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# Newton's Second Law of Motion

Top
 Sub Topics The basic building block of the classical mechanics is the three laws of motion invented by Newton. All three laws are related to some other quantities like inertia, momentum, acceleration etc. Hence these laws plays a vital role in science field. First law of motion or law of inertia tells about the continuous or uniform motion of an object. But in the second law, it tells about the momentum of an object. And the force is given by mass times acceleration of that object. This law has many applications in everyday life.

## What is Newton's Second Law?

Newton's second law states that a force acting on an object is equal to the acceleration of that body times its mass. This law represents the correlation between force and motion. Everybody unconsciously knows the second law of motion. We know that heavier bodies require more force to move the same distance as lighter bodies. However, the second law gives an exact relationship between force, mass, and acceleration. Newton's second law of motion predicts the behavior of objects for which all existing forces are not balanced.

Newton's second law of motion can be stated in another way.

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

## Newton's Second Law Equation

The mathematical representation of the second law is given by

F = ma
Where F is the force
m is the mass of an object
a is the acceleration

The SI unit of the force is given by N (Newton), Or we can write Kgm/s2.

## Newton's Second Law Experiments

1. Keep an empty rectangular box and some heavy books on a table. Then push the empty box across the table. We can see that it is very easy to move the box. Keep the heavy books in the empty box, compared to the previous case we have to apply more force to this box for its motion. This is a simple example to illustrate the second law of motion.

According to second law, the force is directly proportional to the mass of an object. So, in the above experiment it is clear that the mass of the empty box is lesser than the latter case. Hence, the applied force is also lesser compared to the box containing heavy books.

2. Correlation between force and acceleration
This experiment consists of a trolley, pulley, string, and weights. Arrange the apparatus as shown in the figure. When a trolley is connected by a string which is suspended with weights and passing through a pulley. The trolley should be able to run for 1 m which is the length over the trolley accelerates.To avoid friction, slightly tilt the track of the trolley so that it can run downwards without increasing the speed.Then start increasing the weight. Here the mass to be accelerated is the mass of the trolley and the weights while accelerating force is same as that of hanging weight. To allow the trolley to accelerate downward and note down the time taken. Repeat the experiment with different weights and make a note on the time taken.

From the second law it is clear that the acceleration is directly proportional to the applied force and inversely proportional to the mass. So, this trolley experiment reveals the correlation between the force, acceleration and mass.

## Applications of Newton's Second Law

Some of the applications of the second law of motion are given below:

1. Atwood machine
Atwood machine is used to verify the mechanical laws of motion with constant acceleration. The given figure shows the general idea about the Atwood machine. It consists of two different masses which is connected by a string over a mass less pulley.

2. A jet plane
The jet engine creates a thrust or a backward pull or force. If we divided by the mass of the jet plane we can calculate the acceleration of that plane.

3. Gravity
An object,if it is released which will fall to the ground due to the attraction of earth. This is also an application of second law of motion.

## Newton's Second Law Examples

• It is very easy for a man to pull a table, compared to a baby. It depend upon the net force acting on the body.
• It is very difficult to lift a heavy body than the lighter one. This reveals the relationship between the mass and the applied force.
• When a train hits another one of equal force and speed, both of them will travel the same distance and with the same force. If the first train is hooked, the second train will go twice the distance of the first train and the force will be twice.This provides the the relation between force and mass.

## Newton's Second Law Problems

Some of the relevant problems related to the second law of motion are given below:

### Solved Examples

Question 1: Calculate the acceleration produced by a car of mass 850 Kg with a of force 1500N? If the force is 2000N what will be the acceleration?

Solution:

According to the second law,
a =   $\frac{F}{m}$
So, a =  $\frac{1500}{850}$ = 1.76 m/s2
If the force is 2000N, then
a =  $\frac{2000}{850}$ = 2.35 m/s2

Question 2: Calculate the thrust or force produced by a jet plane of mass 20000 Kg to achieve an acceleration of 2 m/s2 .

Solution:

From the second law of motion we know that,
Force = mass × acceleration
So, F = 20000 × 2
= 40000 N

Question 3: Determine the mass of a falling rock, if it produce a force of 150 N?

Solution:

Newton's second law of motion is given by,
F = ma
Here, m= ? ; a = 9.8 m/s2 ; F = 150 N
So, m =  $\frac{F}{a}$
m =  $\frac{150}{9.8}$ = 15.30 Kg

Question 4: Calculate the acceleration of a ball of mass 0.5 Kg and it hits the catcher's hand with a force of 20 N?

Solution:

In this problem it is given that,
m = 0.5 Kg ; F = 20 N
We know that  , F = ma
So,  a =  $\frac{F}{m}$
a = $\frac{20}{0.5}$ = 40 m/s2

Question 5: Consider a car of mass 3000 Kg. If it produce a force of 4000 N, how fast the acceleration will be?

Solution:

According to the second law,
F = ma
So,  a =  $\frac{F}{m}$
a =  $\frac{4000}{3000}$ = 1.33 m/s2