Potential Energy = Kinetic Energy

AI Thread Summary
In discussions about the relationship between kinetic energy (Ke) and potential energy (Pe), it's noted that while students may assume they are equal in certain scenarios, this is not entirely accurate. As a tennis ball falls, its kinetic energy increases while its potential energy decreases, meaning they are not equal at all times. The principle of conservation of energy states that the total energy remains constant, leading to the relationship that the change in potential energy equals the negative change in kinetic energy. This relationship holds true under ideal conditions, such as neglecting air resistance. Understanding these concepts is crucial for grasping basic physics principles and avoiding reliance on memorization alone.
Ohm
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Even the average student can assume in cases where a tennis ball falls freely or is hit that Ke = Pe.
The question is why do we take it as if they are equal?
 
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Originally posted by Ohm
Even the average student can assume in cases where a tennis ball falls freely or is hit that Ke = Pe.
The question is why do we take it as if they are equal?

Average students probably assume a lot of things that aren't correct. It certainly isn't the case that "where a tennis ball falls freely or is hit that Ke= Pe". As a tennis ball falls its Kinetic energy is increasing and its Potential energy is decreasing. They can't always be the same. In addition, while kinetic energy depends upon speed, potential energy is always relative to some arbitrary reference point. Because of that you can always take potential energy to be equal to kinetic energy as some specific time but they won't stay equal.
 
Thanks.
 
What can be equal in those ideal cases is that the change in potential energy = - change in kinetic energy. This comes from the fact that you are dealing with conservatory forces and therefore the total energy is conserved (total energy = kinetic energy+potential energy). Therefore, since the total energy is a constant, if the potential energy goes down, then the kinetic energy goes up (case of a tennis ball falling freely).
 
To say it in a different way, kinetic energy at impact equals potential energy at release for a dropped tennis ball. This is true if you make some assumptions such as no wind resistance.
 
Yup, energy is conserved in isolated systems. Thanks for the insight. Would you believe that i finished Mechanics A-level at school(Average mark 87.5%) and i was not familiar with the reason of equating Loss in Pe with Gain in Ke ? Lately i discovered that i was not familiar with basic physics - I relied heavily on memory when i was doing O-level. In fact, i discovered that the majority of my friends who are doing A-level physics know everything by heart. I mean I can solve simple "critical" questions but when it comes to using basic theory to "extract" an idea, well that's where I get stuck.
Most Uncanny though, is the fact that i managed to get through Mechanics A-level incredibly successfuly. I'm currently searching on the internet to get my self obtained with basic information and get puzzled with questions. I'm going to be using your forums since i do not consider internet to be a perfectly reliable source.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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