Is Mechanical Energy Conserved In An Elastic Collision: Why, When And Detailed Facts And FAQs

This article answers the question “is mechanical energy conserved in an elastic collision?” Collisions are a very common thing in our lives, we can see them happening every now and then.

Collision is not limited to two cars hitting each other or someone getting hit by a car. A ball hitting bat is also an example of collision. However, not all collisions are same, all the collisions are different depending on various parameters. Let us read more about collisions in this article.

What is a collision?

As discussed above, collision can be defined as an event of two or more objects hitting each other. These striking of objects can take in different different manners hence they can be classified into some types.

We shall discuss about those types in detail in further sections. Collisions can happen linearly as well as obliquely. Both have different consequences that also we shall discuss further in this article.

Types of collision

Collisions can differ from impact to impact. Broadly collisions are classified into its two main types. The classification is done on the basis of conservation of kinetic energy.

Below is a brief about different different types of collisions-

  • Inelastic collision– There are some collisions in which the kinetic energy is not conserved after collision takes place. Such type of collisions are called as inelastic collisions. The kinetic energy decreases as it gets dissipated into heat or is used up in deforming the shape of the object.
  • Elastic collision- In elastic collisions, the kinetic energy of the objects remain conserved after collision takes place, this unlike inelastic collisions where only momentum is conserved and not kinetic energy. Kinetic energy may get transferred to another object but does not get lost.

Note that momentum is conserved in both elastic collision and inelastic collision.

Elastic collision formula

As discussed earlier, in elastic collision the momentum as well as kinetic energy is conserved.

The formula for elastic collision can be given as-

m1v1i + m2v2i = m1 v1f + m2v2f

where,

m1 is the mass of first object

m2 is the mass of second object

v1i is the initial velocity of the first object

v2i is the initial velocity of the second object

v1f is the final velocity of the first object

vf2 is the final velocity of the second object

What is co efficient of restitution?

The ratio of final relative velocity after collision to final relative velocity before collision is called as the co efficient of restitution.

This co efficient tells us about the nature of collision. It is denoted by the letter e. Mathematically, this co efficient is given by the formula given below-

e = v2-v1/u1-u2

where,

v2 is the final velocity of second object

v1 is the final velocity of first object

u2 is the initial velocity of second object

u1 is the initial velocity of first object

Why is mechanical energy conserved in elastic collision?

The kinetic energy of the objects are conserved during an elastic collision of those objects. This is the primary characteristic of elastic collision and a necessary condition for a collision to be elastic.

Kinetic energy being a type of mechanical energy, we can say that the mechanical energy is also conserved in an elastic collision as the kinetic energy is conserved The kinetic energy does not get lost or dissipated in to heat as it does in inelastic collision.

Examples of elastic collision

There are many real life cases where we can say that the collision is elastic. As we know that a collision is said to be elastic when both the kinetic energy and the momentum is conserved.

Let us look at some examples of elastic collision where we can see that mechanical energy is being conserved-

  • Ball hitting another ball in the game of billiards– Game of billiards is a perfect example of an elastic collision. The entire kinetic energy is transferred to other ball. Here the kinetic energy is not dissipated or lost. The magnitude of the kinetic energy remains the same throughout.
is mechanical energy conserved in an elastic collision
Image: Pool Table

Image credits: anonymous, PoolTablewithEquipment-nonCC BY-SA 3.0

  • Throwing a ball such that it bounces back to our hand– If we throw a rubber ball then it has a tendency to bounce back to our hand. This is another example of an elastic collision. The ball’s entire potential energy is converted kinetic energy and this kinetic energy is again converted to potential energy once it reaches the hand. But after and before collision the kinetic energy can be said to remain conserved.
  • When a marble ball collides with another marble– A marble colliding with another marble is similar to balls colliding in the game of billiards. The entire kinetic energy is transferred to other marble. The kinetic energy is not lost anywhere else hence it can be said that the kinetic energy is conserved.
  • Newton’s experiment for third law– For explaining Newton’s third law of motion, we can see that when a ball hits the series of balls, the last balls comes out of the series and bounces back with the same kinetic energy. This is an example of elastic collision.

Is car crash an elastic collision?

When two cars collide, we observe a loud sound coming from the crash as well as cars getting deformed from the point of contact.

In elastic collision, the kinetic energy does not get lost or dissipated or get converted to sound or heat energy. Since the car experiences a deformation and loses its kinetic energy after the crash, we can say that a car crash is not an example of elastic collision but an example of inelastic collision.

What do you mean by perfectly elastic collision?

For a perfectly elastic collision, the value of co efficient of restitution is equal to 1. That means the kinetic energy does not change even a bit (considering mass as constant throughout).

When the kinetic energy of the objects does not change even by an insignificant amount, then it is called perfectly elastic collision. This is an ideal case. The nearest example of perfectly elastic collision is striking of balls in the game of billiards. We have discussed about it in above sections.

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