Galilean Relativity & Kinetic Energy

In summary, to find the reference frame in which an object undergoing a perfectly inelastic collision with a second object experiences no change in its kinetic energy, one must consider all reference frames and select the one that satisfies the condition of having the average velocity of the initial and final rest frames. This frame will be the common center of mass rest frame. However, other options may exist depending on the conditions of the problem, such as the trivial rest frame of the object throughout the collision.
  • #1
Raungar
3
0
How would one find the reference frame in which an object [which undergoes a perfectly inelastic collision with a second object] experiences no change in its kinetic energy?
 
Physics news on Phys.org
  • #2
Raungar said:
How would one find the reference frame in which an object [which undergoes a perfectly inelastic collision with a second object] experiences no change in its kinetic energy?
Halfway (or rather half-speed) between initial and final rest frame (which in this case is the common center of mass frame).
 
  • #3
Alright, but suppose the first object starts at a constant velocity and the second at rest; without an initial frame at which both are at rest, the conjecture you present ceases to be useful. So, how might your answer adapt to fit the aforementioned situation?
 
  • #4
ATs answer already includes this situation. The center of mass system is the system in which the total momentum (the sum of the momenta of both objects) is zero. There is no need for a system where both are at rest to define this frame.

Edit: However, it should be pointed out that while this frame satisfies your condition, it is not unique.
 
  • #5
Raungar said:
Alright, but suppose the first object starts at a constant velocity and the second at rest; without an initial frame at which both are at rest, the conjecture you present ceases to be useful. So, how might your answer adapt to fit the aforementioned situation?
A.T. is exactly correct. Your "suppose..." scenario is not relevant for this problem. You have to consider all reference frames and select the one which fits the problem's requirements. A.T. told you how to select it.
 
  • #6
Some confusion might have arisen due to AT and us reading elastic instead of inelastic. AT's more general statement still holds: it is the system with the mean velocity of the objects initial and final velocities.
 
  • #7
Orodruin said:
Some confusion might have arisen due to AT and us reading elastic instead of inelastic.
Oops, you are right. Usually this question is asked about an elastic collision.

The correct frame is indeed the one halfway between the initial and final rest frames (i.e. the object has equal velocity at the beginning and at the end), but it will most definitely not be the center of mass frame for an inelastic collision.
 
  • #8
Well, to be more general, that frame is one such frame. Since there is only one condition and boosts form a 3d vector space (assuming 3d motion is allowed), more options exist.
 
  • #9
Orodruin said:
Some confusion might have arisen due to AT and us reading elastic instead of inelastic.
No, I read perfectly inelastic.

DaleSpam said:
but it will most definitely not be the center of mass frame for an inelastic collision.
That part refereed the final rest frame, not the frame of constant KE. I now see it was ambiguously formulated. It should better read:

Average velocity of initial and final rest frame (the latter being the common center of mass rest frame in this case).
 
  • #10
Orodruin said:
assuming 3d motion is allowed, more options exist.
The OP doesn't explicitly state it must be an inertial frame, so there definitely are more options even in 1d, like the trivial rest frame of the object throughout the collision.
 
  • #11
A.T. said:
No, I read perfectly inelastic.

That part refereed the final rest frame, not the frame of constant KE. I now see it was ambiguously formulated. It should better read:

Average velocity of initial and final rest frame (the latter being the common center of mass rest frame in this case).

That indeed clears things up. I think everyone was reading it the other way and taking it from there.
 
  • #12
A.T. said:
That part refereed the final rest frame, not the frame of constant KE.
Wow! I am on a roll here. First I misunderstood the OP and then twice I misunderstood your post. I think I will just quit while I am behind!
 
  • #13
Thank you all for your input.
 

Related to Galilean Relativity & Kinetic Energy

1. What is Galilean Relativity?

Galilean Relativity is a principle in physics that states that the laws of motion are the same for all observers in uniform motion. This means that the physical laws governing the behavior of objects do not change based on an observer's frame of reference. This principle was first proposed by the Italian scientist Galileo Galilei in the 17th century.

2. What is the difference between Galilean Relativity and Einstein's Theory of Relativity?

The main difference between Galilean Relativity and Einstein's Theory of Relativity is that Galilean Relativity only applies to objects in uniform motion, whereas Einstein's Theory of Relativity applies to all objects, including those in non-uniform motion. Einstein's theory also takes into account the effects of gravity and the curvature of space-time.

3. How does Galilean Relativity affect our understanding of kinetic energy?

Galilean Relativity has a significant impact on our understanding of kinetic energy. According to this principle, the kinetic energy of an object is the same for all observers in uniform motion. This means that the kinetic energy of an object does not change based on an observer's frame of reference, and it is a fundamental property of the object itself.

4. Can Galilean Relativity be applied to all types of motion?

No, Galilean Relativity can only be applied to objects in uniform motion. For objects in non-uniform motion, such as those moving at high speeds or experiencing acceleration, Einstein's Theory of Relativity must be used to accurately describe their behavior.

5. What are some practical applications of Galilean Relativity and Kinetic Energy?

Galilean Relativity and Kinetic Energy have many practical applications in fields such as engineering, mechanics, and astronomy. They are used to design and build machines and structures, predict the motion of objects in space, and understand the behavior of particles at the atomic level. They also play a crucial role in technologies such as GPS and satellite communication systems.

Similar threads

  • Mechanics
Replies
3
Views
105
Replies
5
Views
879
Replies
3
Views
998
Replies
2
Views
746
Replies
5
Views
825
Replies
7
Views
880
Replies
16
Views
1K
Replies
13
Views
1K
  • Mechanics
Replies
11
Views
2K
Replies
34
Views
3K
Back
Top