Year 12 – Advanced Mechanics

New material to the syllabus highlighted in blue
Material modified from the old syllabus in yellow
Projectile motion

Inquiry question: How can models that are used to explain projectile motion be used to analyse and make predictions?

Students:

  • analyse the motion of projectiles by resolving the motion into horizontal and vertical components, making the following assumptions:
    • a constant vertical acceleration due to gravity
    • zero air resistance
  • apply the modelling of projectile motion to quantitatively derive the relationships between the following variables:
    • initial velocity
    • launch angle
    • maximum height
    • time of flight
    • final velocity
    • launch height
    • horizontal range of the projectile (ACSPH099)
  • conduct a practical investigation to collect primary data in order to validate the relationships derived above
  • solve problems, create models and make quantitative predications by applying the equations of motion relationships for uniformly accelerated and constant rectilinear motion

Resource – Projectile Motion – 2 Pages

Circular Motion

Inquiry question: Why do objects move in circles?

Students:

    • conduct investigations to explain and evaluate, for objects executing uniform circular motion, the relationship that exist between:
      • centripetal force
      • mass
      • speed
      • radius
    • analyse the forces acting on an object executing uniform circular motion in a variety of situations, for example:
      • cars moving around horizontal circular bends
      • a mass on a string
      • objects on banked tracks (ACSPH100)
    • solve problems, model and make quantitative predictions about objects executing uniform circular motion in a variety of situations, using the following relationships
      • \vec{a} = \frac{\lvert{\vec{v}}\rvert^{2}}{\vec{r}}
      • \sum{\vec{F}} = \frac{m\lvert{\vec{v}}\rvert^{2}}{\vec{r}}
      • \omega = \frac{\Delta\theta}{t}

Resource – Circular Motion – Concepts – 1 Page

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  • investigate the relationship between the total energy and work done on an object executing uniform circular motion
  • investigate the relationship between the rotation of mechanical systems and the applied torque (\tau = \vec{r}\vec{F}_{\perp} = \lvert\vec{r}\rvert\lvert\vec{F}\rvert\sin{\theta})

Resource – Circular Motion – Energy and Work – 2 pages

Resource – Circular Motion – Rotation and Torque – 2 pages

Motion in Gravitational Fields

Inquiry question: How does the force of gravity determine the motion of planets and satellites?

Students:

  • apply qualitatively and quantitatively Newton’s Law of Universal Gravitation to:
    • determine the force of gravity between two objects (\vec{F} = -\frac{GMm}{\vec{r}^2})
    • investigate the factors that affect the gravitational field strength (\vec{g} = \frac{GM}{\vec{r}^2})

Resource – Gravitational Motion 1 – 2 Pages

  • predict the gravitational field strength at any point in a gravitational field, including at the surface of a planet (ACSPH094, ACSPH095, ACSPH097)
  • investigate the orbital motion of planets and artificial satellites when applying the relationships between the following quantities:
    • gravitational force
    • centripetal force
    • centripetal acceleration
    • mass
    • orbital radius
    • orbital velocity
    • orbital period
  • predict quantitatively the orbital properties of planets and satellites in a variety of situations, including near the earth and geostationary orbits, and relate these to their uses (ACSPH101)
  • investigate the relationship of Kepler’s Laws of Planetary Motion to the forces acting on, and the total energy of, planets in circular and non-circular orbits using: (ACSPH101)
    • {v_o} = \frac{2\pi r}{T}
    • \frac{r^3}{T^2} = \frac{GM}{4\pi^2}
  • derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to a variety of situations, including but not limited to:
    • the concept of escape velocity (v_{esc} = \sqrt{\frac{2GM}{r}})
    • total potential energy of a planet or satellite in its orbit (U = -\frac{GMm}{r})
    • total energy of a planet or satellite in its orbit (E = - \frac{GMm}{2r})
    • energy changes that occur when satellites move between orbits (ACSPH096)
    • Kepler’s Laws of Planetary Motion (ACSPH101)

Resource – Gravitational Motion 2 – 1 Page

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