Elastic Energy Converted to Motion
For an ideal massless linear elastic launcher released from extension x, the stored energy one-half kx squared is equated to the recipient's kinetic-energy gain, subject to any stated efficiency.
Why this shows up in the exam
Catapults and launchers · Rubber-cord projectiles · Energy release from stretched wires
Learn the idea
Released elastic energy becomes kinetic energy only to the extent stated by the model. A stretched cord stores work done during loading; on release that store can launch a body, provided cord mass, losses, and other energy changes are treated as stated.
🧠 Memory hook: Stretch stores a triangle of work; release spends that store.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U_elastic = (1/2)kx² — stored energy of a linear elastic cord
- k = YA/L — axial spring constant for a uniform cord in the linear model
- eta U_elastic = (1/2)mv² — kinetic energy when transfer efficiency eta is specified
How to approach it
- 1Compute axial stiffness or final force
- 2Find stored elastic energy from the loading law
- 3Write the complete energy balance and solve for motion
Common slip-ups that cost marks
- •Using the final stretching force times extension without one-half
- •Ignoring gravitational energy when height changes
- •Assuming perfect transfer when losses are stated
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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