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https://texercises.com/exercise/ruler-made-of-steel/
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Exercise:
A steel ruler alpO shows a length of laO at TaO. What length does it show at TbO? The measured distance does not change.

Solution:
center tikzpicturelatex filldrawcolorbrown!!white fillbrown!!white rectangle .; drawultra thick colorbrown .------.; drawthick colorOrange - .--. nodemidway above s; % Massstab bei °C node at -.-. TaO; filldrawcolorblack fillblack!!white -. rectangle -.; foreach x in ..... draw x-.--x-.; draw- colorgreen!!black .-.--.-. nodemidway below e_; node at -. scriptsize la; % Massstab bei . °C node at -.-. TbO; filldrawcolorblack fillblack!!white -. rectangle -.; foreach x in ..... draw x-.--x-.; draw- colorgreen!!black .---.- nodemidway below e_; node at - scriptsize lbQ; drawcolorgreen ---; drawcolorgreen ---.; tikzpicture center Let e be the length of one unit i.e. mm and x denote the amount of these units. The length s of the measured distance can then be written as: s_ &mustbe s_ x_ e_ x_ e_ x_e_ x_ e_ + alphaDeltavartheta x_ fracx_+alphaDeltavartheta fracla + alp Tb-Ta lb lbP- If the steel ruler gets longer due to the higher temperature it shows less units for the same distance.
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Exercise:
A steel ruler alpO shows a length of laO at TaO. What length does it show at TbO? The measured distance does not change.

Solution:
center tikzpicturelatex filldrawcolorbrown!!white fillbrown!!white rectangle .; drawultra thick colorbrown .------.; drawthick colorOrange - .--. nodemidway above s; % Massstab bei °C node at -.-. TaO; filldrawcolorblack fillblack!!white -. rectangle -.; foreach x in ..... draw x-.--x-.; draw- colorgreen!!black .-.--.-. nodemidway below e_; node at -. scriptsize la; % Massstab bei . °C node at -.-. TbO; filldrawcolorblack fillblack!!white -. rectangle -.; foreach x in ..... draw x-.--x-.; draw- colorgreen!!black .---.- nodemidway below e_; node at - scriptsize lbQ; drawcolorgreen ---; drawcolorgreen ---.; tikzpicture center Let e be the length of one unit i.e. mm and x denote the amount of these units. The length s of the measured distance can then be written as: s_ &mustbe s_ x_ e_ x_ e_ x_e_ x_ e_ + alphaDeltavartheta x_ fracx_+alphaDeltavartheta fracla + alp Tb-Ta lb lbP- If the steel ruler gets longer due to the higher temperature it shows less units for the same distance.
Contained in these collections:
  1. Massstab aus Stahl by TeXercises
    4 | 6

Attributes & Decorations
Tags
ausdehnung, festkörper, thermische ausdehnung, thermodynamik
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Difficulty
(4, default)
Points
4 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration