PHYC10003 Chap.2 Work and Energy
Work and Energy
Work converts a force description into a signed energy transfer by selecting the force component parallel to displacement. This chapter builds the work-energy theorem, explains why perpendicular force can change direction without changing speed, and uses a before-and-after ledger for conservative and dissipative processes. The core discipline is choosing one system boundary and counting each interaction exactly once.
Work sign follows geometry and the selected system, not whether a force seems helpful. An energy ledger begins by naming the system, listing initial stores, adding transfers across the boundary, and comparing the result with final stores. Gravity may appear as external work for an object or as potential-energy change for a larger system, but not both for the same interaction.
Sliding friction can likewise appear as negative external work or as internal thermal increase under a different boundary. Variable forces require signed area on a force-position graph, while curved paths may require the changing local force component. A conservative limit provides a comparison for a dissipative answer: resistance should not increase the final mechanical speed under otherwise identical conditions.
Units, squared-speed scaling, and the impossibility of negative kinetic energy give independent checks. If the ledger predicts negative kinetic energy at a destination, the assumed state is unreachable and the turning point must occur earlier. The final explanation should identify where energy entered, left, or changed form.
What this chapter covers
- 01
Force-displacement dot product
- 02
Positive, negative and zero work
- 03
Net work and kinetic energy
- 04
Conservative interactions
- 05
Mechanical energy
- 06
Friction and thermal transfer
Worked example · free
Include pulling work and friction once
- 1Calculate pulling work as 432 J.
- 1Calculate friction work as minus 144 J.
- 1Set net work equal to 288 J of final kinetic energy.
- 1Solve for speed as 6.93 m/s.
Key terms
- Dot Product
- A dot product multiplies vector magnitudes and the cosine of their included angle to produce a scalar.
- Net Work
- Net work is the sum of work done by all external forces on the chosen object.
- Kinetic Energy
- Kinetic energy is the scalar energy associated with motion and depends on speed squared.
- Conservative Force
- A conservative force permits work to be represented by a change in potential energy.
- Mechanical Energy
- Mechanical energy is the sum of kinetic energy and the potential energies included in a model.
Work and Energy FAQ
Can a force be large and still do no work?
Yes. Work uses the force component along displacement. A normal force during horizontal motion or a centripetal force in uniform circular motion can be large while remaining perpendicular to motion and doing zero work. Always evaluate the local angle when the direction of motion changes along a curved path.
Why is friction work negative?
When kinetic friction points opposite displacement, their dot product is negative. The selected object's mechanical energy decreases while energy is transferred into internal or thermal forms in the wider system.
When is mechanical energy conserved?
Mechanical energy stays constant when the model includes conservative potential energies and no non-conservative transfer changes the mechanical subtotal. Total energy remains conserved more generally, but additional thermal or internal terms may be required.
Exam move
For every problem, write the chosen object or system above the ledger. Draw the displacement and resolve each force parallel and perpendicular to it before evaluating work. Predict the sign of each contribution from the angle, then confirm it through the dot product. Include a zero-work force deliberately in early practice so that large force is not confused with large energy transfer.
List initial kinetic and potential energies, external work, internal or thermal changes, and final energies before substituting. Use one bookkeeping description consistently: if gravity is represented by potential energy, do not also count gravitational work for the same interaction. Apply the same rule to friction when changing the system boundary.
Rework one numerical problem with a crate-only system and then with a crate-plus-floor system, checking that both descriptions predict the same motion while assigning transfers to different terms. Keep all entries symbolic until cancellation and sign choices are visible. Check joules throughout and use squared-speed scaling as a fast reasonableness test.
When force varies with position, sketch the force-position graph and interpret signed area rather than multiplying one force by a total distance. When the path curves, decide whether the force-displacement angle changes along the route. Compare every dissipative result with its conservative limit. A friction calculation that produces greater final speed should immediately trigger a sign review.
A negative final kinetic energy means the proposed endpoint is unreachable under the stated transfers, so solve instead for a stopping location or reconsider the assumed state. Finish each solution with a sentence identifying where energy entered, left, or changed form and why the calculated trend follows from that ledger.
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