Conservation of Momentum in an Isolated System: A Derivation

In summary, the law of conservation of momentum for an isolated system of two interacting particles can be derived by applying Newton's second law to each particle and Newton's third law to the system. This means that the total force inside the system will remain zero, leading to the conclusion that the total change in momentum is also zero. This can also be represented by the equation F = dp/dt, which can be derived from Newton's second law.
  • #1
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Homework Statement



Derive a law of conservation of momentum for an isolated system consisting of two interacting particles.

Homework Equations



It says that "The law is derived by applying Newton's second law to each particle and Newton's third law to the system."

The Attempt at a Solution



I don't understand this at all... if you could explain me with an example, that would be so great...
 
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  • #2
Newtons second law:

[tex]\overrightarrow{F}\,=\,\overrightarrow{m}\,a[/tex]

Newtons third law:

"Whenever A exerts a force on B, B simultaneously exerts a force on A with the same magnitude in the opposite direction." - "[URL

What would you do to combine the forces of two particles?
 
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  • #3
well, does that mean

-ma=ma for representing the situation where two particles collide?

but i still don't understand how to proceed tp get

initial total momentum =final total momentum
 
  • #4
I think that for this problem it's easier to use the other version of Newtons second law:
F = dp/dt (change in momentum)*
Because of Newtons second law the total force inside a system will stay 0, so what does that say about the total change in momentum?
*From this you can derive F = ma:
F = dp/dt = d(mv)/dt = mdv/dt = ma
 
  • #5
all right, I think I got it. Thanx!
 

1. What is the momentum equation and why is it important in science?

The momentum equation, also known as Newton's second law of motion, states that the force acting on an object is equal to its mass multiplied by its acceleration. This equation is important in science because it helps us understand how objects move and interact with each other.

2. How is the momentum equation derived?

The momentum equation can be derived from Newton's first law of motion, which states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. By combining this with the definition of acceleration, we can arrive at the momentum equation.

3. What are the units of measurement for momentum?

The units of measurement for momentum are kilogram-meters per second (kg·m/s) in the SI system. This unit represents the product of an object's mass and velocity, which are both important factors in determining momentum.

4. How is the momentum equation used in real-world applications?

The momentum equation is used in many real-world applications, such as predicting the trajectory of a projectile, analyzing the forces on a moving car, and understanding the motion of objects in fluid dynamics. It is also used in engineering to design structures and machines that can withstand or generate large amounts of force.

5. Is the momentum equation always valid, or are there certain conditions where it does not apply?

The momentum equation is a fundamental law of physics and is valid in almost all scenarios. However, it does not take into account relativistic effects at extremely high speeds or quantum effects at the atomic level. In these cases, more advanced equations must be used to accurately describe the motion of objects.

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