1. 2. Newtonian Mechanics Newton’s law Motion under constant forces
Position dependent forces
Velocity dependent forces
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2. 2.2 Motion under a constant force
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3. Bottom 에서의 속도는?
마찰이 있을 때와 없을 때
마찰이 있을 때
마찰이 없을 때
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4. 2.3 Position dependent force
Potential E can be defined as
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5. v0 Free fall Maximum height of a ball thrown upward
2.3 Position dependent force continued
Free fall v0 h
Maximum height of a ball thrown upward
For a given initial velocity, there always exists maximum height.
Is it correct?
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6. Variation of Gravity with height
2.3 Position dependent force continued
Variation of Gravity with height
Definition of the gravitational acceleration
Escape speed
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7. = + Morse function V(x) : potential energy of a diatomic molecule x
2.3 Position dependent force continued
Morse function V(x) : potential energy of a diatomic molecule = + x
Therefore, x=x0 is the equilibrium position.
separation of the atoms
and –V0 is the binding energy.
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8. Near the equilibrium position V(x) can be expanded
2.3 Position dependent force continued
Near the equilibrium position V(x) can be expanded
The potential becomes parabolic in the leading order,
And it can be considered as a simple harmonic oscillator problem.
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9. Maximum separation at room temp.?
2.3 Position dependent force continued
Hydrogen molecule
Maximum separation at room temp.?
Binding energy = eV
Equilibrium separation = nm
Delta = nm
Room temp. ~ 1/40 eV
X = nm
~3.6% change in size
which means thermal expansion
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10. 2.4 velocity dependent force
in SI unit,
The ratio
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11. As time goes to infinity, it converges to a point.
2.3 velocity dependent force continued
linear resistance
(Dominant in low speed)
quadratic resistance
(Dominant in high speed)
As time goes to infinity, it converges to a point.
As time goes to infinity, does it converge???
It shows logarithmic divergence!!!
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12. vertical fall through a fluid (linear resistance)mg
-C1v
As time goes to infinity, the velocity approaches to –mg/c1.
Terminal velocity
where the terminal speed = , and =
It occurs when F = 0.
If an object is dropped, after , v = vt
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13. vertical fall through a fluid (quadratic resistance)
If an object is dropped, after , v = vt
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14. Terminal speed of raindrops and basketballs
Raindrop ~ 0.1 mm
Basketball ~ 0.25 m
The ratio
raindrops
basketballs
The ratio = 0.14 v
v = 7.1m/s
linear term dominates.
The ratio = 350 v
v = m/s
quadratic term dominates.
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15. The end 2. Newtonian Mechanics Newton’s law
Motion under constant forces
Position dependent forces
Velocity dependent forces
The end
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