Newton’s second law of motion and Impulse
In this topic Newton’s second law of motion and Impulse , we will explain Newton’s second law of motion , expression for force, Impulse and application of concept of impulse . The reasoning questions of this topic and numericals ( specially based on Impulse) is very important for class examination and also for other competitive examination like JEE/NEET .
But before to know this topic, it is necessary the students must have the concept of Newtons first law of motion and inertia . For the notes on Newton’s first law and inertia click here-
Newtons second law of motion and impulse –
As we know from Newton’s first law of motion ‘every body remain in its position of rest or of uniform motion in a straight line , till no external force acts on it’ . Just think what will happen when external force acts on the body . This effect of acting a force on the body is described by Newton’s second law of motion .
To watch the video on Newton’s second law – click on the link given below-
Newtons second law of motion ( Force law)-
Newton’s second law of motion states that , when an external force applied on a body , then rate in change in momentum is directly proportional to the applied force , and change takes place in the direction of applied force . this law is also known as the law of force.
We have to take care of its two parts (i) rate of change of momentum is directly proportional to the applied force and , (ii) change in momentum occurs in the direction of applied force .
Expression of force from newtons second law of motion –
Let a body of mass ‘m’ moving with velocity ‘v’ .
Then , its linear momentum will be p = mv ;
As newton’s second law states force F α dp/dt ; or F= k dp/dt ……………..(i)
But here , p=mv .
So putting this value of p in equation (i) we get
F=k d(mv)/dt =k m (dv/dt) = k ma; [where dv/dt=a( acceleration) ],
Experimentally it is found k=1
So we can say, F =ma ;
Unit of force is kg-m/s2 or kg-ms-2 OR Newton (N)
Its dimension is [ M L T-2] ;
To know the impulse we must know . What is impulsive force?
Impulsive force – It a large force acts on a body for short time which is the cause of change in momentum . example- Blow a hammer on a nail, force exerted by a bat when it hits a ball, etc.
Impulse – When a large force acts on a body for short time which is the cause of change in momentum, then the product of force and time for which it acts on the body is called impulse or Impulse of force which is equal to the change in linear momentum of the body.
So we can write impulse I = Fav. x t = Pf – Pi = Δp
Proof– From Newton’s second law we know ;
Force F = dp /dt ;
But momentum P = mv ( m- mass of the body and v is its velocity);
So we can write F dt = dp ;
Integrating both sides with appropriate limits we get ,
∫ Fdt =∫dp = p2-p1
Or , Fav.t = p2-p1 = I
So we can say if the force varying with time ( or force is the function of time ) then we can write
Impulse I = ∫F dt .
If we plot the force v/s time curve , then the area under the curve gives the impulse .
A. When a constant force acts on a body then force v/s time graph is given below . the area under the line AB gives the impulse .
B. When a variable force acts on a body then force v/s time graph is given below . the area under the line ABC gives the impulse ;
The unit and dimension of the impulse is same as linear momentum .
Application of concept of impulse – ( It also work as reasoning questions in your class examinations)
(a) Automobiles are provided with shockers.
(b) China wares are packed under straw paper.
(c) A cricket players lower his hand while catching a ball.
(d) A person falling from a certain height gets more injuries when he falls on a cemented or tough floor than when he falls from a heap of sand.
If we goes to the reason of all the points mentioned above then answers of all the questions will be same .
As we know, impulse = F x t = change in momentum
For the same impulse force F = impulse / time . i.e. F α 1/t
when time of impact increases due to some processes then force acts on the body decreases .
To watch of the video of this topic click here-