Derivation of Law of Conservation of Momentum - The product of an object's velocity and mass is the object's momentum. It's a quantity with a vector. The overall momentum of an isolated system is conserved, according to conservation of momentum, a fundamental law of physics. In other words, if no external force acts on a system of objects, their overall momentum remains constant during any interaction. The vector sum of individual momentum is the overall momentum. In any physical process, momentum is conserved.
JEE Main 2025: Physics Formula | Study Materials | High Scoring Topics | Preparation Guide
JEE Main 2025: Syllabus | Sample Papers | Mock Tests | PYQs | Study Plan 100 Days
NEET 2025: Syllabus | High Scoring Topics | PYQs
Under the reasonable assumption that space is uniform, the law of conservation of momentum is established both empirically and theoretically. The law of momentum is found in nature, and the assertion is merely a theoretical statement based on the results of the studies.
State law of conservation of linear momentum
If there is no external force acting on an isolated system, its overall momentum remains constant. As a result, if a system's total linear momentum remains constant, the resultant force exerted on it is zero. In the absence of external torque, angular momentum is conserved as well.
Also read -
Newton's third law states that when object A produces a force on object B, object B responds with a force of the same magnitude but opposite direction. Newton derived the law of conservation of momentum from this concept.
Consider two colliding particles A and B with masses of m1 and m2 with starting and ultimate velocities of u1 and v1 for A and u2 and v2 for B, respectively. The contact time between two particles is denoted by the letter t.
Change in momentum of particle A is
A=m1 (v1-u1)
Change in momentum of particle B is
B=m2 (v2-u2)
From third law of motion we can write,
FBA=-FAB
FBA=m2×a2=m2(v2-u2)/t
FBA=m1×a1=m1(v1-u1)/t
m2(v2-u2)/t=-m1(v1-u1)/t
m1u1+m2u2=m1v1+m2v2
As a result, if no external force is exerted on the system, the momentum after the collision is identical to the momentum before the collision.
As a result, the equation of the law of conservation of momentum is as follows: m1u1+m2u2 represents the total momentum of particles A and B before the collision, and m1v1+m2v2 represents the total momentum of particles A and B after the collision.
Related Topics Links, |
Derivation of momentum or law of conservation of momentum in One-dimensional
A one-dimensional collision of two objects can be used to explain momentum conservation. Two objects with masses of m1 and m2 collide while moving in a straight line at velocities of u1 and u2, respectively. They gain velocities v1 and v2 in the same direction after colliding.
Before the impact, the total momentum
pi=m1u1+m2u2
After the impact, the total momentum
pf=m1v1+m2v2
Total momentum is conserved if no other force acts on the system of two objects. Therefore,
pi=pf
m1u1+m2u2=m1v1+m2v2
NCERT Physics Notes :
Derivation of law of conservation of momentum in Two-Dimensional
The overall momentum is pix=p1=m1u1 along the X-axis and piy=m2u2 along the Y-axis before the collision. The overall momentum after the collision is pfx=(m+M)ucosθ along the X-axis and pfy=(m+M)usinθ along the Y-axis
where m is mass and (m+M) is the resultant mass when particles get trapped inside it.
pix=pfx
m1v1=(m+M)ucosθ (1)
piy=pfy
m2v2=(m+M)usinθ (2)
As a result of squaring and adding equations (1) and (2),
(m1v1)2+(m2v2)2=(m+M)2u2(cos2θ+sin2θ)
It is the combined object's speed.
This determines the direction of the velocity.
Read also :
Also check-
The law of conservation of momentum is one of the most essential laws in physics. The following is how the law of energy conservation is represented. When objects 1 and 2 collide in a restricted space, the energy of the two things before the collision is equal to the force of the two articles after the collision. That is, the force picked up by item 2 is equal to the energy expended by object 1. This shows that the absolute force of the objects is monitored in a Framework, i.e., the total energy is constant and equal.
If no external force acts on an isolated system, its total momentum remains constant. As a result, if a system's total linear momentum remains constant, the force exerted on it is zero. In the absence of external torque, angular momentum is also conserved.
The law of conservation of momentum applies to all physical processes. Here are several examples:
Collision: The conservation of momentum and energy governs the collision of things.
The momentum of the propellant gas causes the rocket to go in the opposite direction. This is due to the law of conservation of momentum.
When a bullet is ejected from a gun, the gun suffers recoil momentum.
The importance of linear momentum conservation in a system or body in motion is that it maintains total momentum and is equal to the product of mass and vector velocity when an external force is applied.
Linear momentum p is expressed symbolically as:
p=mv
Where,
The mass of the system is m, and its velocity is v.
As a result, the S.I unit of momentum is kg.m/sec.
The net external force is equal to the change in momentum of a system divided by the rate of change of time, according to Newton's 2nd law of motion.
17 Sep'24 01:01 PM
16 Sep'24 02:33 PM
14 Sep'24 03:55 AM
14 Sep'24 03:53 AM
14 Sep'24 03:51 AM
14 Sep'24 03:48 AM
14 Sep'24 03:46 AM
13 Sep'24 04:42 AM
13 Sep'24 04:41 AM
13 Sep'24 04:20 AM