How Newton approximated force as change of momentum?

In summary, Calculus is a branch of mathematics that deals with the summation of continuous values represented by a function. It is used to describe processes in a concise way.
  • #1
joseph_seb
6
0
why Newton had taken force as change in momentum per time?
i mean i need to get physical interpretation?what is this force actually?
also help me to get an idea about energy in sense(core concept)?
not with some equations?
i see these equations every time?but didn't know meanining?
somebody please help with these or give the name of texts which i should refer to?
 
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  • #2
If you are going to get a good grasp of Physics then you will have to, at some point, start to see the mathematical relationships between quaitities as the best way of describing what goes on. An equation (particularly a simple one) states what happens so much better than a long sentence involving instances and examples.
If you look at Wiki (or all over the Web, in fact) for statements about Newton's Laws then they always end up with a bit of Maths. Just do a search and read as many links as you can.

(A form of) Calculus was invented by Newton in order to discuss the way that things vary in a concise way and differential Calculus describes so many processes very well. The "physical interpretation" that you seek may not always be there for some, even elementary relationships. If you are in a position to get hold of the elements of Maths and Calculus then you would find that approach very useful. The 'feeling' for Physics tends to follow the Maths, rather than the other way round.
 
  • #3
Instead of asking what force is, consider what force is used for. The sum of forces is the change in momentum over time. That's not an approximation. The concept of force let's us express the conservation of momentum in another way. It's useful for decomposing the change in momentum of an object into the sum of contributions coming from other objects. Between each pair of objects, you have an equal and opposite force between them. As such, force represents a transfer of momentum between two objects.
 
  • #4
It's a case of choosing your definitions so as to best capture your intuitive notion of "force" or whatever you want to describe. In the end all you can deal with is the relationships between the quantities you have defined, and there may be other similar definitions which capture other aspects of the intuitive notions you have in mind.
 
  • #5
@sophiecentaur
you said, Calculus was invented by Newton in order to discuss the way that things vary in a concise way,ie,if it is integral calculus,it is the summation of continuous values represented by function,ie we it has a meaning;i'd like to get a simliar kinda explanation,ie,how the eqn f=dp/dt states what happens so much better than a long sentence involving instances and examples;ie,if u were the one to formulate this eqn, what is ur logic
 
  • #6
@Khashishi
then what is momentum?
 

FAQ: How Newton approximated force as change of momentum?

What is the concept of force according to Newton's approximation?

Newton approximated force as the change in momentum over time, which is known as the rate of change of momentum.

Why did Newton choose to use momentum to approximate force?

Newton believed that momentum, which is the product of mass and velocity, was a more accurate measure of an object's motion and its resistance to changes in that motion compared to just using velocity or acceleration.

How did Newton's approximation of force contribute to the development of classical mechanics?

By introducing the concept of momentum and its relationship to force, Newton's approximation formed the basis of the laws of motion and the principles of classical mechanics, which are still widely used in physics today.

What are some limitations of Newton's approximation of force?

Newton's approximation assumes that the mass and velocity of an object remain constant, which is not always the case in real-world scenarios. It also does not account for other factors such as air resistance or friction, which can affect an object's motion.

How is Newton's approximation of force still relevant in modern physics?

Despite its limitations, Newton's approximation of force is still used in many areas of physics, such as mechanics and dynamics, and its principles have been expanded upon by other theories such as relativity and quantum mechanics.

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