Newton’s Second (2nd) Law of Motion

Isaac Newton is one of the well known and famous scientist and especially known for his work in physics. Newton has done a great work by giving physical laws of motion and there are total three laws of motion which are given by Newton, these laws of motion describe a physical relationship in between of the force and body on which force is acting and the motion which is created due to this force.

What is Newton’s Second Law

He was also awarded the title of “sir” for his great contribution in the field of physics. He has given a lot of laws in his life like as law of gravitation, the equation of motion, Kepler’s law of Planetary motion and so on but today we are going to know about Newton’s second law of motion in details.

What is the law of inertia?

The first law of motion which was given by Newton predicts that the force which is acting on anybody shows a balanced behavior. So, the first law of motion is known as the law of inertia. According to Newton if objects are in the condition of equilibrium then they will not accelerate which means that acceleration will only take place when there is net or unbalanced force which is acting over an object and which in result will produce an acceleration in the object by simply changing its speed, direction or both speed and direction.

Newton’s second Law Definition

So, we are here to talk about the Newton second law of motion basically the second law pertains that behavior of the object in which all forces which are existing are not in balanced condition.

Newton’s 2nd Law

Newton’s Second Law of Motion states that –

If an acceleration is acting upon any object then it depends on two variables from which the first one is the net force acting on the body and the second one is mass of the object

This statement means that the acceleration which is produced in anybody is directly dependent on the net force which acting over an object or body and it will be inversely proportional to the mass of that particular object which means that if the force acting over body gets increased then tell acceleration of body will also increase and in similar if the mass of the body increased then the acceleration of object or body will decrease.

So, the second law of motion simply gives an explanation towards the behavior of any object on which the acting forces are not balanced. In simple words, this law states that the main cause of acceleration acting over the body is a force acting upon that object as it is directly proportional to the force which is produced and inversely proportional to the mass of that object which reduces acceleration. You should also remember a point that the direction in which net force is acting will always in the same direction where acceleration is produced so, if you know the direction of either acceleration or net acting forces then you can easily calculate the direction of another one which is unknown.

Formula of Newton’s Second Law of motion

A book which was written by Sir Issac newton which is ” Principia Mathematica Philosophiae Naturalis ” , in this book he has proposed all of his three laws of motion. We have come to know that in the second law of motion Force acting on any object is equal to the change in the momentum of body with a change in its time and it is known that momentum is defined as the product of mass m with velocity v. So , there is a formula for the second law of motion which we are going to discuss that how it derives.

Just go to the image shown above and assume that we are having an airplane which is situated at a point 0 and the location of airplane is denoted by x0 and time by t0. The mass of airplane is m0 and it is travelling with the velocity of v0 , the external force which is acting over the airplane is denoted by F due to this force the airplane will move in a particular direction to some distance so this new location will be known as the x1 and the time taken in this movement is denoted by t1 and due to this motion the mass and velocity of airplane will also change and these changes in mass will be denoted by m1 and the velocity is denoted by v1. So , these all were our assumptions now will be simply take a difference in between both conditions at rest and in motion , it will be shown as :

F = ( m1 * v1 – m0 * v0 ) / ( t1 – t0 )

As , till now we have come to know that the second law of newton talks about the change in momentum of an object which is ( m * v ) so , we are unable to take the separate change in velocity or mass of the object that how much is the difference in them but now we only knows the product of them which is m*v. Now , let us take another assumption that the value of mass is constant which means that there is no change in the value of mass. This is a very good assumption in the case of airplane as there will be only a slight change in mass which will be due to the burning of fuel when plane is on motion but it is comparatively low in terms of mass of the airplane. So , we will not assume this change and consider that the mass of airplane is constant when it is moving from point 0 to 1. Now , for the mass to be constant the second law of motion will be like :

F = m * ( v1 – v0 ) / ( t1 – t0 )

Now , the definition of acceleration is change in velocity with respect to the change in time which we can clear see in the above equation so , the term ( v1 – v0 ) / ( t1 – t0 ) will be replaced by the acceleration a due to which the second law of motion will got reduced to the follow

F = m * a 

                                                                 F = ma

This is a relation which is found for an object which is having constant mass so , it will good for only those objects whose mass is constant. By this equation we can conclude that the Force is directly proportional to the acceleration which means if force increase then acceleration will also get increased. So , this is the main formula for the newton second law of motion.

 

Newton’s Second Law Examples

So , the second law of motion says that the net force which is acting on an object or system is equal to the rate of change in its momentum. It will become more clear of we have some law of inertia examples let us have a look over some of the examples of second law of motion :

1. Push or Pull

Let us prepare a scenario in our mind that we are pushing a bicycle on one hand and at the other time we are pushing our car , you can easily calculate that you needs to put a lot of force for pushing your car for moving it with equal acceleration as compared to the force required for moving a bicycle. As the mass of bicycle is less so it require less force for producing acceleration while on the other hand the mass of your car is greater and it requires more force for making it to accelerate. Now , just call your 3 or 4 friends and all of you simultaneously apply force on the car you will see that this time it will move easily and the acceleration will be more as compared to the single force of your it is because the mass of car is same but the amount of applied force has been increased now which produce more acceleration.

2. Tossing a stone away

Now , in this situation just simply try to kick a rock which is almost impossible as it will not show any acceleration but in the same if you toss a small pebble in water then it will produce a large acceleration. This is because the mass of pebble is very low as compared to rock and tell acceleration is produced more in the heavy mass objects while it will be more in lighter mass object on applying same amount of force.

3. Weigh your capacity

We have seen a lot of time that a bunch of people are lifting a big box which has a weight of around 100 kg but a single person can never imagine even to move that box it will require more than 10 persons for moving it while on the other hand you can easily carry your pencil box any where as it weighs very less.

4. Catching a ball

This another example of catching a ball also follow the second law of motion. In this context we have sometimes seen that before catching a ball the professional sportsmen just put or swing their hand a slightly back after catching the ball instantly because it helps he ball by providing more time for losing its speed which will increase the time and will reduce ∆p / ∆t and this will end by requiring less force by the sportsman to catch the ball.

So , these all above mentioned examples are the best examples for second law of motion and it will clear your concept more.

Newton’s Second Law Worksheet

We have learned almost everything about newton second law of motion. Now, we are going to provide you a worksheet in which you will get some question related to second law of motion , this is for your practice and by solving these questions you will come to know that how much have you understand this law but before moving for the worksheet let us know how to solve numericals of second law of motion –

 

Ques – 1: There is an object with mass 5 kg and it is moving with the velocity of 10 m/s. Calculate the applied force on the object.

And : The given values are –

Mass m = 5 kg

Acceleration a = 10 m/s

Force = ?

By formula of Newton’s second law of motion

F = ma

F = 5 * 10

F = 50 N

 

Ques – 2 : You are having an object which is moving with the velocity of 30 m/ s and have the mass of 6 kg. Calculate force applied.

Ans – 2 : The given values are –

m = 6 kg

a = 30 m/s

F = ?

By using formula of second law of motion

F = ma

= 6 * 30

= 180 N

So , in this way you can easily solve the numerical based on the second law of motion.

This is the worksheet which is having some numerical or theoretical questions just for boosting up your knowledge and checking your understanding related to Newton’s second law of motion.

Newton’s Second Law for Kids

 For Kids it is not easy to understand these bookish languages or derivations and numericals but it is important for them to know about the second law of motion although there are lots of videos are available on social sites which easily and in an effective way expresses the second law of motion so , if you are having any kid and wanted to tell them about newton and its second law of motion then you can simply show them video or for them the formula F = ma is enough they do not need to go in depth an overview is enough for their knowledge.

Newtons Second Law of Motion

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