Introduction
HSA Notes brings complete, exam-focused solved notes to help Class 11 (1st Year, HSSC-I) students score high marks in their FBISE Physics board exam.
This page covers Unit 5, Work and Energy, prepared strictly according to the FBISE New Book (NBF) syllabus, covering work, conservative and non-conservative fields, kinetic energy, and the work-energy theorem, along with fully solved MCQs, questions, numericals, and assignments from HSA Notes.
Work
Definition: Work is the transfer of energy that occurs when a force causes the displacement of a body. Mathematically, work is defined using the dot product of the force and displacement vectors:
W = F · d = Fd cos θ
where F is the magnitude of the applied force, d is the magnitude of the displacement, and θ is the angle between the force and displacement vectors.
Units: Work is measured in Joules (J), where 1 Joule = 1 Newton-metre (1 J = 1 N·m).
Positive, Negative, and Zero Work:
- Work is positive when 0° ≤ θ < 90°, meaning the force has a component in the direction of displacement.
- Work is zero when θ = 90°, meaning the force is entirely perpendicular to the displacement.
- Work is negative when 90° < θ ≤ 180°, meaning the force acts opposite to the direction of displacement.
Work from a Force-Displacement Graph: The area under a force versus displacement (F-d) graph represents the work done. When the force is constant, this area forms a simple rectangle, and the work is found by direct multiplication. When the force varies with displacement, the area must be found using integration, since the graph is no longer a simple geometric shape.
Conservative and Non-Conservative Fields
Forces in Physics are classified into two categories based on how the work they do depends on the path taken by the body.
Conservative forces do work that is independent of the path taken between two points; the work done around any closed loop is exactly zero, and mechanical energy is conserved under their action. Common examples include gravitational force, the elastic (spring) force, and the electrostatic force.
Non-conservative forces do work that depends on the specific path taken, and they dissipate mechanical energy, usually converting it into heat. Common examples include friction and air resistance.
Kinetic Energy
Definition: Kinetic energy is the energy possessed by a body due to its motion, given by:
KE = ½ m v²
Derivation: Kinetic energy can be derived directly from the definition of work combined with the equations of motion covered in Unit 3. Starting from W = Fd and Newton’s second law F = ma, this gives W = mad. Using the third equation of motion, vf² − vᵢ² = 2ad, and solving for ad gives:
W = ½ m vf² − ½ m vᵢ²
This result shows that the work done on a body equals the change in its kinetic energy, connecting force and motion directly to energy.
Work-Energy Theorem
The work-energy theorem states that the net work done on a body equals the change in its kinetic energy:
W_net = ΔKE = ½ m vf² − ½ m vᵢ²
In a resistive medium, where non-conservative forces such as friction act on the body, the net work must also include the negative work done by these dissipative forces, alongside the work done by any applied or conservative forces.
Efficiency: In real systems, not all input energy is converted into useful output energy, due to losses such as friction and heat. Efficiency is defined as:
η = (E_out / E_in) × 100%
An ideal machine would have 100% efficiency, with no energy losses, but real machines always have an efficiency of less than 100% due to unavoidable energy dissipation.
HSA Notes Features
- Complete solved MCQs based on the FBISE paper pattern
- Short and comprehensive questions with clear answers
- Solved numericals with full working and correct units
- Solved textbook exercises covering every question
- Assignments and practice questions for self-assessment and revision
- Full Work and Energy notes for Class 11, based on the FBISE new book, available in PDF form at hsanotes.com
Why This Unit Matters
Work and Energy introduces the concept of energy conservation, one of the most powerful and widely applied principles in all of Physics. T
he work-energy theorem provides an alternative method for solving motion problems that is often faster than using the equations of motion directly, especially when forces vary or when only initial and final speeds are known.
The distinction between conservative and non-conservative forces becomes essential again in later units, particularly when analyzing energy losses in Fluid Mechanics and real-world machines. A strong grasp of this unit also makes concepts like potential energy, power, and efficiency far easier to apply correctly in numerical problems.
Available Across All FBISE Institutions
These notes are built for students across all FBISE-affiliated schools and colleges, including Islamabad Model Colleges, F.G. Colleges, Army Public Schools & Colleges, Punjab Colleges, Dr. A.Q. Khan Colleges, Fazaia Inter Colleges, IMCB, IMCG, and Sir Syed Colleges.
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Frequently Asked Questions
How is work defined mathematically?
Work is defined as the dot product of the force and displacement vectors, W = Fd cos θ, where θ is the angle between the direction of the applied force and the direction of displacement.
What is the difference between conservative and non-conservative forces?
Conservative forces, such as gravity, do work that is independent of the path taken and conserve mechanical energy, while non-conservative forces, such as friction, do path-dependent work and dissipate energy, usually as heat.
How is the work-energy theorem derived?
It is derived by combining the definition of work, W = Fd, with Newton’s second law and the third equation of motion, resulting in the net work done on a body being equal to the change in its kinetic energy.
Why is efficiency always less than 100% in real machines?
Because real machines always experience some energy loss due to non-conservative forces such as friction and air resistance, meaning not all input energy is converted into useful output energy.
Conclusion
With Unit 5, Work and Energy, fully covered, Class 11 FBISE students now have a solid understanding of work, conservative and non-conservative forces, kinetic energy, and the work-energy theorem, all central concepts that recur throughout the rest of the Physics syllabus. Practice the solved numericals and MCQs on this page alongside past papers, and consider joining our online classes for guided, exam-focused preparation, to build the accuracy and confidence needed for your board exam.
Best of luck for your Class 11 Physics exam!