IB Physics SL A.3 Work, energy and power Notes

Energy conservation starts with the chosen system. If the system is isolated, the total energy inside it stays constant even though energy can move between kinetic, gravitational potential, elastic, thermal, chemical, or internal stores. If the system is not isolated, energy may enter or leave by work done, heating, radiation, or electrical transfer. IB answers should avoid saying energy is lost. A better phrase is that energy is transferred or dissipated to the surroundings, often becoming less useful for the intended process.

For a described process, define the system and explain how energy is conserved while changing stores or crossing the boundary.

Work is not a new energy store; it is a way energy is transferred. A force does work only when the object has a displacement and the force has a component along that displacement. For a constant force, W = Fs cosθ. Positive work transfers energy into the object or chosen system; negative work transfers energy out of it or reduces a mechanical energy store. A perpendicular force, such as ideal centripetal force in uniform circular motion, does no work because cos90° = 0.

Explain or calculate the work done by a force, including the direction of energy transfer.

Sankey diagrams are visual energy accounts. The width of each arrow represents the amount of energy transferred, or sometimes the power flow if the diagram is per unit time. The total input must equal the total output when all pathways are included. Useful output is the energy transferred into the intended store or pathway; dissipated output is energy transferred to less useful stores, often thermal energy of the surroundings. Read the diagram by comparing widths or labelled values, not by the physical length of an arrow.

Use a Sankey diagram to identify input, useful output, dissipated output, and the energy or power represented by arrow widths.

This calculation card is about choosing the correct component and area. If force is constant and parallel to displacement, work is simply force times displacement. If the force is angled, first resolve it along the displacement, F_parallel = F cosθ, then multiply by s. A constant-force graph against displacement gives a rectangular area, so W is the area under the F_parallel-s graph. When the force opposes displacement, the work done by that force is negative.

A constant force moves an object through a displacement. Calculate the work done and interpret it from a force-displacement graph.

The work-energy idea turns a force-and-displacement problem into an energy-change problem. For one object, the net or resultant work is equal to the change in kinetic energy, W_net = ΔE_k = E_k,final - E_k,initial. For a broader system, work done across the boundary transfers energy into or out of the system and may change gravitational, elastic, thermal, or kinetic stores. This is why the setup matters: identify the system, decide whether you are using resultant work or work by a named force, then name the energy store being changed.

Use the work-energy theorem to relate work done by the resultant force to the change in kinetic energy, or explain energy changes for a chosen system.

Mechanical energy is a useful subset of total energy. It includes kinetic energy plus potential energy stores that can be converted mechanically, mainly gravitational potential and elastic potential in A.3. Use E_k = 1/2mv^2 for motion, E_p = mgh for height changes near Earth with constant g, and E_el = 1/2kx^2 for Hooke’s-law springs. If friction, drag, heating, or deformation is important, some mechanical energy is transferred into non-mechanical stores, so total mechanical energy may not be conserved.

Identify the mechanical energy stores in a situation and write the expression for total mechanical energy.

Use mechanical energy conservation only after checking the model conditions. If gravity and ideal springs are the only forces doing work, energy can transfer between kinetic, gravitational potential, and elastic potential stores without changing their total. If friction, air resistance, an external motor, or deformation is significant, mechanical energy changes because energy transfers into or out of non-mechanical stores. Then write an energy account with an added dissipated or external work term instead of forcing mechanical energy to be constant.

State whether mechanical energy is conserved in a described system and write the appropriate energy equation.

Mechanical energy transformations describe which stores increase and decrease during a process. A falling object loses gravitational potential energy and gains kinetic energy. A rising object does the reverse. An ideal spring can store energy elastically and release it as kinetic energy. With friction or drag, the transformation is not purely mechanical: some mechanical energy is transferred to thermal/internal stores. When writing an energy equation, name the stores before choosing formulas.

Describe the energy transformations in a mechanical process and state whether mechanical energy remains in mechanical stores.

Kinetic energy depends on mass and speed, not velocity direction. Use speed in E_k = 1/2mv^2, so a negative velocity does not make negative kinetic energy. Because speed is squared, changes in speed have a large effect: twice the speed gives four times the kinetic energy. The alternative form E_k = p^2/(2m) is useful when momentum and mass are known.

Calculate kinetic energy from mass and speed, or compare kinetic energies when speed or momentum changes.

Gravitational potential energy near Earth is a height-based energy store. Because the zero level is chosen by the solver, absolute E_p values are less important than changes. Use ΔE_p = mgΔh when g is approximately constant over the height change. Lifting an object increases E_p; lowering or falling decreases E_p and can transfer energy to kinetic or other stores. Be careful to use vertical height change, not distance travelled along a slope.

Calculate the change in gravitational potential energy for an object moving between two heights near Earth.

A spring stores elastic potential energy when it is stretched or compressed from its natural length. In the Hooke’s-law region, force increases linearly with extension, F = kx, so the energy stored is the triangular area under the force-extension graph: E_el = 1/2kx^2. Use x as the displacement from natural length, not the full length of the spring. Because x is squared, stretching and compressing by the same amount store the same energy, as long as the spring remains elastic.

Calculate the elastic potential energy stored in a spring and state the condition for using the formula.

Power tells how quickly energy is transferred. If 500 J is transferred in 10 s, the average power is 50 W. The same energy transferred in a shorter time has greater power. In mechanical problems, P = Fv is valid when F is the component of force along the motion; more generally use P = F_parallel v. Distinguish average power over a time interval from instantaneous power at a moment.

Calculate average power from energy transferred or work done over time, and apply P = Fv when a force moves at constant speed.

Efficiency measures how much of the supplied energy or power becomes the useful output. The denominator is total input, not wasted output. The numerator is the useful output for the intended purpose. If powers are used, they must refer to the same process/time interval, so the time cancels. A realistic device has efficiency less than 1 or less than 100% because some energy is dissipated to less useful stores.

Calculate the efficiency of a device from useful output and total input energy or power.

This card compares how much energy different fuels release for the same mass. If a fuel has a value in J kg^-1, multiply by the fuel mass in kg to find total energy released. Convert MJ kg^-1 to J kg^-1 when needed. A high energy-per-mass fuel is useful when mass matters, but it does not automatically mean the device using it is efficient or powerful; efficiency depends on useful output divided by input, and power depends on time.

Compare two fuels using energy released per unit mass, or calculate energy released from a given fuel mass.

A.3 is an energy-accounting topic. Start by choosing the system and the energy stores. If the question gives a force and displacement, use work. If it gives before/after speeds, heights, or springs, choose the relevant energy stores. If it gives time, use power. If it gives useful and input pathways, use efficiency. If it compares fuels, use energy per unit mass. The strongest IB answers state the model condition before the arithmetic.

A mixed A.3 problem includes a device, motion, or fuel data. State the model choice and condition before calculating.