Topic 2: Mechanics

2.1 Motion

2.1 Essential idea: Motion may be described and analysed by the use of graphs and equations.

2.1 Nature of science:

Observations: The ideas of motion are fundamental to many areas of physics, providing a link to the consideration of forces and their implication. The kinematic equations for uniform acceleration were developed through careful observations of the natural world. (1.8)

2.1 Understandings:

• Distance and displacement

• Speed and velocity

• Acceleration

• Graphs describing motion

• Equations of motion for uniform acceleration

• Projectile motion

• Fluid resistance and terminal speed

2.1 Applications and skills:

• Determining instantaneous and average values for velocity, speed and acceleration

• Solving problems using equations of motion for uniform acceleration

• Sketching and interpreting motion graphs

• Determining the acceleration of free-fall experimentally

• Analysing projectile motion, including the resolution of vertical and horizontal components of acceleration, velocity and displacement

• Qualitatively describing the effect of fluid resistance on falling objects or projectiles, including reaching terminal speed

2.1 Guidance:

• Calculations will be restricted to those neglecting air resistance

• Projectile motion will only involve problems using a constant value of g close to the surface of the Earth

• The equation of the path of a projectile will not be required

2.1 International-mindedness:

• International cooperation is needed for tracking shipping, land-based transport, aircraft and objects in space

2.1 Theory of knowledge:

• The independence of horizontal and vertical motion in projectile motion seems to be counter-intuitive. How do scientists work around their intuitions? How do scientists make use of their intuitions?

2.1 Utilization:

• Diving, parachuting and similar activities where fluid resistance affects motion

• The accurate use of ballistics requires careful analysis

• Biomechanics (see Sports, exercise and health science SL)

• Quadratic functions (also in Math)

• The kinematic equations are treated in calculus form in Mathematics HL

2.1 Aims:

• Aim 2: much of the development of classical physics has been built on the advances in kinematics

• Aim 6: experiments, including use of data logging, could include (but are not limited to): determination of g, estimating speed using travel timetables, analysing projectile motion, and investigating motion through a fluid

• Aim 7: technology has allowed for more accurate and precise measurements of motion, including video analysis of real-life projectiles and modelling/simulations of terminal velocity

2.1 Data booklet reference:

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2.2 Forces

2.2 Essential idea: Classical physics requires a force to change a state of motion, as suggested by Newton in his laws of motion.

2.2 Nature of science:

Using mathematics: Isaac Newton provided the basis for much of our understanding of forces and motion by formalizing the previous work of scientists through the application of mathematics by inventing calculus to assist with this. (2.4)

Intuition: The tale of the falling apple describes simply one of the many flashes of intuition that went into the publication of Philosophiæ Naturalis Principia Mathematica in 1687. (1.5)

2.2 Understandings:

• Objects as point particles

• Free-body diagrams

• Translational equilibrium

• Newton’s laws of motion

• Solid friction

2.2 Applications and skills:

• Representing forces as vectors

• Sketching and interpreting free-body diagrams

• Describing the consequences of Newton’s first law for translational equilibrium

• Using Newton’s second law quantitatively and qualitatively

• Identifying force pairs in the context of Newton’s third law

• Solving problems involving forces and determining resultant force

• Describing solid friction (static and dynamic) by coefficients of friction

2.2 Guidance:

• Students should label forces using commonly accepted names or symbols (for example: weight or force of gravity or mg)

• Free-body diagrams should show scaled vector lengths acting from the point of application

• Examples and questions will be limited to constant mass

• mg should be identified as weight

• Calculations relating to the determination of resultant forces will be restricted to one- and two-dimensional situations

2.2 Theory of knowledge:

• Classical physics believed that the whole of the future of the universe could be predicted from knowledge of the present state. To what extent can knowledge of the present give us knowledge of the future?

2.2 Utilization:

• Motion of charged particles in fields (see Physics sub-topics 5.4, 6.1, 11.1, 12.2)

• Application of friction in circular motion (see Physics sub-topic 6.1)

• Construction (considering ancient and modern approaches to safety, longevity and consideration of local weather and geological influences)

• Biomechanics (see Sports, exercise and health science SL sub-topic 4.3)

2.2 Aims:

• Aims 2 and 3: Newton’s work is often described by the quote from a letter he wrote to his rival, Robert Hooke, 11 years before the publication of Philosophi & Naturalis Principia Mathematica, which states: “What Descartes did was a good step. You have added much several ways, and especially in taking the colours of thin plates into philosophical consideration. If I have seen a little further it is by standing on the shoulders of Giants.” It should be remembered that this quote is also inspired, this time by writers who had been using versions of it for at least 500 years before Newton’s time.

• Aim 6: experiments could include (but are not limited to): verification of

Newton’s second law; investigating forces in equilibrium; determination of the

effects of friction

2.2 Data booklet reference:

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2.3 Work, Energy, and Power

2.3 Essential idea: The fundamental concept of energy lays the basis upon which much of science is built.

2.3 Nature of science:

Theories: Many phenomena can be fundamentally understood through application of the theory of conservation of energy. Over time, scientists have utilized this theory both to explain natural phenomena and, more importantly, to predict the outcome of previously unknown interactions. The concept of energy has evolved as a result of recognition of the relationship between mass and energy. (2.2)

2.3 Understandings:

• Kinetic energy

• Gravitational potential energy

• Elastic potential energy

• Work done as energy transfer

• Power as rate of energy transfer

• Principle of conservation of energy

• Efficiency

2.3 Applications and skills:

• Discussing the conservation of total energy within energy transformations

• Sketching and interpreting force–distance graphs

• Determining work done including cases where a resistive force acts

• Solving problems involving power

• Quantitatively describing efficiency in energy transfers

2.3 Guidance:

• Cases where the line of action of the force and the displacement are not parallel should be considered

• Examples should include force–distance graphs for variable forces

2.3 Theory of knowledge:

• To what extent is scientific knowledge based on fundamental concepts such as energy? What happens to scientific knowledge when our understanding of such fundamental concepts changes or evolves?

2.3 Utilization:

• Energy is also covered in other group 4 subjects (for example, see: Biology topics 2, 4 and 8; Chemistry topics 5, 15, and C; Sports, exercise and health science topics 3, A.2, C.3 and D.3; Environmental systems and societies topics 1, 2, and 3)

• Energy conversions are essential for electrical energy generation (see Physics topic 5 and sub-topic 8.1)

• Energy changes occurring in simple harmonic motion (see Physics sub-topics 4.1 and 9.1)

2.3 Aims:

• Aim 6: experiments could include (but are not limited to): relationship of kinetic and gravitational potential energy for a falling mass; power and efficiency of mechanical objects; comparison of different situations involving elastic potential energy

• Aim 8: by linking this sub-topic with topic 8, students should be aware of the importance of efficiency and its impact of conserving the fuel used for energy production

2.3 Data booklet reference

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2.4 Momentum and Impulse

2.4 Essential idea: Conservation of momentum is an example of a law that is never violated.

2.4 Nature of science:

The concept of momentum and the principle of momentum conservation can be used to analyse and predict the outcome of a wide range of physical interactions, from macroscopic motion to microscopic collisions. (1.9)

2.4 Understandings:

• Newton’s second law expressed in terms of rate of change of momentum

• Impulse and force–time graphs

• Conservation of linear momentum

• Elastic collisions, inelastic collisions and explosions

2.4 Applications and skills:

• Applying conservation of momentum in simple isolated systems including (but not limited to) collisions, explosions, or water jets

• Using Newton’s second law quantitatively and qualitatively in cases where mass is not constant

• Sketching and interpreting force–time graphs

• Determining impulse in various contexts including (but not limited to) car safety and sports

• Qualitatively and quantitatively comparing situations involving elastic collisions, inelastic collisions and explosions

2.4 Guidance:

• Students should be aware that F = ma is equivalent of F=p/t only when mass is constant

• Solving simultaneous equations involving conservation of momentum and energy in collisions will not be required

• Calculations relating to collisions and explosions will be restricted to one dimensional situations

• A comparison between energy involved in inelastic collisions (in which kinetic energy is not conserved) and the conservation of (total) energy should be made.

2.4 International-mindedness:

• Automobile passive safety standards have been adopted across the globe based on research conducted in many countries

2.4 Theory of knowledge:

• Do conservation laws restrict or enable further development in physics?

2.4 Utilization:

• Jet engines and rockets

• Martial arts

• Particle theory and collisions (see Physics sub-topic 3.1)

2.4 Aims:

• Aim 3: conservation laws in science disciplines have played a major role in outlining the limits within which scientific theories are developed

• Aim 6: experiments could include (but are not limited to): analysis of collisions with respect to energy transfer; impulse investigations to determine velocity, force, time, or mass; determination of amount of

transformed energy in inelastic collisions

• Aim 7: technology has allowed for more accurate and precise measurements of force and momentum, including video analysis of real-life collisions and modelling/simulations of molecular collisions

2.4 Data booklet reference:

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Topic 6: Circular Motion and gravitation

6.1 Circular motion

6.1 Essential idea: A force applied perpendicular to its displacement can result in circular motion.

6.1 Nature of science:

Observable universe: Observations and subsequent deductions led to the realization that the force must act radially inwards in all cases of circular motion. (1.1)

6.1 Understandings:

• Period, frequency, angular displacement and angular velocity

• Centripetal force

• Centripetal acceleration

6.1 Applications and skills:

• Identifying the forces providing the centripetal forces such as tension, friction, gravitational, electrical, or magnetic

• Solving problems involving centripetal force, centripetal acceleration, period, frequency, angular displacement, linear speed and angular velocity

• Qualitatively and quantitatively describing examples of circular motion including cases of vertical and horizontal circular motion

6.1 Guidance:

• Banking will be considered qualitatively only

6.1 International-mindedness:

• International collaboration is needed in establishing effective rocket launch sites to benefit space programs

6.1 Theory of knowledge:

• Foucault’s pendulum gives a simple observable proof of the rotation of the earth, which is largely unobservable. How can we have knowledge of things that are unobservable?

6.1 Utilization:

• Motion of charged particles in magnetic fields (see Physics sub-topic 5.4)

• Mass spectrometry (see Chemistry sub-topics 2.1 and 11.3)

• Playground and amusement park rides often use the principles of circular motion in their design

6.1 Aims:

• Aim 6: experiments could include (but are not limited to): mass on a string; observation and quantification of loop-the-loop experiences; friction of a mass on a turntable

• Aim 7: technology has allowed for more accurate and precise measurements of circular motion, including data loggers for force measurements and video analysis of objects moving in circular motion

6.1 Data booklet reference:

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6.2 Newton’s law of gravitation

6.2 Essential idea: The Newtonian idea of gravitational force acting between two spherical bodies and the laws of mechanics create a model that can be used to calculate the motion of planets.

6.2 Nature of science:

Laws: Newton’s law of gravitation and the laws of mechanics are the foundation for deterministic classical physics. These can be used to make predictions but do not explain why the observed phenomena exist. (2.4)

6.2 Understandings:

• Newton’s law of gravitation

• Gravitational field strength

6.2 Applications and skills:

• Describing the relationship between gravitational force and centripetal force

• Applying Newton’s law of gravitation to the motion of an object in circular orbit around a point mass

• Solving problems involving gravitational force, gravitational field strength, orbital speed and orbital period

• Determining the resultant gravitational field strength due to two bodies

6.2 Guidance:

• Newton’s law of gravitation should be extended to spherical masses of uniform density by assuming that their mass is concentrated at their center

• Gravitational field strength at a point is the force per unit mass experienced by a small point mass at that point

• Calculations of the resultant gravitational field strength due to two bodies will be restricted to points along the straight line joining the bodies

6.2 Theory of knowledge:

• The laws of mechanics along with the law of gravitation create the deterministic nature of classical physics. Are classical physics and modern physics compatible? Do other areas of knowledge also have a similar division between classical and modern in their historical development?

6.2 Utilization:

• The law of gravitation is essential in describing the motion of satellites, planets, moons and entire galaxies

• Comparison to Coulomb’s law (see Physics sub-topic 5.1)

6.2 Aims:

• Aim 4: the theory of gravitation when combined and synthesized with the rest of the laws of mechanics allows detailed predictions about the future position and motion of planets

6.2 Data booklet reference: