This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.
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Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
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Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
Markdown
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Math
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Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3
\( 2 \times 3 \)
2^{34}
234
a_{i-1}
ai−1
\frac{2}{3}
32
\sqrt{2}
2
\sum_{i=1}^3
∑i=13
\sin \theta
sinθ
\boxed{123}
123
Comments
For the hanging steel ball, the centre of mass will shift downward when it expands due to heating
since the wire's length cant change in any way (positive or negative) , and hence the net energy supplied to it is
Q+mgh which must reflect as temperature change at the end (since its kinetic energy is 0 at all times , and the wire cannot do any work upon the ball since its length is fixed)
whereas on the one on the ground, the work done is Q-mgh which must reflect as temperature change at the end (once again, the grounds normal reaction cant do any work on it, but some amount of heat must be expended to raise the level of centre of mass)
so the hanging steel ball acquires greater temperature
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
**bold**
or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
...\]
to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
For the hanging steel ball, the centre of mass will shift downward when it expands due to heating
since the wire's length cant change in any way (positive or negative) , and hence the net energy supplied to it is
Q+mgh which must reflect as temperature change at the end (since its kinetic energy is 0 at all times , and the wire cannot do any work upon the ball since its length is fixed)
whereas on the one on the ground, the work done is Q-mgh which must reflect as temperature change at the end (once again, the grounds normal reaction cant do any work on it, but some amount of heat must be expended to raise the level of centre of mass)
so the hanging steel ball acquires greater temperature
i think so, am i right or close?