Work, Energy & Power: NEB Class 11 Physics Guide

Curriculum and source boundary

Why energy methods follow Dynamics

Dynamics tracks forces and acceleration step by step. Energy methods can connect initial and final states without requiring the detailed time history. Review Dynamics for force diagrams and Vectors for the dot product. The current CDC Physics Grade 11 page is the Nepal scope checkpoint.

The OpenStax work section, work–energy theorem reference, energy conservation section and power section support the concepts used here. International references deepen but do not replace current Nepal course requirements.

Energy transfer by force

Work, angle and sign

For a constant force F and displacement s with angle θ between them, W = Fs cos θ. Only the component of force parallel to displacement transfers energy through mechanical work. Work is positive when that component supports displacement, negative when it opposes displacement and zero when force is perpendicular or displacement is zero.

The joule is N m = kg m² s⁻². Work is scalar even though force and displacement are vectors; it arises from their dot product. Do not assign a spatial direction to work.

For a variable force along x, work equals the signed area under the force–position graph over the interval. Area below the x-axis contributes negative work. This graph method generalizes the constant rectangle Fs.

Net work changes speed

Kinetic energy and the work–energy theorem

Kinetic energy is K = ½mv². It depends on speed magnitude, so it is scalar and non-negative. The net work done on a body equals its change in kinetic energy: W_net = ΔK = ½mv_f² − ½mv_i².

Positive net work increases kinetic energy; negative net work decreases it. A force can do positive work while another does negative work. The theorem uses their total. It is often efficient when displacement and speeds are known but time is absent.

Energy stored by configuration

Gravitational and elastic potential energy

Potential energy belongs to a system and depends on configuration. Near Earth’s surface, gravitational potential-energy change is ΔU_g = mgΔh. Only the height difference matters within the uniform-field model; the zero level is chosen for convenience.

For an ideal spring following Hooke’s law, elastic potential energy relative to equilibrium is U_s = ½kx². The displacement x is extension or compression from equilibrium, not total spring length. Both extension and compression give non-negative stored energy because x is squared.

For a conservative force, work equals negative change in potential energy: W_c = −ΔU. Gravity does positive work when an object descends and gravitational potential energy decreases. The OpenStax conservative and non-conservative forces section explains why conservative work depends on endpoints rather than path.

Choose the system boundary

Conservation of mechanical and total energy

If only conservative forces do work within the chosen system, mechanical energy K + U remains constant. If friction or another non-conservative interaction transfers energy, include its work or thermal/internal energy rather than claiming energy vanished.

This convention treats W_nc as work on the system. Other textbooks may arrange terms differently; define your convention. Energy conservation is broader than mechanical-energy conservation: total energy remains accounted for even when mechanical energy becomes thermal energy, sound or deformation.

1. Choose the system: object alone, object–Earth or object–spring.
2. Choose initial and final states plus a convenient potential-energy zero.
3. List energy stores in each state.
4. Include transfers across the boundary: external work or heating.
5. Solve symbolically and check that energy units and signs balance.

How fast energy transfers

Power and efficiency

Average power is P = W/Δt or ΔE/Δt. Instantaneous mechanical power for a force on a moving point is P = F · v = Fv cos θ. The watt is joule per second. Power is not energy; two machines can do the same work while the more powerful one does it faster.

Efficiency compares useful output energy or power with total input: η = useful output / input. It is dimensionless and often expressed as a percentage. A real passive machine cannot have efficiency above 100%; an answer above one signals inconsistent inputs, outputs or units.

Worked examples

Work, energy and power in Nepal-relevant situations

Choose the efficient model

A work–energy problem-solving method

1. Sketch the initial and final states, displacement and relevant forces.
2. Choose the system and a potential-energy zero.
3. Decide whether direct work, work–energy or conservation is most efficient.
4. Write the energy equation symbolically with signs.
5. Substitute SI units and avoid premature rounding.
6. Check sign, energy balance, limiting case and efficiency range.

Use the study guide for a learning plan and the practice set for mixed evidence.

Common traps

Mistakes that break the energy account

Try without notes

Practice and self-check

1. Find work by a 25 N force over 6 m at 60° to displacement.
2. A 3 kg object speeds from 2 to 8 m s⁻¹. Find net work.
3. Compare gravitational potential changes for two paths reaching the same height.
4. Explain mechanical-energy change when friction acts.
5. A machine does 12 kJ in 30 s. Find average power.
6. Design two machines that do equal work with different power.

References and next steps

Sources and related study guides

• CDC Nepal: Physics Grade 11
• OpenStax: Work
• OpenStax: Work–Energy Theorem
• OpenStax: Conservation of Energy
• OpenStax: Power
• PhET: Energy Skate Park Basics

Continue with the Class 11 Physics revision roadmap after completing the worked practice set. Academic scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.