This article answers the question “is mechanical energy conserved in an inelastic collision?” Collisions are a very common part of our daily lives. Collision does not necessarily mean two cars hitting each other someone getting hit by a car. Even a ball hitting bat is an example of collision. Although, not all collisions are same, they are different depending on various parameters. We will read further about collisions in this article. Collision is an event of two or more objects striking each other. Collisions can be of different types according to the angle of collision, final velocities of these objects etc. Different types of collision commonly known are inelastic and elastic collision. We will study further about these types and their sub types in later sections of this article. Collisions can differ according to the angle of collision and final velocities of objects after collision. The different types of collision are- m1v1i + m2v2i = (m1 + m2) vf where, m1 is the mass of first object v1i is the initial velocity of first object m2 is the mass of second object v2i is the initial velocity of second object vf is the combined final velocity of first and second object Image: Bouncing of a ball is an example of series of inelastic collisionsImage credits: MichaelMaggs Edit by Richard Bartz, Bouncing ball strobe edit, CC BY-SA 3.0
m1v1i + m2v2i = m1v1f+ 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?Co efficient of restitution can be defined as the ratio of final relative velocity after collision of the bodies to the final relative velocity before the collision of the two objects. It is denoted by e. Mathematically, co efficient of restitution can be given as- 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 What is the significance of co efficient of restitution?The co efficient of restitution helps us understand the types of collision taking place. Below is the list of values of co efficient of restitution and its meaning.
In most common cases, the value of co efficient of restitution lies between 0 and 1. Why is mechanical energy not conserved in inelastic collision?In simple words, we can say that mechanical energy in an inelastic collision does not get conserved. This is so because the kinetic energy of the object after collision is dissipated into heat energy. The heat energy is produced as a result of internal friction. Heat energy not being a type of mechanical energy, we can say that kinetic energy is not conserved during the event of inelastic collision and hence, mechanical energy is not conserved in an elastic collision. Is total mechanical energy conserved in an inelastic collision?Kinetic energy and potential energy together constitute what we known as mechanical energy. During an inelastic collision, some amount of mechanical energy is dissipated and converted to heat energy or some times this energy is used in deforming the object. Hence we can say that total mechanical energy is not conserved during inelastic collision as the energy is converted in to some other form. Where does mechanical energy go in an elastic collision?We all know this fact about energy that it cannot never be created nor be destroyed. What we can do with energy is that we can only convert it from one from to another. In inelastic collision, the kinetic energy reduces as it gets dissipated in to heat energy or gets used up in deforming the shape of body. So we can say that mechanical energy gets converted to heat energy or gets used up in deforming the object after collision. What is perfectly inelastic collision?When the object loses maximum or all of its kinetic energy, it can be said that it underwent a perfectly inelastic collision. The value of e or co efficient of restitution for a perfectly inelastic collision is zero. This implies that kinetic energy after collision is zero. That means the kinetic energy is completely dissipated into heat or used up in deformation of shape of object. Examples of inelastic collisionA collision can be said inelastic when we can see the value of kinetic energy decreasing after the collision. Let us see some examples of inelastic collision. They are given below-
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