Conservation of energy thought experiment | Mathematics | Page 1

split agate Mar 22, 2024, 3:25 AM

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Hi guys, our teacher gave a thought experiment and I just want to know if my thinking process is correct.
Suppose objects A and B are mass M hanging from 2 strings length L. Object A is inclined to the left h height at angle theta. B is hanging down from the ceiling perfectly.
Assume when releasing A, the collision will be perfectly elastic.

How high will object A reach after the collision in terms of H?

Here's my solution:

Ep = mgh
Ek = 1/2(mv^2)

Ep = Ek
mgh = 1/2mv^2

After collision Ep and Ek will be divided perfectly between the two object

Ep/2 = Ek

mgh/2 = 1/2mv^2

mgh = 0.5mv^2/2
mgh = 1/4mv^2

h = 1/4mv^2/mg

m and m cancels out
g (gravitational acceleration of earth considered as 10 for simplicity)

h = 1/4v^2/10

h = v^2/40

I would like to know what you guys think the solution should be.

violet egretBOT Mar 22, 2024, 3:25 AM

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split agate Mar 22, 2024, 3:27 AM

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<@&286206848099549185>

noble relic Mar 22, 2024, 4:21 AM

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@split agateyou can't violate conservation of momentum, the system was moving right and it will continue moving right after the collision

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as far as i understand it will just reflect everything, A will be motionless and B will rise to H

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like balls in pool

viral verge Mar 22, 2024, 4:43 AM

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frownyfrog is right

noble relic Mar 22, 2024, 4:57 AM

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when A and B elastically collide, conservation of momentum allows A to have any speed, which defines the speed of B
conservation of energy does that too, in a different relation
and there's like one unique way where they intersect

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(as far as i understand)

viral verge Mar 22, 2024, 5:08 AM

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yep

noble relic Mar 22, 2024, 5:33 AM

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unless you mean it's not a head on collision, and they have some unknown size and complicated stuff like that, then i don't know

viral verge Mar 22, 2024, 6:04 AM

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it's the same stuff just with vectors

the drawing is horrible. I think it safe to assume for the experiment that we're simplifying this to a 1D problem because either:

the radius of the masses is 0 //which I hate because how could they collide or not be blackholes
the masses are anchored with offsets = mass' radius and parallel to the horizontal component of the raised pendulum

split agate Mar 22, 2024, 1:27 PM

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noble relic <@448979105275445253>you can't violate conservation of momentum, the system was ...

so when A collides to B, B will reach the height of A initialy

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then when B collides back to A, A will reach it's initial height?

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@noble relic

noble relic Mar 22, 2024, 1:28 PM

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uh huh

split agate Mar 22, 2024, 1:28 PM

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ok

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thanks pookie

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.close

#Conservation of energy thought experiment