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Class 9 Work and Energy (Advanced): cheat sheet
CBSE Science. Conservative and non-conservative forces, potential energy and work, Hooke's law, the energy stored in a spring, and where energy goes when friction acts.
Key ideas
- A conservative force (gravity, a spring) does work that depends only on the start and end, and none round a closed path.
- A non-conservative force (friction, drag) does work that depends on the path and turns energy into heat.
- For a conservative force, the work it does equals the fall in potential energy.
- Within the elastic limit, a spring's extension is proportional to the force; a stiff spring has a large k.
- The spring force rises steadily from 0 to kx, so the average force is kx/2 and the work is the area under the F–x graph.
- A released spring turns its stored energy into kinetic energy; the speed is greatest at its natural length.
Remember
| Work and potential energy | W = −ΔU; near the Earth U = mgh |
| Hooke's law | F = kx (restoring force −kx), k in N/m |
| Spring energy | U = ½kx²; from x₁ to x₂: W = ½k(x₂² − x₁²) |
| Spring to speed | ½kx² = ½mv², so v = x√(k/m) |
| Wire and rod | energy in a stretched wire = ½ × force × extension; standing a rod up: W = mg × L/2 |
Watch out
- Leaving extensions in cm: convert to metres before using ½kx².
- Using ½k(x₂ − x₁)² instead of ½k(x₂² − x₁²).
- Giving the work done by gravity on the way up a positive sign.
Worked example
A 17 kg box slides across a floor at 12 m/s and stops after 3 m because of friction. Find (a) its kinetic energy at the start, (b) the work done on it by friction (with its sign) and (c) the friction force. (d) Is friction conservative? (Yes or No) (Give the answer to 2 decimal places where needed.)
Working: (a) ½ × 17 × 12²; (b) friction removes all the kinetic energy; (c) 1,224 ÷ 3; (d) the energy turns into heat and cannot be recovered
Answer: (a) 1,224 J; (b) −1,224 J; (c) 408 N; (d) No
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