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# Newton's Second Law of Motion

Newton's first law explains what happens to an object when no force acts on it, it either remains at rest or moves in a straight line with constant speed.

Newtons Second Law answers the question of what happens to an object when one or more forces act on it. "Force is not the cause of motion, force is the cause of changes in motion."
Consider that there is a block which is lying on the floor. If force of F N is applied to the block, the block will surpass the force of friction between the block and the surface and start moving with the acceleration "a".

In the second case the force applied doubles or we can say that force of 2F N is applied to the block then the acceleration of the block will also doubles and becomes "2a". If we make the force 3F the acceleration will become "3a" and so on.

It shows that the acceleration is directly proportional to the net resultant force applied. If more net resultant force is applied to the object, more would be the acceleration of the object.

Now we will explain the relationship between mass and acceleration first. Mass of an object shows how much inertia is contained in the object. If the mass of object is more, lesser would be its acceleration under the same applied force F. For example, if force F produces an acceleration of 6 m/sec2 in an object having mass m, then acceleration of the object will be halved equal to 3 m/sec2; the mass of the object is doubled and if the same force F Newton is applied to the object.

To formulate the mass and calculate it quantitatively, if same force F Newton is applied to the two objects having mass m1 and m2 and having accelerations a1 and a2 respectively,

Then the ratio of the mass can be defined as the inverse ratio of the accelerations produced by applying same force to both the objects.

$\frac{m_{1}}{m_{2}}$=$\frac{a_{2}}{a_{1}}$

Relation between the applied force and the acceleration is already explained. Now, we will discuss the relationship between the acceleration and the mass further. From above discussion we can conclude that the acceleration magnitudes are inversely proportional to the ratio of their masses.

$\frac{m_{2}}{m_{1}}$=$\frac{a_{1}}{a_{2}}$

This results in Newtons Second Law.

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## What is Newton's Second Law of Motion?

"Acceleration of the objects is directly proportional to the net or resultant force acting on it and inversely proportional to the mass of the object. "

F = m $\times$ a

Where,
'F' is the force applied to the object
'm' is the mass of the object, Unit of mass is kilograms (kg).
'a' is the acceleration of the object

When force F is applied to the object. Suppose that force F is applied to the object and this result in change in the velocity of the object from its initial velocity v1 at the time interval t1, to the velocity v2 at time interval t2.

If we consider that the mass of the object remains same then,

F = m $\frac{dv}{dt}$

F = m $\frac{v_{2} - v_{1}}{t_{2} - t_{1}}$

If mass of the object also changes when force F is applied to the object then,

F = $\frac{(m_{2}v_{2}- m_{1}v_{1})} {(t_{2}-t_{1})}$

Unit of Force:
SI unit of the force is Newton which is equal to the force applied on the object having mass of 1Kg, produces an acceleration of 1 Kg m/sec2.
1 Newton = 1kg m/sec2

## Weight and Gravity Force

Every object on earth is attracted towards the earth. This force which is exerted on the object by the earth is called as the gravity force (Fg). The direction of gravity force is towards the center of the earth and is called as the weight of the object concerned.

There is a difference between the mass and the weight of the object.

Freely falling object towards the earth experiences an acceleration of 'g' towards the center of the earth and if the mass of the object is m, then the weight of the object is equal to
$F_{g} = mg$

Where, g = 9.8 m/sec2

If one weight of 8 Newton and another weight of 2 Newton is thrown above with the same applied force. Then the 2 Newton weight will travel at higher speed and has more acceleration than the 2 Newton weight with the same amount of force, as the mass of 2N weigh is less.

1. As the weight of the object depends on the value of acceleration g, weight of the object varies as the geographic location changes.
2. As the object moves away from the center of the earth the value of 'g' decreases and its weight decreases.
3. Another example is that value of 'g' on the moon is 1/6th of the value on the earth.

## Newton's Second Law of Motion Examples

### Solved Examples

Question 1: Suppose that there is a first piece of rock which weighs 5 Newton. Force F is applied to this first piece of work and it produces an acceleration of a. Now if there is a second piece of rock. What force need to be applied to the second piece of rock to produce acceleration of 10a. Mass of both the pieces of rock is same.
Solution:

Here, mass of both the pieces of rock is same, to produce the acceleration of 10a , force applied would be equal to

F2 = m x 10a
= 10F1

Therefore, 10 times of the force applied to the first rock needs to be applied to the second rock to produce an acceleration of 10a.

Question 2: If Force equal to 10N is applied to the object having mass 2kg. Find the acceleration of the object?
Solution:

Here, we need to find the acceleration of the object, so we will apply the Newton’s second law which can be stated as the
F = ma

Newton’s second law of motion:
10 = 2a
a = $\frac{10}{2}$
a = 5 m/sec2

Question 3: Consider the problem on that on the object having initial mass of 4 kg. Two forces are acting on the object. Force F1 equal to 10 Newton and another force F2 equal to 4 Newton’s. Direction of F2 is opposite to the direction of F1. Suppose that mass of the object decreases from 4 kg to 2 kg when forces are applied to the object. Calculate the acceleration of the object.
Solution:

Now here the resultant force acting on the object is
$F_{1}$ - $F_{2}$ = 10 - 4 = 6N

Resultant force direction is same as the direction of the F1.
Resultant force = ($m_{2}$ - $m_{1}$) a
Therefore,
a = $\frac{6}{2}$
a = 3 m / sec2

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