The conservation of momentum calculator will help you in describing the motion of two colliding objects. Are you wondering what is momentum? Do you want to gain a better understanding of the law of conservation of momentum? Are you perplexed by the concepts of an elastic and inelastic collision? Or maybe you can't tell the difference between kinetic energy and momentum conservation principles? Whatever the reason, this article is here to help you. Prefer watching rather than reading? Check out our video lesson on conservation of momentum here: 
The principle of momentum conservation says that for an isolated system, the sum of the momentums of all objects is constant (it doesn't change). An isolated system is a system of objects (it can be, and typically is, more than one body) that doesn't interact with anything outside the system. In such a system, no momentum disappears: whatever is lost by one object is gained by the other. Imagine two toy cars on a table. Let's assume they form an isolated system - no external force acts on them, and the table is frictionless. One of the cars moves at a constant speed of 3 km/h and hits the second toy car (that remained stationary), causing it to move. You can observe that the first car visibly slows down after the collision. This result happened because some momentum was transferred from the first car to the second car.
We can distinguish three types of collisions:
You may notice that while the law of conservation of momentum is valid in all collisions, the sum of all objects' kinetic energy changes in some cases. The potential energy, however, stays the same (what is in line with the potential energy formula).
You can use our conservation of momentum calculator to consider all cases of collisions. To calculate the velocities of two colliding objects, simply follow these steps:
According to the principle of conservation of momentum, the total linear momentum of an isolated system, i.e., a system for which the net external force is zero, is constant.
In order to conserve momentum, there should be no net external force acting on the system. If the net external force is not zero, momentum is not conserved.
The recoil of a gun when we fire a bullet from it is an example of conservation of momentum. Both the bullet and the gun are at rest before the bullet is fired. When the bullet is fired, it moves in the forward direction. The gun moves in the backward direction to conserve the total momentum of the system.
The principle that makes a rocket move is the law of conservation of linear momentum. The fuel burnt in the rocket produces hot gas. The hot gas is ejected from the exhaust nozzle and goes in one direction. The rocket goes in the opposite direction to conserve momentum. In physics, an inelastic collision occurs when some amount of kinetic energy of a colliding object/system is lost. The colliding particles stick together, and the maximum amount of kinetic energy is lost in a perfectly inelastic collision. In such cases, kinetic energy lost is used in bonding the two bodies together. Problems involving collisions are usually solved using the conservation of momentum and energy. An inelastic collision is such a type of collision that takes place between two objects in which some energy is lost. In the case of inelastic collision, momentum is conserved but the kinetic energy is not conserved. Most of the collisions in daily life are inelastic in nature.
The special case of inelastic collision is known as a perfectly inelastic collision. Here, two objects stick together after collision and move as a single object. Refer to the figure above. For example, when a wet mudball is thrown against a wall, the mudball sticks to the wall.
When two objects collide under inelastic conditions, the final velocity with which the object moves is given by- \(\begin{array}{l}V=\frac{(M_{1}V_{1}+M_{2}V_{2})}{(M_{1}+M_{2})}\end{array} \) Where,
For inelastic collision in two dimensions, conservation of momentum is applied separately along each axis. Since Momentum is a vector equation, there is one conservation of momentum equation per dimension. There is only one conservation of energy equation.
Most of the collision we see in our day to day life falls under inelastic collision. Some of them are listed below. Real World Examples Of Inelastic Collision
In the case of inelastic collision, the kinetic energy is not conserved. The loss of kinetic energy is due to internal friction. It may turn into vibrational energy of the atoms, causing a heating effect and the bodies are deformed. Elastic Collision Any collision in which the collided objects get separated after the collision is known as an elastic collision. In the case of elastic collision, kinetic energy gets conserved. One must use both conservations of momentum and conservation of energy to find the motions of the objects later. Some examples of elastic collisions are ping-pong balls, billiards, etc.
Shankha is going by a slippery snowy hill. He has a mass of 20kg, and he is sliding the hill at a velocity of 5m/s. Shankha’s elder brother has a mass of 30kg. His brother is moving slower with a velocity of 2m/s. Shankha collides to his brother. Then both of them keep going down the hill as one unit. Calculate the resulting velocity of Shankha. Solution:Given, M1= 20kg M2= 30kg V1= 5m/s V2= 2m/s \(\begin{array}{l}V=\frac{(20kg)\times (5m/s)+(30kg)\times (2m/s)}{(20kg+30kg)}\\ \\ =\frac{100\: kg.m/s+60\: kg.m/s}{50\: kg}\\ \\ =\frac{160\: kg.m/s}{50\: kg}\\ \\ =3.20\: m/s\end{array} \) Thus, after Shankha collides, the combined velocity of Shankha and his brother is 3.20m/s. Problem 2:Shankha driving a 20000 kg truck and travelling eastwards at a speed of 10m/s. He hit the rear end of a 1400kg car at the stop signal. The collision caused both vehicles to stick together. What is the final momentum of the vehicle? Solution:Given, Mt = 20000kg Mc= -1400kg Vt =10m/s Vc = 0m/s Formula : Momentum P = MV According to the conservation of momentum Pi = Pf (MV)t+(MV)c = (Mt+Mc)V (20000×10)(1400×0)=(20000+1400)×V 20000/3400 = V V=5.8m/s Thus, after collision Shankha’s truck and car striking together will move with a speed of 5.8m/s.
Yes, momentum is conserved in an inelastic collision.
No, kinetic energy is not conserved in an inelastic collision.
A collision is an event in which two or more objects exert forces on each other for a short interval of time. Inelastic collision as the kinetic energy is not conserved here. Types of collision are:
Hope you have got a brief knowledge of inelastic collision, formulas, terms, examples and applications. For a better understanding of collision, do read the related articles and answer the practice questions. Related Physics ConceptsCollisions are all around us. Watch the video and understand what collisions are.
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