samuelmeier187
Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

22. What is the length of a pendulum that has a period of 0.500 s?

Please show all of your steps to find the solution.

Sagot :

fieryanswererft

6.21 cm

  • use the pendulum formula : [tex]\sf \bold{\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}}[/tex]

where

  • T is time or period
  • π is pie = 22/7
  • L is pendulum length
  • g is acceleration due to gravity

Given:

  • T = 0.500 s
  • g = 9.8 m/s²

solving step-wise:

[tex]\dashrightarrow \mathrm{T}=2 \pi \sqrt{\dfrac{\mathrm{L}}{\mathrm{g}}}[/tex]

[tex]\sf \dashrightarrow \mathrm{0.5}=2 \pi \sqrt{\dfrac{\mathrm{L}}{\mathrm{9.8}}}[/tex]

[tex]\dashrightarrow \mathrm{\dfrac{0.5}{2 \pi } }=\sqrt{\dfrac{\mathrm{L}}{\mathrm{9.8}}}[/tex]

[tex]\dashrightarrow\sqrt{\dfrac{\mathrm{L}}{\mathrm{9.8}}}= \mathrm{\dfrac{0.5}{2 \pi } }[/tex]

[tex]\sf \dashrightarrow{\dfrac{\mathrm{L}}{\mathrm{9.8}}}= (\mathrm{\dfrac{0.5}{2 \pi } })^2[/tex]

[tex]\sf \dashrightarrow{{\mathrm{L}}= (\mathrm{\dfrac{0.5}{2 \pi } })^2*9.8[/tex]

[tex]\sf \dashrightarrow{{\mathrm{L}}=0.06205922 \ m[/tex]

  • 1 m → 100 cm

[tex]\sf \dashrightarrow{{\mathrm{L}}=6.2059\ cm[/tex]

[tex]\sf \dashrightarrow{{\mathrm{L}}=6.21\ cm[/tex]             { rounded to nearest hundredth }

Let's see

[tex]\\ \rm\rightarrowtail T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

[tex]\\ \rm\rightarrowtail 0.5=2\pi \sqrt{\dfrac{l}{9.8}}[/tex]

[tex]\\ \rm\rightarrowtail 0.783=\pi \sqrt{l}[/tex]

[tex]\\ \rm\rightarrowtail 0.2494=\sqrt{l}[/tex]

[tex]\\ \rm\rightarrowtail \ell=0.0622m[/tex]

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.