The Law of Conservation Problem (Application)

[tmang]

1.A large superball and a small superball are dropped from the same initial height H. Both balls bounce back up to a height h , which is just a bit less than H. If, however, the small superball is placed immediately above the large superball and both are dropped to the ground simultaneously from height H, the small superball rebounds to a height h␣ >>> H! Explain this in terms of the Conservation Laws.
2. Conservation Laws
3.The small ball lands above the large ball. It ‘meets’ the large ball on its rebound, and so is given energy and
momentum by the large ball before it (the small ball) rebounds off the large ball and reverses its own direction.I can only solve it partly.. Can someone please explain this and the answer?

 

[AJ Bentley]

The large ball rebounds from the ground as before so it has energy enough to get to the original rebound height of 'H'.

However, this time on the way up, it collides with the small ball, transferring some of it's energy to the small ball. (You can calculate exactly how much by treating it as a simple billiard ball collision with conservation of energy and momentum). Having lost that energy, it cannot bounce so high this time.

The smaller ball, just before the collision has enough energy to bounce back to the height h but it now gains the energy transferred to it by collision with the big ball and so has enough energy to get higher than before. You can show how much higher by noting that the extra K.E. now becomes Potential Energy.

 

[tmang]

ahh.. I get it now.. I was missing the key points of the Law of Conservation.. Thank you so much for your great help! thank you..

 

[AJ Bentley]

Y'r welcome

 

[rwisz]

The Law of Conservation of Energy and the Law of Conservation of Momentum are two fundamental principles in physics that state that energy and momentum cannot be created or destroyed, only transferred or transformed.

In the first scenario, when the large and small superballs are dropped separately, they each have their own initial potential energy (due to their height) and kinetic energy (due to their motion). When they bounce back up, some of this energy is lost due to friction and other factors, resulting in a lower rebound height. This is in accordance with the Law of Conservation of Energy, as the total energy of the system (the superball and Earth) remains constant.

However, in the second scenario, when the small superball is placed on top of the large superball and they are dropped together, something interesting happens. As the small superball falls, it collides with the large superball, transferring some of its energy and momentum to the large superball. This results in the small superball rebounding to a greater height than before, as it now has the additional energy and momentum from the large superball. This is in accordance with the Law of Conservation of Momentum, as the total momentum of the system (the two superballs and Earth) remains constant.

In summary, the Law of Conservation of Energy and the Law of Conservation of Momentum can explain the different rebound heights of the small superball in the two scenarios. By understanding and applying these laws, we can better understand and predict the behavior of objects in motion.