Inelastic collisions with constant momentum

In summary, the conversation discusses the calculation of kinetic energy before a collision and the discrepancy of the required answer of 1/2 mv². The expert agrees with the calculation and notes a potential error in the book. It is mentioned that the books specifies "identical" objects, but it is clarified that objects of the same mass are all that is required kinematically. The use of "identical" may be for economy of words and to convey the idea of symmetry. However, it is pointed out that the book actually states "the same two objects", implying that they are the same as in the preceding question.
  • #1
haha0p1
46
9
Homework Statement
The total momentum before the collision in an inelastic collisions is 0, but the total kinetic energy before the collision is 1/2mv². Calculate how the total kinetic energy before collision is 1/2mv².
Relevant Equations
Ek=1/2mv²
Kinetic energy before collision =1/2 mv² + 1/2 mv² = mv² (since energy is a scalar quantity, the direction does not matter). Kindly tell why am I not getting the required answer i.e: 1/2 mv². Am I doing the calculation wrong?
IMG_20230102_154827.jpg
 
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  • #2
Hi,

I agree with your calculation. An unfortunate error in the book.

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  • #3
It's interesting that the book specifies the "same object" or "identical" objects, where all that is required kinematically is objects of the same mass!
 
  • #4
PeroK said:
It's interesting that the book specifies the "same object" or "identical" objects, where all that is required kinematically is objects of the same mass!
Truee
 
  • #5
PeroK said:
It's interesting that the book specifies the "same object" or "identical" objects, where all that is required kinematically is objects of the same mass!
I think it's economy of words. "Identical objects" is shorter than "objects of the same mass" and conveys the idea of symmetry. "Identical" becomes relatively conciser when the masses also carry equal charges.
 
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  • #6
PeroK said:
It's interesting that the book specifies the "same object"
No, it says "the same two objects". Presumably the same two as in the preceding question.
 

1. What is an inelastic collision with constant momentum?

An inelastic collision with constant momentum is a type of collision in which the total momentum of the system remains constant, but some of the kinetic energy is lost during the collision. This means that the objects involved in the collision will stick together and move with a common velocity after the collision.

2. How is the momentum conserved in an inelastic collision with constant momentum?

The total momentum of a system is always conserved in an inelastic collision with constant momentum. This means that the sum of the momentum of all the objects before the collision is equal to the sum of the momentum of all the objects after the collision.

3. What is the difference between an inelastic collision with constant momentum and an elastic collision?

In an elastic collision, both the total momentum and the total kinetic energy of the system are conserved. This means that the objects involved in the collision will bounce off each other and continue moving with their original velocities. In an inelastic collision with constant momentum, only the total momentum is conserved and some of the kinetic energy is lost.

4. How is the coefficient of restitution related to inelastic collisions with constant momentum?

The coefficient of restitution is a measure of the elasticity of a collision. In an inelastic collision with constant momentum, the coefficient of restitution is equal to 0, meaning that there is no rebound or separation between the objects after the collision. This is because all the kinetic energy is lost during the collision.

5. What are some real-life examples of inelastic collisions with constant momentum?

Some examples of inelastic collisions with constant momentum include a car crash, a ball hitting the ground, or two objects sticking together after a collision. In these situations, the total momentum of the system remains constant, but some of the kinetic energy is lost due to the deformation or sticking together of the objects involved.

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