as an equation. 

Then using a proportionality constant k, we can write 

F = km

In the case of Newton's second law, it is possible to create an amazing result. Since the term 'force' is not explained anywhere, (Newton's first law gives the concept only) by using the second law this will be measured for the first time. So, we have to give a value for the constant. We can say, when Newton's second law will be applied, if the proportionality constant is considered as 1, then the equation we will get is the measure of force. How easily a proportionality relation is converted into an equation. Therefore, we can write Newton's second law of motion as an equation. If the force is F and the proportionality constant is considered as 1, then 

F - ma 

That this small and simple equation can make a revolutionary change in the world of physics is difficult to believe. 

The unit of force is Newton (N). Dimension of force is [F] = MLT-2 

It has to be remembered that Newton's second law of motion is true not only for linear motion but this is true for any type of motion. We have known about gravitational force, by using Newton's second law, we will be able to explain the motion of the planets revolving around the sun due to the gravitational force. But in this book, we will limit the use of Newton's second law only to linear motion. If force is applied to an object, then by using Newton's second law, its acceleration can easily be determined. (If force is divided by mass, acceleration can be found). If acceleration is known, the velocity or distance traveled can be determined by using the laws of motion. 

Otherwise, we can say that if we see an object in motion and can calculate its acceleration, then if its mass is known, it is possible to calculate the force acting on it.