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Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance.https://en.m.wikipedia.org/wiki/Temperature
Kinetic energy is 1/2 m.v^2For oscillating motion, the average velocity might be zero, but the kinetic energy is not.
When a pendulum is at the top of its swing, what is its kinetic energy?What's the potential energy?What about when it's at the bottom?What's the total energy of the swinging pendulum?Does the total energy change with time (in an idealised case)?What is the average total energy?Is the average total energy of the pendulum the same as the average kinetic energy of the pendulum?
i'm hoping that hamdani yusuf has caught on to the fact that the average energy of a vibrating system is NOT the average kinetic energy.Sorry if I threw in a bit of a red herring earlier. I was making the point that the velocity isn't the only thing happening.The system still has energy, even when the velocity (or speed) is zero.
Quote from: hamdani yusuf on 18/10/2024 17:14:22Kinetic energy is 1/2 m.v^2For oscillating motion, the average velocity might be zero, but the kinetic energy is not.Possible misunderstanding here. k.e. is not (m vxv)/2 (a vector) but (m |v|2)/2 - a scalar multiple of speed, not velocity. The average speed of a pendulum is not zero.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is 12mv2{\textstyle {\frac {1}{2}}mv^{2}}.[2]https://en.m.wikipedia.org/wiki/Kinetic_energy
average of Kinetic+potential
Temperature is more related to kinetic energy instead of the total energy.
Where do you get that cross product from?
... and since Kinetic+potential is a constant, you don't need to average it.
So, a fast moving snow ball (like a comet) is hot...Well. that's one approach.
Only in ideal case.
Quote from: hamdani yusuf on 20/10/2024 13:36:53Where do you get that cross product from?It represents the square of velocity.Whilst the average velocity of a pendulum is zero, its average speed is not.
The square of a vector typically refers to the square of its magnitude (or length), not the vector itself. Mathematically, if v is a vector with components , the square of its magnitude is given by:|\mathbf{v}|^2 = v_1^2 + v_2^2 + \dots + v_n^2This is essentially the dot product of the vector with itself:\mathbf{v} \cdot \mathbf{v} = |\mathbf{v}|^2So, squaring a vector usually means taking the sum of the squares of its components, yielding a scalar value (not another vector).ChatGPT
Quote from: Bored chemist on 20/10/2024 13:54:45... and since Kinetic+potential is a constant, you don't need to average it.Only in ideal case.
Physics is about ideal gases, weightless strings, etc. So you can assume your pendulum is swinging in a vacuum, suspended from a frictionless pivot.
In physics, the symbol x is typically used for vector cross product, which is not what you were trying to describe.
Quote from: alancalverd on 21/10/2024 09:50:05Physics is about ideal gases, weightless strings, etc. So you can assume your pendulum is swinging in a vacuum, suspended from a frictionless pivot.It depends on the level of complexity. High school physics already takes friction into account.
Do you know what an analogy is?
OK, so, do you recognise that the pendulum was an analogy for the ZPE?And do you realise that, in this context, there's no energy loss?