Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

On your first trip to Planet X you happen to take along a 100 g mass, a 40-cm-long spring, a meter stick, and a stopwatch. You're curious about the free-fall acceleration on Planet X, where ordinary tasks seem easier than on earth, but you can't find this information in your Visitor's Guide. One night you suspend the spring from the ceiling in your room and hang the mass from it. You find that the mass stretches the spring by 22.6 cm . You then pull the mass down 10.9 cm and release it. With the stopwatch you find that 10 oscillations take 18.8 s .

Sagot :

okpalawalter8

Answer:

[tex]g=2.513m/s^2[/tex]

Explanation:

From the question we are told that:

Mass Taken [tex]m=100g \approx 100*10^{-3}[/tex]

Strain on Spring [tex]l_s=22.6cm \approx 22.6*10^{2}[/tex]

Distance pulled down [tex]d_d=10.9[/tex]

Time for ten oscillations take [tex]t=18.8s[/tex]

 

Generally the equation for angular velocity is mathematically given by

[tex]\omega=2\pi\\\omega=2\pi*\frac{10\ oscillations}{t}\\\\\omega=2\pif=2\pi*\frac{10\ oscillations}{18.8}\\Also\\\omega=\sqrt{\frac{k}{m}} \\\omega=\sqrt{\frac{k}{100*10^{-3}}}[/tex]

Therefore

[tex]{2\pi*\frac{10\ oscillations}{18.8}}=\sqrt{\frac{k}{100*10^{-3}}} \\k=\sqrt{2\pi*\frac{10\ oscillations}{18.8}}*100*10^{-3}\\k=1.112N/m[/tex]  

Generally the equation for Acceleration due to gravity is mathematically given by

[tex]F=mg\\mg=k l_s\\g=\frac{k l_s}{m}\\g=\frac{1.112*2.6*10^{2}}{100*10^{-3}}[/tex]

[tex]g=2.513m/s^2[/tex]

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.