§-Module

Module 5: Advanced Mechanics

8 dot points across 3 inquiry questions, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

Inquiry Question 1: 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

Projectile motion. Resolving velocity into components, applying SUVAT to each axis independently, the standard worked range and maximum height example, and the traps markers look for.

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Inquiry Question 2: Why do objects move in circles?

Investigate the relationship between the forces acting on objects in non-uniform circular motion (banked tracks, conical pendulums, vertical circles) and apply the relationship tau = r F sin theta for torque

Non-uniform circular motion. Banked tracks, the conical pendulum, vertical loops, the role of torque, and the worked banking-angle calculation that markers expect.

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Conduct investigations to explain and evaluate, for objects executing uniform circular motion, the relationships that exist between centripetal force, mass, speed and radius, and solve problems using the relationships a_c = v^2 / r, v = 2 pi r / T, F_c = m v^2 / r and omega = delta theta / delta t

Uniform circular motion. Centripetal acceleration and force, the link between period, speed and radius, the standard worked car-on-a-bend example, and the conceptual traps about what provides the centripetal force.

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Inquiry Question 3: How does the force of gravity determine the motion of planets and satellites?

Predict quantitatively the orbital properties of planets and artificial satellites in a variety of situations, including near-Earth and geostationary orbits, using the relationship between orbital speed, radius, and period

Orbital motion of artificial satellites. The derivation of orbital speed from gravity-as-centripetal-force, low Earth and geostationary orbits, the worked LEO example, and the patterns markers look for.

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Derive and apply the concept of gravitational potential energy in a radial gravitational field, U = -G M m / r, including the concept of escape velocity

Gravitational potential energy in radial fields. Why U is negative, how it differs from the mgh approximation, the derivation of escape velocity, and the standard worked example using Earth.

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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 = 2 pi r / T and T^2 / r^3 = 4 pi^2 / (G M)

Kepler's three laws. Elliptical orbits, equal areas in equal times, the period-radius relationship, the derivation from Newton's laws, and the worked geostationary-satellite example.

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Apply the concepts of gravitational potential energy and kinetic energy to determine the total energy of a planet or satellite in its orbit, and the energy changes that occur when satellites move between orbits

Energy in orbits. Total mechanical energy E = -G M m / (2r), the K and U relationship in circular orbits, energy changes during orbit transfers, and the worked Hohmann-style example.

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Apply qualitatively and quantitatively Newton's Law of Universal Gravitation, F = G m_1 m_2 / r^2, to determine the magnitude of force, gravitational field strength g = G M / r^2, and acceleration due to gravity at different points in a radial gravitational field

Newton's Law of Universal Gravitation. The inverse-square law, gravitational field strength, calculating g at different altitudes, and the worked surface-gravity example.

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