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Ascending with Cannon: Calculating Height and Energy Potentials

Explore the physics of shooting a cannonball upwards, ignoring air resistance, to achieve maximum height above the Earth's surface. Analyze the conservation of energy and gravitational potential energy to understand the dynamics involved in reaching greater altitudes. Utilize relevant equations to calculate the varying heights and energy potentials based on different models. Investigate the differences between the general model (green) and the potential energy and velocity model (red).

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Ascending with Cannon: Calculating Height and Energy Potentials

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Presentation Transcript

  1. ammutaan korkealle mikko rahikka 2010

  2. ammu • ammutaan tykillä ylöspäin • olkoon alkunopeus v0 • kuvitellaan, että ei ole ilmanvastusta • nousukorkeus on h

  3. energia säilyy ja ollaan lähellä Maan pintaa

  4. pyritään korkeammalle • unohdetaan että Maa pyörii, tai ammutaan Pohjoisnavalta ylöspäin • R = Maan säde Pohjoisnavalla = 6357000 m • M = Maan massa = 5,974·1024 kg • G = gravitaatiovakio= 6,67259·10-11Nm2/kg2 • h = nousukorkeus • v =10 m/s

  5. energia säilyy • gravitaatiokentän potentiaalienergialla • pohdi mistä tuo ero johtuu, onko se pelkkä pyöristysvirhe vai …? • itseasiassa tuon saisi sievemmäksikin • Wolfram Alphalla solve-G*m*M/R+(m*v^2) /2 = -G*m*M/(R+x) for x

  6. mallien ero korkeus (m) • vihreä on yleisellä mallilla, putoamiskiihtyvyys pienenee ylöspäin mentäessä • punainen on mgh potentiaalienergia nopeus (m/s)

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