GigglingSquid319
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#1
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#1
Use Newton's laws of motion and a requirement for simple harmonic motion to explain why the amplitude of oscillation of the iodine ion is about 0.08 picometers when the amplitude of oscillation of the hydrogen ion is about 10 picometers.

(Background: There's a mechanical model of a molecule consisting of two unequal masses connected by a spring of force constant 292Nm^-1, the ions oscillate in SHM when disturbed.)

I've got that Newton's 2nd Law is F=ma and that Newton's 3rd law gives that F (Hydrogen) and F (Iodine) are equal... And that Simple Harmonic Motion requires acceleration to be directly proportional to -displacement... But I dont understand how they link in this question?
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MantisToboggan
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#2
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(Original post by GigglingSquid319)
Use Newton's laws of motion and a requirement for simple harmonic motion to explain why the amplitude of oscillation of the iodine ion is about 0.08 picometers when the amplitude of oscillation of the hydrogen ion is about 10 picometers.

(Background: There's a mechanical model of a molecule consisting of two unequal masses connected by a spring of force constant 292Nm^-1, the ions oscillate in SHM when disturbed.)

I've got that Newton's 2nd Law is F=ma and that Newton's 3rd law gives that F (Hydrogen) and F (Iodine) are equal... And that Simple Harmonic Motion requires acceleration to be directly proportional to -displacement... But I dont understand how they link in this question?
I don't know exactly what the mark scheme says but I assume that since the iodine atom has a higher mass, for the same force, it's max acceleration will be lower. This means that since displacement is proportional to acceleration, the max displacement will also be lower as a result.
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MantisToboggan
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#3
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(Original post by MantisToboggan)
I don't know exactly what the mark scheme says but I assume that since the iodine atom has a higher mass, for the same force, it's max acceleration will be lower. This means that since displacement is proportional to acceleration, the max displacement will also be lower as a result.
This links to newtons 2nd law simplified to f=ma
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Kyx
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#4
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#4
I assume we can assume they act as if they are springs?

So T= 2 * pi * (sqrt)[m/k]


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Eimmanuel
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#5
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(Original post by GigglingSquid319)
Use Newton's laws of motion and a requirement for simple harmonic motion to explain why the amplitude of oscillation of the iodine ion is about 0.08 picometers when the amplitude of oscillation of the hydrogen ion is about 10 picometers.

(Background: There's a mechanical model of a molecule consisting of two unequal masses connected by a spring of force constant 292Nm^-1, the ions oscillate in SHM when disturbed.)

I've got that Newton's 2nd Law is F=ma and that Newton's 3rd law gives that F (Hydrogen) and F (Iodine) are equal... And that Simple Harmonic Motion requires acceleration to be directly proportional to -displacement... But I dont understand how they link in this question?

Added to what MantisToboggan has explained, we can model the force between hydrogen and iodine ions as a simple spring force – kx where k is the spring constant and x is the displacement of the ion.

So we can write Newton’s second law as:

kx = ma
so we can say acceleration is directly proportional to the displacement.

 \dfrac{x_I}{x_H} = \dfrac{a_I}{a_H}


From F = mIaI and F = mHaH, we would get

 \dfrac{x_I}{x_H} = \dfrac{a_I}{a_H} = \dfrac{m_H}{m_I}

Hope it helps.
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GigglingSquid319
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#6
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#6
Thank you guys for your explanations!
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