4.State Newton’s 2nd law of motion in terms of momentum and define
momentum of a body.
Answers
Newton's second law
The second law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force. Any net force is equal to the rate of change of the momentum.
Momentum
Momentum is the physical quantity which is the measure of the quantity of motion of a moving body.
Answer:
Newton's second law
The second law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.
The second law can also be stated in terms of an object's acceleration. Since Newton's second law is valid only for constant-mass systems,[20][21][22] m can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus,
where F is the net force applied, m is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.
The above statements hint that the second law is merely a definition of {\displaystyle \mathbf {F} }\mathbf {F} , not an observation of intrinsic nature. However, current physics restate the second law in measurable steps:
(1) defining the term one unit of mass by a specified "stone",
(2) defining the term 'one unit of force' by a specified spring with specified length,
(3) measuring by experiment or proving by theory (with a principle that every direction of space are equivalent), that force can be added as a mathematical vector,
(4) finally conclude that {\displaystyle \mathbf {F} =m\mathbf {a} ~}{\displaystyle \mathbf {F} =m\mathbf {a} ~}.
These steps hint the second law is an intrinsic feature of nature.
The second law also implies the conservation of momentum: When the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.
Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below).
Newton's second law is an approximation that is increasingly worse at high speeds because of relativistic effects.
According to modern ideas of how Newton was using his terminology,[23] the law is understood, in modern terms, as an equivalent of:
The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.
Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading:
If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.
The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations.[24]
Impulse
An impulse J occurs when a force F acts over an interval of time Δt, and it is given by[25][26]
Since force is the time derivative of momentum, it follows that
{\displaystyle \mathbf {J} =\Delta \mathbf {p} =m\Delta \mathbf {v} ~.}{\displaystyle \mathbf {J} =\Delta \mathbf {p} =m\Delta \mathbf {v} ~.}
This relation between impulse and momentum is closer to Newton's wording of the second law.[27]
Impulse is a concept frequently used in the analysis of collisions and impacts.[28]
Variable-mass systems
Main article: Variable-mass system
Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law;[21] that is, the following formula is wrong:[22]
The falsehood of this formula can be seen by noting that it does not respect Galilean invariance: A variable-mass object with F = 0 in one frame will be seen to have F ≠ 0 in another frame.[20] The correct equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected or accreted mass
Hope you like it
plz mark it as the brainliest
plz follow me