Elastic Energy and Applications

Name: Elastic Energy and Applications
Author: StemPy Lab

A stretched wire stores energy, like a spring. A rope, a beam and a mountain all have a limit. In this course we find the elastic energy of a wire, we study wires in series and in parallel and the stress of a heated rod, and we use the safety factor to choose the rope of a crane, the shape of a beam and the greatest height of a mountain.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Elastic potential energy
Stretching a wire takes work, which is stored as elastic energy: $U = \tfrac12 F\,\Delta L$ , the area under the force-stretch line. Per unit volume, $u = \tfrac12 \times \text{stress} \times \text{strain} = \dfrac{\text{stress}^2}{2Y}$ . Rubber loses some energy as heat each time it is stretched and let go, which is shown by the loop of its stress-strain graph.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Wires in series, wires in parallel and thermal stress
Wires end to end (in series) carry the same force, and their stretches add. Wires side by side (in parallel) share one stretch, and their forces add; stiffer wires take more of the load. A rod clamped so it cannot expand builds up a thermal stress $Y\alpha\,\Delta T$ when heated, which is why rails and bridges have gaps.
1 simulation2 practice questions1 Python program4 problems
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Lesson 3about 25 min
Elasticity in design: ropes, beams and mountains
Engineers keep stresses well below the breaking stress with a safety factor. A rope is sized from the load times the safety factor. A beam loaded at its middle sags $\delta = \dfrac{Wl^3}{4bd^3Y}$ , so depth matters most, which is why beams stand on edge and girders are I-shaped. Rock flows under its own weight above $h = \dfrac{\sigma}{\rho g}$ , which limits the height of mountains.
1 simulation2 practice questions1 Python program4 problems2 Python labs1 note
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Elastic Energy and Applications: Practice Paper

20 questions · 40 min

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Elastic Energy and Applications

Course outline (3 lessons)

Elastic potential energy

Wires in series, wires in parallel and thermal stress

Elasticity in design: ropes, beams and mountains

Test Your Learning

Your teacher

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