@@ -6,24 +6,31 @@ Box on an incline
66
77All vectors are in newton.
88
9-
109{.float-img-left}
1110
11+ Notation:
12+ fg = gravitational accelleration
13+ m = mass of box
14+
1215> fg = V2 0 (- 10 )
1316> m = 2
14- > alpha = 30
15- >
17+
1618> unit_normal :: Double -> Vector2 Double
1719> unit_normal a = V2 (cos a) (sin a)
18- >
20+
21+ Force against the incline from the box:
22+
1923> f_l_ :: Vector2 Double -> Angle -> Vector2 Double
2024> f_l_ fa a = scale ((magnitude fa) * (cos a)) (unit_normal (a- (pi / 2 )))
21- >
25+
26+ The normal against the incline:
27+
2228> fn :: Vector2 Double -> Angle -> Vector2 Double
2329> fn fa a = negate (f_l_ fa a)
2430
2531Frictionfree incline:
2632
33+ Force resultant:
2734
2835> fr :: Vector2 Double -> Angle -> Vector2 Double
2936> fr fa a = (fn fa a) + fa
@@ -52,24 +59,14 @@ Odd: Motsatt gravitation ger något underligt? Vi säger fortfarande att norm
5259
5360Good: 90* lutning - faller med G.
5461
55-
5662*Main> fr (V2 0 10) (pi/3)
5763
5864(-4.330127018922194 x, 7.499999999999999 y)
5965
60-
6166*Main> fr (V2 0 10) (pi/4)
6267
6368(-5.0 x, 4.999999999999999 y)
6469
65- Good: 45* lutning - 5N både i x och y led. Pyth: 5^2 + 5^2 =/= 10^2
66-
67- det borde bli: 100 = a^2 + a^2
68- 50 = a^2
69- 5*sqrt(2) = a
70-
71- och det är det ju. xD
72-
7370*Main> fr (V2 0 10) (pi/6)
7471
7572(-4.330127018922193 x, 2.499999999999999 y)
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