The same rod is compressed by forces with the same magnitude in the opposite direction. The rod is stretched a length Δ L Δ L when a force is applied parallel to its length. Most materials will behave in this manner if the deformation is less than about 0.1% or about 1 part in 10 3 10 3. Finally, all three strings return to their normal lengths when the force is removed, provided the deformation is small. Thicker nylon strings and ones made of steel stretch less for the same applied force, implying they have a larger k k (see Figure 5.12). For example, a guitar string made of nylon stretches when it is tightened, and the elongation Δ L Δ L is proportional to the force applied (at least for small deformations). The proportionality constant k k depends upon a number of factors for the material. Note that in this graph the slope increases just before fracture, indicating that a small increase in F F is producing a large increase in L L near the fracture. The shape of the curve near fracture depends on several factors, including how the force F F is applied. Still greater forces permanently deform the object until it finally fractures. For larger forces, the graph is curved but the deformation is still elastic- Δ L Δ L will return to zero if the force is removed. The slope of the straight region is 1 k 1 k. The straight segment is the linear region where Hooke’s law is obeyed. In equation form, Hooke’s law is given byįigure 5.11 A graph of deformation Δ L Δ L versus applied force F F. Second, the size of the deformation is proportional to the force-that is, for small deformations, Hooke’s law is obeyed. First, the object returns to its original shape when the force is removed-that is, the deformation is elastic for small deformations. For small deformations, two important characteristics are observed. Even very small forces are known to cause some deformation. A change in shape due to the application of a force is a deformation. ![]() ![]() If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. Determine the change in length given mass, length and radius.Describe with examples the young’s modulus, shear modulus and bulk modulus.Discuss the three types of deformations such as changes in length, sideways shear and changes in volume.Explain Hooke’s law using graphical representation between deformation and applied force.Setting QUARTO_PRINT_STACK=true in your environment will cause Quarto to print a stack trace when an error occurs.By the end of this section, you will be able to: Checking Knitr engine render.OK Get a stack trace Users/cscheid/repos/github/quarto-dev/quarto-web/renv/library/R-4.2/aarch64-apple-darwin20 Path: /Library/Frameworks/R.framework/Resources Path: /Users/cscheid/virtualenvs/homebrew-python3/bin/python3 Path: /Users/cscheid/repos/github/quarto-dev/quarto-cli/package/dist/bin ![]() Checking versions of quarto dependencies.OK Here’s an example of the output it generates: Checking versions of quarto binary dependencies. ![]() You can check the version of Quarto and its dependencies by running quarto check. Basics Check the version of quarto and its dependencies As always, we welcome feedback and bug reports on the Quarto issue tracker, but this page might help you get up and running quickly. This page documents a number of strategies you can employ in case you run into problems with Quarto.
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