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Physics/src/Examples/Box_incline.lhs

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@@ -6,24 +6,31 @@ Box on an incline
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All vectors are in newton.
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![Incline](incline.png){.float-img-left}
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Notation:
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fg = gravitational accelleration
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m = mass of box
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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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> unit_normal :: Double -> Vector2 Double
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> unit_normal a = V2 (cos a) (sin a)
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>
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Force against the incline from the box:
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> f_l_ :: Vector2 Double -> Angle -> Vector2 Double
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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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The normal against the incline:
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> fn :: Vector2 Double -> Angle -> Vector2 Double
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> fn fa a = negate (f_l_ fa a)
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Frictionfree incline:
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Force resultant:
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> fr :: Vector2 Double -> Angle -> Vector2 Double
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> fr fa a = (fn fa a) + fa
@@ -52,24 +59,14 @@ Odd: Motsatt gravitation ger något underligt? Vi säger fortfarande att norm
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Good: 90* lutning - faller med G.
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*Main> fr (V2 0 10) (pi/3)
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(-4.330127018922194 x, 7.499999999999999 y)
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*Main> fr (V2 0 10) (pi/4)
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(-5.0 x, 4.999999999999999 y)
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Good: 45* lutning - 5N både i x och y led. Pyth: 5^2 + 5^2 =/= 10^2
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det borde bli: 100 = a^2 + a^2
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50 = a^2
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5*sqrt(2) = a
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och det är det ju. xD
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*Main> fr (V2 0 10) (pi/6)
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(-4.330127018922193 x, 2.499999999999999 y)

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