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Physics/src/Examples/Gungbraeda.lhs

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@@ -13,7 +13,7 @@ Exam excercise 3, 2017-01-13
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> balk_L = 5.0 # length
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> two = 2.0 # one
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![Gungbraede](Gungbraede.png){.float-img-left}
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![Teeter](teeter.png){.float-img-left}
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Direct implication:
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Physics/src/Examples/krafter_pa_lador.lhs

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@@ -4,41 +4,39 @@ Box on an incline
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> import Vector.Vector
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Alla vektorer är i Newton
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All vectors are in newton.
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![Lutande plan](lutande_plan.png){.float-img-left}
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![Incline](incline.png){.float-img-left}
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> fg = V2 0 (-10)
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> m = 2
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> alpha = 30
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>
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> enh_normal :: Double -> Vector2
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> enh_normal a = V2 (cos a) (sin a)
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> unit_normal :: Double -> Vector2
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> unit_normal a = V2 (cos a) (sin a)
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>
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> f_l_ :: Vector2 -> Angle -> Vector2
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> f_l_ fa a = scale ((magnitude fa) * (cos a)) (enh_normal (a-(pi/2)))
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> f_l_ fa a = scale ((magnitude fa) * (cos a)) (unit_normal (a-(pi/2)))
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>
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> fn :: Vector2 -> Angle -> Vector2
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> fn fa a = negate (f_l_ fa a)
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Friktionsfritt plan:
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Frictionfree incline:
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> fr :: Vector2 -> Angle -> Vector2
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> fr fa a = (fn fa a) + fa
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** Tester:**
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** Tests:**
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------------
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*Main> fr (V2 0 10) 0
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(0.0 x, 0.0 y)
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Good: Inge lutning - står still.
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Good: No inclination - stands still.
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*Main> fr (V2 0 (-10)) 0
@@ -77,7 +75,7 @@ Good: 45* lutning - 5N både i x och y led. Pyth: 5^2 + 5^2 =/= 10^2
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(-4.330127018922193 x, 2.499999999999999 y)
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**Friktionskonstant - i rörelse:**
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**Frictionconstant - in motion:**
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\begin{align}
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F_{friction} = \mu * F_{normal} \iff \mu = \frac{F_{friction}}{F_{normal}}
@@ -86,24 +84,27 @@ Good: 45* lutning - 5N både i x och y led. Pyth: 5^2 + 5^2 =/= 10^2
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> us = 0.5
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> uk = 0.4
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Add image how friction depends if there is movement.
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> type FricConst = Double
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friktionen
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Friction:
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friks = Fn * us, us = friktion statisk
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friks = Fn * us, us = friction static
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frikk = Fn * uk, uk = friktion kinetisk
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frikk = Fn * uk, uk = friction kinetic
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Vi har normalkraften, o beh bara konstanterna.
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We have the normal force and only needs the constants.
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Speed har inget att göra med N för friktion? Dock gäller F*m = Nm = work = J = bugatti bränner däck.
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The current speed does not affect the friction. However F*M = Nm = work = J -> racer cars burn tires.
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> motscalar :: FricConst -> Vector2 -> Scalar
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> motscalar u f = u * (magnitude f)
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Från en rörelse eller vekt, fixa komplementet
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> enh_vekt :: Vector2 -> Vector2
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> enh_vekt v | magnitude v == 0 = (V2 0 0)
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> | otherwise = scale (1 / (magnitude v)) v
@@ -115,7 +116,7 @@ Från en rörelse eller vekt, fixa komplementet
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> motkraftv :: FricConst -> Vector2 -> Vector2 -> Vector2
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> motkraftv u n v = scale (u * (magnitude n)) (negate (enh_vekt v))
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Nu ska vi bara summera
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Now we just need to sum the force vectors:
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> fru :: Vector2 -> Angle -> FricConst -> Vector2
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> fru fa a u = (fr fa a) + (motkraftv u (fn fa a) (fr fa a))
@@ -167,9 +168,7 @@ Den statiska friktionen är konstig. Den borde stå still vid låg vinkel o hög
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Jag summerar ju visserligen krafterna, så det är nog något lurt med friktionshanteringen.
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Tester:
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Tests:
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fr
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*Main> fr fg (pi/3)

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