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A. Space, time and motion
A.1 Kinematics
Guiding questions
How can the motion of a body be described quantitatively and qualitatively?
How can the position of a body in space and time be predicted?
How can the analysis of motion in one and two dimensions be used to solve real-life problems?
Understandings
Standard level and higher level: 9 hours
Students should understand:
• that the motion of bodies through space and time can be described and analysed in terms of position, velocity, and acceleration
• velocity is the rate of change of position, and acceleration is the rate of change of velocity
• the change in position is the displacement
• the difference between distance and displacement
• the difference between instantaneous and average values of velocity, speed and acceleration, and how to determine them
• the equations of motion for solving problems with uniformly accelerated motion as given by
s=u+v2t
v=u+at
s=ut+12at2
v2=u2+2as
• motion with uniform and non-uniform acceleration
• the behaviour of projectiles in the absence of fluid resistance, and the application of the equations of motion resolved into vertical and horizontal components
• the qualitative effect of fluid resistance on projectiles, including time of flight, trajectory, velocity, acceleration, range and terminal speed.
Additional higher level
There is no additional higher level content in A.1
Guidance
A quantitative approach to projectile motion will be limited to situations where fluid resistance is absent or can be neglected.
The trajectory of projectile motion is parabolic in the absence of fluid resistance, but the equation of the trajectory is not required.
Familiarity with projectiles launched horizontally, at angles above, and at angles below the horizontal is required.
Projectile motion will only involve problems using a constant value of g close to the surface of the Earth.
Fluid resistance refers to the effects of gases and liquids on the motion of a body.
Linking questions
How does the motion of a mass in a gravitational field compare to the motion of a charged particle in an electric field?
How are the equations for rotational motion related to those for linear motion?
When can certain types of problems on projectile motion be solved by applying conservation of energy instead of kinematic equations?
How effectively do the equations of motion model Newton’s laws of dynamics?
How does a gravitational force allow for orbital motion?
How does the motion of an object change within a gravitational field?
How does graphical analysis allow for the determination of other physical quantities? (NOS)
A.2 Forces and momentum
Guiding questions
How can forces acting on a system be represented both visually and algebraically?
How can Newton’s laws be modelled mathematically?
How can knowledge of forces and momentum be used to predict the behaviour of interacting bodies?
Understandings
Standard level and higher level: 10 hours
Students should understand:
• Newton’s three laws of motion
• forces as interactions between bodies
• that forces acting on a body can be represented in a free-body diagram
• that free-body diagrams can be analysed to find the resultant force on a system
• the nature and use of the following contact forces
◦ normal force FN is the component of the contact force acting perpendicular to the surface that counteracts the body
◦ surface frictional force Ff acting in a direction parallel to the plane of contact between a body and a surface, on a stationary body as given by Ff≤μsFN or a body in motion as given by Ff=μdFN where μs and μd are the coefficients of static and dynamic friction respectively
◦ tension
◦ elastic restoring force FH following Hooke’s law as given by FH=–kx where k is the spring constant
◦ viscous drag force Fd acting on a small sphere opposing its motion through a fluid as given by Fd=6πηrv where η is the fluid viscosity, r is the radius of the sphere and v is the velocity of the sphere through the fluid
◦ buoyancy Fb acting on a body due to the displacement of the fluid as given by Fb=ρVg where V is the volume of fluid displaced
• the nature and use of the following field forces
◦ gravitational force Fg is the weight of the body and calculated is given by Fg=mg
◦ electric force Fe
◦ magnetic force Fm
• that linear momentum as given by p=mv remains constant unless the system is acted upon by a resultant external force
• that a resultant external force applied to a system constitutes an impulse J as given by J=FΔt where F is the average resultant force and Δt is the time of contact
• that the applied external impulse equals the change in momentum of the system
• that Newton’s second law in the form F=ma assumes mass is constant whereas F=ΔpΔt allows for situations where mass is changing
• the elastic and inelastic collisions of two bodies
• explosions
• energy considerations in elastic collisions, inelastic collisions, and explosions
• that bodies moving along a circular trajectory at a constant speed experience an acceleration that is directed radially towards the centre of the circle—known as a centripetal acceleration as given by a=v2r=ω2r=4π2rT2
• that circular motion is caused by a centripetal force acting perpendicular to the velocity
• that a centripetal force causes the body to change direction even if its magnitude of velocity may remain constant
• that the motion along a circular trajectory can be described in terms of the angular velocity ω which is related to the linear speed v by the equation as given by v=2πrT=ωr.
Additional higher level
There is no additional higher level content in A.2.
Guidance
Sketches and interpretations of free-body diagrams and a determination of the resultant force are for one- and two-dimensional situations only.
Forces should be labelled using commonly accepted names or symbols.
Newton’s first law will be applied to problems involving translational equilibrium.
Examples of Newton’s third law will include the identification of force pairs in various situations.
The use of simultaneous equations involving conservation of momentum and energy in collisions is not required.
A quantitative approach to collisions and explosions is for one-dimensional situations for standard level students and for two-dimensional situations for higher level students.
Situations should involve both uniform and non-uniform circular motion in both horizontal and vertical planes.
Analysis of forces on bodies in non-uniform circular motion in a vertical plane at points other than the top or bottom is not required.
Quantitative treatment of problems involving banked surfaces is not required.
Linking questions
How do collisions between charge carriers and the atomic cores of a conductor result in thermal energy transfer?
How can knowledge of electrical and magnetic forces allow the prediction of changes to the motion of charged particles?
How does the application of a restoring force acting on a particle result in simple harmonic motion?
How are concepts of equilibrium and conservation applied to understand matter and motion from the smallest atom to the whole universe?
Why is no work done on a body moving along a circular trajectory?
In which way is conservation of momentum relevant to the workings of a nuclear power station?
If experimental measurements contain uncertainties, how can laws be developed based on experimental evidence? (NOS)
What assumptions about the forces between molecules of gas allow for ideal gas behaviour? (NOS)
A.3 Work, energy and power Guiding questions
How are concepts of work, energy and power used to predict changes within a system?
How can a consideration of energetics be used as a method to solve problems in kinematics? How can transfer of energy be used to do work?
Understandings
Standard level and higher level: 8 hours
Students should understand:
the principle of the conservation of energy
that work done by a force is equivalent to a transfer of energy
that energy transfers can be represented on a Sankey diagram
that work W done on a body by a constant force depends on the component of the force along the line of displacement as given by W = Fs cos θ
that work done by the resultant force on a system is equal to the change in the energy of the system
that mechanical energy is the sum of kinetic energy, gravitational potential energy and elastic potential energy
that in the absence of frictional, resistive forces, the total mechanical energy of a system is conserved
that if mechanical energy is conserved, work is the amount of energy transformed between different forms of mechanical energy in a system, such as: the kinetic energy of translational motion as given by Ek = 1 mv2 = p2 2 2m
◦ the gravitational potential energy, when close to the surface of the Earth as given by ΔEp = mgΔh
◦ the elastic potential energy as given by EH = 12k(Δx)2
• that power developed P is the rate of work done, or the rate of energy transfer, as given by P = ΔW = Fv
Δt
• efficiency η in terms of energy transfer or power as given by
η = useful work out = useful power out total work in total power in
• energy density of the fuel sources.
Additional higher level
There is no additional higher level content in A.3.
Guidance
The change in the total mechanical energy of a system should be interpreted in terms of the work done on the system by any non-conservative force.
Linking questions
Which other quantities in physics involve rates of change?
How is the equilibrium state of a system, such as the Earth’s atmosphere or a star, determined? How do travelling waves allow for a transfer of energy without a resultant displacement of matter?
Why is the equation for the change in gravitational potential energy only relevant close to the surface of the Earth, and what happens when moving further away from the surface?
Where do the laws of conservation apply in other areas of physics? (NOS)
A.4 Rigid body mechanics Guiding questions
How can the understanding of linear motion be applied to rotational motion?
How is the understanding of the torques acting on a system used to predict changes in rotational motion? How does the distribution of mass within a body affect its rotational motion?
Understandings
Standard level and higher level
There is no standard level content in A.4.
Additional higher level: 7 hours
Students should understand:
the torque τ of a force about an axis as given by τ = Fr sin θ
that bodies in rotational equilibrium have a resultant torque of zero
that an unbalanced torque applied to an extended, rigid body will cause angular acceleration
that the rotation of a body can be described in terms of angular displacement, angular velocity and angular acceleration
that equations of motion for uniform angular acceleration can be used to predict the body’s angular position θ, angular displacement Δθ, angular speed ω and angular acceleration α, as given by
Δθ = ωf + ωi t 2
ωf = ωi + αt
Δ θ = ω i t + 12 α t 2
ωf2 = ωi2 + 2αΔθ
that the moment of inertia I depends on the distribution of mass of an extended body about an axis of
rotation
the moment of inertia for a system of point masses as given by I = Σmr2
Newton’s second law for rotation as given by τ = Iα where τ is the average torque
that an extended body rotating with an angular speed has an angular momentum L as given by
L = Iω
that angular momentum remains constant unless the body is acted upon by a resultant torque
that the action of a resultant torque constitutes an angular impulse ΔL as given by ΔL = τΔt = Δ(Iω) •
the kinetic energy of rotational motion as given by Ek = 1 Iω2 = L2 . 2 2I
Guidance
The vector nature of torque and angular momentum need not be addressed, but the sense (clockwise or counter-clockwise) of a torque should be included.
A calculation of the centre of mass of bodies is not required; there should be an understanding that when considering linear motion, the mass of an extended body may be taken as concentrated at the centre of mass.
The equation for the moment of inertia of a specific mass distribution will be provided when necessary. Simultaneous rotational and translational motion will be restricted to rolling without slipping.
Angular speed will be used rather than angular velocity as a formal vector treatment.
The term angular velocity will be used although a formal vector treatment is not required.
Situations should involve change of moment of inertia in extended bodies and coupled pairs of bodies.
Linking questions
How does rotation apply to the motion of charged particles or satellites in orbit?
How does conservation of angular momentum lead to the determination of the Bohr radius?
How does a torque lead to simple harmonic motion?
How are the laws of conservation and equations of motion in the context of rotational motion analogous to those governing linear motion?
How can rotation lead to the generation of an electric current?
A.5 Galilean and special relativity Guiding questions
How do observers in different reference frames describe events in terms of space and time?
How does special relativity change our understanding of motion compared to Galilean relativity? How are space–time diagrams used to represent relativistic motion?
Understandings
Standard level and higher level
There is no standard level content in A.5.
Additional higher level: 8 hours
Students should understand:
reference frames
that Newton’s laws of motion are the same in all inertial reference frames and this is known as Galilean relativity
that in Galilean relativity the position x′ and time t′ of an event are given by x′ = x–vt and t′ = t
that Galilean transformation equations lead to the velocity addition equation as given by u′ = u–v
the two postulates of special relativity
that the postulates of special relativity lead to the Lorentz transformation equations for the coordinates of an event in two inertial reference frames as given by
x′ = γ(x–vt) t′ = γ t–vx c2 whereγ= 12 u′= u–v 1– uv
that the space–time interval Δs between two events is an invariant quantity as given by (Δs)2 = (cΔt)2–(Δx)2
proper time interval and proper length
time dilation as given by Δt = γΔt0
length contraction as given by L = L0 γ
the relativity of simultaneity
space–time diagrams
that the angle between the world line of a moving particle and the time axis on a space–time diagram
is related to the particle’s speed as given by tan θ = vc
that muon decay experiments provide experimental evidence for time dilation and length contraction.
Guidance
An inertial reference frame is non-accelerating.
The derivation of the Lorentz transformation equations and the relativistic velocity addition equations are not required.
The derivation of the time dilation and length contraction equations is not required.
The time axis on space–time diagrams will be labelled ct.
The discussion of world lines of moving particles will be limited to constant velocity.
Time dilation, length contraction and simultaneity can be visualized using space–time diagrams.
The scales on the time axes ct and ct′ and on the space axes x and x′ of two inertial reference frames moving relative to one another are not the same and are defined by lines of constant space–time interval.
Linking questions
How are equations of linear motion adapted in relativistic contexts?
Why is the equation for the Doppler effect for light so different from that for sound?
Special relativity places a limit on the speed of light. What other limits exist in physics? (NOS)