
What is the coefficient of restitution?
Answer
445.2k+ views
3 likes
Hint: During a collision process between two bodies, there can be a change in the velocity of the two bodies undergoing collision. So the ratio between the difference of the final velocity to the difference of initial velocities of the two bodies is known as the coefficient of restitution.
Complete step by step answer:
Consider two bodies of mass travelling with a velocity initially. After the collision the velocity of these two masses changes to .
Suppose the two masses are undergoing elastic collision in which the kinetic energy and the momentum of the system is conserved. So, we can write,
…. Equation (1)
……Equation (2)
From equation (1), we can write.
…. Equation (3)
From equation (2), we can write
… Equation (4)
Substituting equation (4) in equation (3), we get
Where, e is the coefficient of restitution.
is the relative velocity after collision.
is the relative velocity before collision.
In the case of elastic collision, you can see that the value of e is 1. Which means that the relative velocity after the collision and the relative velocity before collision remains the same.
So the coefficient of restitution can be defined as the ratio of relative velocity after the collision to the relative velocity before the collision.
Note: For an inelastic collision, the coefficient of restitution is always less than one and greater than zero . Since some of the energy is lost in the form of heat or sound during the collision, the kinetic energy before the collision will not be equal to the kinetic energy after the collision. But the momentum remains conserved in all types of collision.
If the value of e is less than zero or negative, it means that the two objects continue to move in the same direction before and after the collision.
Coefficient of restitution can also be defined as the ratio of the square root of the final kinetic energy after the collision to the square root of the initial kinetic energy before collision.
Complete step by step answer:
Consider two bodies of mass
Suppose the two masses are undergoing elastic collision in which the kinetic energy and the momentum of the system is conserved. So, we can write,
From equation (1), we can write.
From equation (2), we can write
Substituting equation (4) in equation (3), we get
Where, e is the coefficient of restitution.
In the case of elastic collision, you can see that the value of e is 1. Which means that the relative velocity after the collision and the relative velocity before collision remains the same.
So the coefficient of restitution can be defined as the ratio of relative velocity after the collision to the relative velocity before the collision.
Note: For an inelastic collision, the coefficient of restitution is always less than one and greater than zero
If the value of e is less than zero or negative, it means that the two objects continue to move in the same direction before and after the collision.
Coefficient of restitution can also be defined as the ratio of the square root of the final kinetic energy after the collision to the square root of the initial kinetic energy before collision.
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
How much is 23 kg in pounds class 11 chemistry CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Where can free central placentation be seen class 11 biology CBSE

What is the molecular weight of NaOH class 11 chemistry CBSE

What is the chemical name of Iron class 11 chemistry CBSE
