Advanced Mechanics

This lesson comprises eight (8) master classes focusing on:

• Gravitational filed
• Projectile motion
• Uniform circular motion
• Rotational motion
• Orbits
• Kepler's laws
• Energy of orbits

Content:

PH12-12

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

• 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
• Conduct a practical investigation to collect primary data in order to validate the relationships derived above.
• Solve problems, create models and make quantitative predictions by applying the equations of motion relationships for uniformly accelerated and constant rectilinear motion

Why do objects move in circles?

• Conduct investigations to explain and evaluate, for objects executing uniform circular motion, the relationships 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
• Solve problems, model and make quantitative predictions about objects executing uniform circular motion in a variety of situations, using the following relationships:
  • \( a_c=\frac{v^2}{r} \)
  • \( v=\frac{2 \pi r}{T} \)
  • \(F_c=\frac{mv^2}{r} \)
  • \( \omega=\frac{ \bigtriangleup \theta}{t} \)

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

• Apply qualitatively and quantitatively Newton's Law of Universal Gravitation to:
  • determine the force of gravity between two objects \( F=\frac{GMm}{r^2} \)
  • investigate the factors that affect the gravitational field strength \( g=\frac{GM}{r^2} \)
  • predict the gravitational field strength at any point in a gravitational field, including at the surface of a planet
• 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
• 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:
  • \( v=\frac{2 \pi r}{T} \)
  • \( \frac{r^3}{T^2}=\frac{GM}{4 \pi_2} \)
• 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 \( U+K=-\frac{GMm}{2r} \)
  • energy changes that occur when satellites move between orbits
  • Kepler’s Laws of Planetary Motion

PH12-4

• Select qualitative and quantitative data and information and represent them using a range of formats, digital technologies and appropriate media
• Apply quantitative processes where appropriate
• Evaluate and improve the quality of data

PH12-5

• Derive trends, patterns and relationships in data and information
• Assess error, uncertainty and limitations in data
• Assess the relevance, accuracy, validity and reliability of primary and secondary data and suggest improvements to investigations

PH12-6

• Use modelling (including mathematical examples) to explain phenomena, make predictions and solve problems using evidence from primary and secondary sources
• Use scientific evidence and critical thinking skills to solve problems

PH12-7

• Select and use suitable forms of digital, visual, written and/or oral forms of communication
• Select and apply appropriate scientific notations, nomenclature and scientific language to communicate in a variety of contexts
• Construct evidence-based arguments and engage in peer feedback to evaluate an argument or conclusion