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1800-102-2727There are many physical phenomena that happen around us that can be explained by Newton’s laws of motion. Like we are able to walk effortlessly on the rough horizontal surface but if it is smooth it's hard. How two objects of different masses dropped from top of the building have the same acceleration. In this article we will briefly understand three laws of motion and then solve some examples.
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You've probably seen in movies that when someone jumps out of a moving car, they invariably fall in the direction of the moving vehicle. Newton's first law of motion provides an explanation for this circumstance.
It states that a body remains in the state of rest or uniform motion in a straight line unless and until an external force acts on it.
The item does not accelerate in the illustration below because the resultant force is zero.
Net force on object can be expressed as,
$\overrightarrow{F}=\overrightarrow{{F}_{1}}+\overrightarrow{{F}_{2}}+\overrightarrow{{F}_{3}}$
But, $\overrightarrow{{F}_{1}}+\overrightarrow{{F}_{2}}+\overrightarrow{{F}_{2}}=0$
$\Rightarrow \overrightarrow{a}=0$
According to Newton's first law of motion, a body won't begin to move unless and until an outside force acts on it. It cannot stop or adjust its speed after it has started moving unless another force acts on it.
The first law is additionally referred to as the law of inertia.
Inertia: The resistance of a particle to change its state of rest or of uniform motion along a straight line is called inertia.
There are three types of inertia:
In contrast to the first law of motion, the second law of motion deals with the behavior of objects when forces are acting on them. The more precise second rule of motion is frequently employed to determine what happens when a force is present.
Newton’s second law of motion states that the acceleration of a particle as measured from an inertial frame is given by the vector sum of all the forces acting on the particle divided by its mass.
Mathematically we can write,
$\overrightarrow{a}=\overrightarrow{\frac{F}{m}}$
$\overrightarrow{F}=m\overrightarrow{a}$
Here a : acceleration of object
F : net force on object
m : mass of object
The second law is frequently referred to as the momentum law.
It can be stated as the rate of change of momentum of an object is equal to the net external force and in the direction of net force.
Momentum (P ) is expressed as,
$\overrightarrow{P}=m\overrightarrow{V}$
Here V : velocity of object
$\overrightarrow{F}=\frac{d\overrightarrow{P}}{dt}$
$\overrightarrow{F}=\frac{d\left(m\overrightarrow{V}\right)}{dt}$
$\overrightarrow{F}=m\frac{d\overrightarrow{V}}{dt}$……….Considering constant mass
$\overrightarrow{F}=m\overrightarrow{a}$
You must have seen the Iron Man movie if you're an Avengers fan. You must have questioned Tony Stark's ability to fly while donning the suit. By applying Newton's third law of motion, you may comprehend this.
Newton’s third law of motion states that to every action, there is an equal and opposite reaction. That means if a body A exerts a force F on another body B, then B exerts a force -F on A, the two forces acting along the line joining the bodies.
From the two examples you can understand how two bodies interact with each other.
Here
$\overrightarrow{{F}_{AB}}=$ Force on A by B
$\overrightarrow{{F}_{AB}}=$ Force on B by A
Note: The two forces in Newton's third law are called the action – reaction pair.
Examples:
Conditions of Action- Reaction pair:
Following are the conditions for the forces to be action-reaction pair:
A system is composed of two or more objects. Ex- ball -earth, man - suitcase etc.
Internal and external forces
It is classified as an internal force if the action-reaction pair is present in the system under consideration; otherwise, it is known as an external force. Both the action and the reaction forces are present inside system 1 as depicted in the given image. The forces are hence referred to as internal forces.
In system 2, the reaction force is outside the system. Hence, force N1 is known as external force, whereas N2 force is not considered as it is not inside the system.
The diagrammatic representation of a body that is isolated from its surroundings, showing all the external forces acting on it, is known as the free-body diagram (FBD).
Steps while drawing the FBD
Note: On a body that is regarded as a point, the entirety of Newtonian mechanics is applied. So, in drawing forces in FBD, always start with the body as a point. The body can be represented graphically by any shape.
The net force operating on an object is represented as the vector sum of all external forces acting on that object.
According to the figure, the body is being subjected to a number of forces that vary in strength and direction, which will have an overall impact on the outcome.
From figure,
$\overrightarrow{{F}_{net}}=\overrightarrow{{F}_{1}}+\overrightarrow{{F}_{2}}+\overrightarrow{{F}_{3}}+.....+\overrightarrow{{F}_{n}}$
$\overrightarrow{{F}_{net}}=\sum _{i=1}^{n}\overrightarrow{{F}_{i}}$
When the net external force on an object is zero, then the object is said to be in a state of translational equilibrium.
Mathematically,
$\mathrm{\Sigma}({\overrightarrow{F}}_{ext}{)}_{system}=0$
Which means net force along each axis should be zero.
So,
$\mathrm{\Sigma}{\overrightarrow{F}}_{x}=0\mathrm{\Sigma}{\overrightarrow{F}}_{y}=0\mathrm{\Sigma}{\overrightarrow{F}}_{z}=0$
Video Explanation: 1) Newton's 2nd Law
Q. A 15 kg block is kept on a floor that is smooth. At t=0, a 30 N force is exerted on it. Find the block's acceleration.
A. There is no friction in this area because the floor is smooth. Mass will therefore accelerate as a result of applied force.
We know,
$\overrightarrow{F}=m\overrightarrow{a}$
$\overrightarrow{a}=\overrightarrow{\frac{F}{m}}$
$a=\frac{30}{15}$
$a=2m{s}^{-2}$
Therefore the acceleration of block is 2 ms^{-2}.
Q. A force F is pushing two bodies A and B with masses m and M, respectively, in the direction of the positive x-axis. Draw FBD.
A. Following is the free body diagram of A and B.
Q. If the force applied on the object is doubled and mass is halved what will be the ratio of new acceleration and previous acceleration?
Options: (A) 1 (B) 2 (C) 4 (D) 8
A. (C).
From newton's second law F=ma
Then ${a}_{old}=\frac{F}{m}$ and ${a}_{new}=\frac{2F}{m/2}=\frac{4F}{m}=4{a}_{old}$
Therefore $\frac{{a}_{new}}{{a}_{old}}=4$
Q. The momentum of a particle moving in straight line is given as $\overrightarrow{P\left(t\right)}={t}^{2}+2t+5Ns.$ Find the force on the particle at t=3 sec.
A. From newton's second law,
$\overrightarrow{F}=\frac{d\overrightarrow{P}}{dt}$
$\overrightarrow{F}=\frac{d({t}^{2}+2t+5)}{dt}$
$\overrightarrow{F}=2t+2$
At t=3 sec
$\overrightarrow{F}=2\times 3+2$
$\overrightarrow{F}=8N$
Q. What are the characteristics of normal force?
A. It is a force that always acts perpendicular to the surface of contact. It is a perpendicular component of contact force.
Q. What is meant by an action-reaction pair?
A. The force exerted on an object is the action force, and the force experienced by the object as a consequence of Newton's third law is the reaction. These forces are equal in magnitude but opposite in direction.
Q. What is Net Force ?
A. The vector sum of all the external forces that are acting on a system represents the net force on that system.
Q. Do weight and normal force acting on a block placed on a flat surface are action-reaction pairs?
A. No, because both forces are acting on the same body. Also for action reaction pair forces need to be of the same nature. But it's not true in the case of weight and normal force.