Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
The average density of the rod is 0.704 kg/m.
For given question,
We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.
We need to find the
The length of rod is, L = 5 m.
The linear density of rod is, ρ = 10/( x + 4) kg/m
To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,
The expression for the average density is given as,
⇒ ρ'
[tex]=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx[/tex] ......................(1)
Using u = x + 4
du = dx
u₁ = x₁ + 4
u₁ = 0 + 4
u₁ = 4
and
u₂ = x₂ + 4
u₂ = 5 + 4
u₂ = 9
By entering the values above into (1), we have:
⇒ ρ'
[tex]=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352][/tex]
= 0.704
Thus, we can conclude that the average density of the rod is 0.704 kg/m.
Learn more about the average density here:
https://brainly.com/question/15118421
#SPJ4
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.