1. The problem statement, all variables and given/known data
when a cable with non-zero mass is connected to a pole at both ends, the shape it assumes is called a catenary.
it can be shown that for an electrical wire whose linear mass density is .9 kg/m strung between poles 30m apart(and making a 22 degree angle at each end) the mathematical equation is
a) an electircal wire of linear mass density .9 kg/m is strung, between poles 30m apart, from west to east on earth. initially the current flowing is zero and therefore the wires shape is that of a catenary. what is the weight of the wire?HINT: the length of the wire(which is not 30m) is found by integrating dl over the catenary. Use the fact the
dl=dx[sqrt(1+(dy/dx)^2) in order to have an integration over the x-axis.
It shows a picture with an equation for the wire. y=(38.1m)[cosh(x/38.1m)-1]
2. Relevant equations
equation for the wire ....y=(38.1m)[cosh(x/38.1m)-1]
length of the wire.... dl=dx[sqrt(1+(dy/dx)^2)
He also gave us all of the equations and proofs of hyperbolic functions.
3. The attempt at a solution
I was not sure what to do since i have never done a problem like this. I was neither shown in class how to do anything close to this.
I started with integrating the length of the wire function. Im having problems with the integration though. im not sure what to do after this or if its even right what im doing.
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