User:FatF/Aufgabenlösungen

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Aufgabenlösungen

3.17

Angabe

  • geg.: Höhe (h = 15m)
  • ges.: Anfangsgeschwindigkeit (v0); Steigzeit (ts); Fallzeit (tf)

Rechnung

4.3

geg.:

  • F = 50 N
  • s = 80 cm

ges.:

  • D
  • WSp

a)

[math]D = \frac{F}{s}[/math]

[math]D = \frac{50 N}{0,8 m}[/math]

[math]D = 62,5 \frac{N}{m}[/math]


[math]W_Sp = \frac{1}{2} D * s^2[/math]

[math]W_Sp1 = \frac{1}{2} 62,5 \frac{N}{m} * (0,8 m)^2[/math]

[math]W_Sp1 = 20 J \frac{}{}[/math]


b)

geg.: s_2 = 50 cm + 80 cm = 1,3 m

ges.: WSp2


[math]W_Sp2 = \frac{1}{2} 62,5 \frac{N}{m} * (1,3 m)^2 - W_Sp1[/math]

[math]W_Sp2 = 52,8 J - 20 J = 32,8 J \frac{}{}[/math]

c)

ges.: F

[math]F = D * s \frac{}{}[/math]

[math]F = 62,5 \frac{N}{m} * 1,3 m[/math]

[math]F = 1,3 N \frac{}{}[/math]


3.9

[math]h = 15m \frac{}{}[/math]

[math]h = \frac{v_2}{2g}[/math]

[math]v_0 = \sqrt[]{30 * 9.81}\frac{m}{s}[/math]

[math]v_0 = 17,16 \frac{m}{s}[/math]


[math]t_s = \frac{v_0}{g}[/math]

[math]t_s = \frac{17,6}{9,81}s[/math]

[math]t_s = 1,75 s \frac{}{}[/math]


[math]t_s = t_f \frac{}{}[/math]

[math]t_s = 1,75 s \frac{}{}[/math]

4.7 Hell Racer

[math]E_kin = \frac{1}{2}*m*v^2[/math]

[math]E_kin = \frac{1}{2}*0,070*40^2 J[/math]

[math]E_kin = \frac{}{} 0,56 J[/math]


[math]E_pot = \frac{}{} m*g*h[/math]

[math]E_pot = \frac{}{} m*g*2r[/math]

[math]E_pot = \frac{}{} 0,070*9,81*2*0,50 J[/math]

[math]E_pot = \frac{}{} 0,69 J[/math]

4.16

geg.:

  • m1 = 1700 kg
  • m2 = 650 kg
  • v1 = 54 km/h = 15 m/s
  • v2 = 36 km/h = 10 m/s

Impulsverhalten

a)

p = p'

p1 + p2 = p'

m1v1 + m2v2 = (m1 + m2) * u

[math]u = \frac{m_1v_1 + m_2v_2}{m_1 + m_2} \frac{m}{s}[/math]

[math]u = \frac{1700*15 + 650*10}{1700 + 650} \frac{m}{s}[/math]

[math]u = \frac{32000}{2350} \frac{m}{s}[/math]

[math]u = 14 \frac{m}{s}[/math]

b)

[math]E_{kin} = \frac{1}{2} m_1 v_1^2 = 191 kJ[/math]

[math]E'_{kin} = \frac{1}{2} m_2 u^2 = 158 kJ[/math]

>>> [math]\delta E = 33 kJ \frac{}{}[/math]


5.6

a)

geg.:

  • Masse m = 0,80 kg
  • Radius r = 50 cm
  • Geschwindigkeit v = 3,4 m/s

ges.:

  • (Umkreis u)
  • (Kraft FZ)
  • (Kraft mit Erdanziehungskraft FZ.grav)
  • Kraft unten am Kreis FZ.unten
  • Kraft oben am Kreis FZ.oben

[math]u = 2r\pi = 3,14 m \frac{}{}[/math]


[math]T = \frac{u}{v}[/math]

[math]T = \frac{3,14 m}{3,4 m}[/math]

[math]T = 0,924 s \frac{}{}[/math]


[math]\Omega = \frac{2\pi}{T}[/math]


[math]F_Z = m\Omega^2r \frac{}{}[/math]

[math]F_Z = 0,80 kg (\frac{2\pi}{0,924s})^2 0,50m[/math]

[math]F_Z = 18,49 N \frac{}{}[/math]


[math]g = 9,81 \frac{N}{kg}[/math]


[math]F_{Z.grav} = 9,81 \frac{N}{kg} 0,8 kg[/math]

[math]F_{Z.grav} = 7,84 N \frac{}{}[/math]


[math]F_{Z.oben} = F_Z - 7,84 N \frac{}{}[/math]

[math]F_{Z.oben} = 10,65 N \frac{}{}[/math]


[math]F_{Z.unten} = F_Z + 7,84 N \frac{}{}[/math]

[math]F_{Z.unten} = 26,35 N \frac{}{}[/math]