NEB Class 11 • Physics • Worked Practice

Work, Energy & Power Practice Set: NEB 11 Physics

Test work signs, force–position graphs, the work–energy theorem, potential energy, conservation, power and efficiency with complete checks.

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Foundation, theorem, conservation and transfer levels · Twelve worked problems plus a timed challenge · Every solution checks signs, units or energy balance

How to use this set: Attempt each problem before opening its solution. Sketch initial/final states, name the system, predict work signs, write the symbolic energy relation and finish with a unit or balance check. Record the first wrong decision.

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Practice boundary

What this set measures

This set covers constant and variable-force work, kinetic and potential energy, the work–energy theorem, conservation with friction, power and efficiency. Review the concept guide or study guide when a method is unfamiliar. The current CDC Physics Grade 11 page is the Nepal scope checkpoint.

The problems use the work–energy and conservation boundaries described by OpenStax and the endpoint/path distinction in conservative-force theory.

Level 1

Work and sign problems

1. Angled pull

A 50 N force pulls a trolley 6.0 m at 60° to displacement. Find work.

Solution: W = Fs cosθ = 50×6×cos60° = 150 J. The perpendicular component does zero work on the horizontal displacement.

2. Friction work

Kinetic friction 12 N opposes 9 m of sliding.

Solution: θ = 180°, so W = 12×9×cos180° = −108 J. The negative sign indicates mechanical energy transfer from the sliding motion.

3. Zero work

A student carries a bag horizontally at constant height while exerting an upward support force. What work does that upward force do?

Solution: Zero, because force is perpendicular to horizontal displacement. This statement concerns mechanical work on the bag, not biological energy used by the student.

4. Force–position graph

Force rises linearly from 0 to 8 N over 5 m.

Solution: Work is triangular area = ½×5×8 = 20 J. The graph unit N m confirms joules.

Level 2

Work–energy theorem problems

5. Speed increase

A 4 kg object speeds from 2 to 6 m s−1. Find net work.

Solution: Wnet = ½×4×(6²−2²) = 64 J. Positive net work matches increased speed.

6. Find final speed

Net work 75 J acts on a 3 kg body initially at 5 m s−1.

Solution: 75 = ½×3(v²−25). Thus v² = 75 and v ≈ 8.66 m s−1.

Check: Positive net work gives final speed above 5 m s−1.

7. Braking distance from energy

A 1000 kg vehicle at 20 m s−1 stops under constant 5000 N resistance. Find stopping distance.

Solution: Work −5000s equals ΔK = 0−½×1000×20² = −200,000 J. Therefore s = 40 m.

Check: Both resistance work and kinetic-energy change are negative.

Level 3

Potential-energy questions

8. Climbing stairs

A 55 kg student rises 4.0 m. Find gravitational potential-energy increase using g = 9.8 m s−2.

Solution: ΔU = mgΔh = 55×9.8×4 = 2156 J. The path shape does not affect gravitational potential change.

9. Spring storage

An ideal spring with k = 200 N m−1 is compressed 0.10 m.

Solution: U = ½kx² = 0.5×200×0.10² = 1.0 J. Use compression from equilibrium, not total length.

Level 4

Energy-conservation problems

10. Frictionless descent

A body starts from rest 5.0 m above a reference and slides without friction. Find speed at the bottom.

Solution: mgh = ½mv², so v = √(2gh) = √98 ≈ 9.90 m s−1. Mass cancels.

Check: Greater height would produce greater speed; speed is non-negative.

11. Rough descent

A 2 kg block starts from rest and loses 30 J to thermal energy while descending 4.0 m.

Solution: Initial gravitational energy = 2×9.8×4 = 78.4 J. Final kinetic energy = 78.4−30 = 48.4 J. From ½×2×v² = 48.4, v ≈ 6.96 m s−1.

Check: This is below the frictionless value √(2g×4) ≈ 8.85 m s−1.

12. Spring launch

A 0.50 kg block is launched by a spring k = 100 N m−1 compressed 0.20 m on a frictionless surface.

Solution: ½kx² = ½mv². Thus v = x√(k/m) = 0.20√200 ≈ 2.83 m s−1.

Level 5

Power and efficiency problems

13. Average power

A motor does 18 kJ of work in 30 s.

Solution: P = 18,000/30 = 600 W. Convert kilojoules before division.

14. Lifting power

A 200 kg load rises at constant 0.50 m s−1. Find ideal power.

Solution: P = Fv = mgv = 200×9.8×0.50 = 980 W.

15. Efficiency

A machine takes 2.0 kW input and delivers 1.5 kW useful output.

Solution: η = 1.5/2.0 = 0.75 = 75%. The remaining input transfers to other forms such as thermal energy.

Level 6

Multi-stage and comparison problems

16. Pulling against friction

A 5 kg crate is pulled 10 m by a 30 N horizontal force while friction is 8 N. It starts from rest. Find final speed.

Solution: Applied work = 300 J; friction work = −80 J, so net work = 220 J. From 220 = ½×5×v², v = √88 ≈ 9.38 m s−1.

Check: Using only applied work would overestimate speed because it ignores the negative contribution.

17. Energy on two routes

Two students lift identical 10 kg bags to the same 6 m balcony. One uses stairs of length 12 m and the other a vertical rope. Neglect losses. Compare work against gravity.

Solution: Each increases gravitational potential energy by mgh = 10×9.8×6 = 588 J. Conservative gravitational work depends on height change, not route length. The longer path may require a smaller component of force but not less ideal work.

18. Power with efficiency

A pump lifts water at 20 kg s−1 through 15 m and operates at 70% efficiency. Find ideal useful gravitational power and required input power.

Solution: Useful power = ṁgh = 20×9.8×15 = 2940 W. Input = 2940/0.70 = 4200 W = 4.2 kW.

Check: Input exceeds useful output, as required for efficiency below 100%.

For each problem, write an energy ledger with initial stores, transfers and final stores. The ledger should balance numerically; if it does not, locate an omitted force, height reference or unit conversion before changing formulas.

15-minute challenge

Mixed questions without labels

  1. A 20 N force at 120° to displacement acts over 4 m. Find work.
  2. Net work −48 J acts on a 2 kg object initially at 8 m s−1. Find final speed.
  3. Compare gravitational work along two paths between identical heights.
  4. A 70% efficient device receives 5 kW. Find useful power.
  5. Sketch an F–x graph with positive and negative regions but zero net work.

Answers: (1) −40 J. (2) 4 m s−1. (3) equal for gravity. (4) 3.5 kW. (5) make signed areas equal.

Use PhET Energy Skate Park: Basics after predicting kinetic, potential and thermal bar changes.

Error analysis

What to inspect when an energy answer fails

Angle/sign error

Did you use the angle between force and displacement and predict the work sign?

System error

Did you define object–Earth or object–spring for potential energy?

Transfer error

Did frictional mechanical loss appear as thermal/internal energy?

Unit error

Were kJ, kW, minutes and seconds converted consistently?

For online or physical NEB tuition, call 9846662070 with the attempted energy account.

Questions about the Work, Energy and Power practice set

How should I score an energy solution?

Credit the system and states, work signs, symbolic energy relation, substitution, unit and an independent balance or limiting check.

Why is work sometimes negative?

Work is negative when the force component is opposite displacement, causing a negative contribution to energy transfer or kinetic-energy change.

Can I always conserve mechanical energy?

No. Include non-conservative transfers such as friction or external work. Total energy is conserved, but K+U alone may change.

Why does mass cancel in some descent problems?

Both gravitational potential energy mgh and kinetic energy ½mv² contain mass, so it cancels in the ideal frictionless model.

How do I check an efficiency answer?

Useful output must not exceed input for an ordinary passive device, so efficiency should lie between zero and one or 0% and 100%.

Where can I get help with NEB Class 11 Work, Energy and Power?

For current online or physical tuition options, call 9846662070 and confirm schedule, class mode, teacher availability and fees.

Frequently asked questions

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

Use the Physics revision roadmap to schedule cumulative Mechanics practice. Academic scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

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