- #1
SiriusAboutAstronomy
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Homework Statement
So the problem starts out like this
Stick of the Gods! You hold one end of a stick, but it has no other end. It simply extends into infinity. Its one-dimensional density distribution is given by:
λ=(λinitial)times(e^(-x/L))
λ is the density
The problem doesn't state what x is, and maybe that is what is tripping me up, I think it refers to the distance from one end of the stick.
L is the length of the stick.
A) what is the mass?
B) Where is the center of mass in terms of m and L?
C) What is the moment of inertia about the end you are holding in terms of m and L?
D) What is the moment of inertia about the center of mass in terms of m and L?
The Attempt at a Solution
I think if I could figure out A) then I could figure out the rest, I am just looking for someone to point me in the right direction. I posted B-D so anyone could know more details about what the question is concerning in A.
So I know what in general λ=mass/length, so do I just end up with m=Ltimesλ? I feel like that is too simple.
I also know that m= the integral from (in this case) 0 to infinity of the density, but I am not sure how to integrate that because I don't know what I would be integrating with respect to, x? Is x the variable? And if I do do that, the I have an infinite value for the mass, but I am assuming that the problem wouldn't want me to find an infinite value, so I must be doing it wrong.
When I integrated, I got m=-L(λinitial)e^(-x/L).