Physics

A long thin rod lies along the x-axis from the origin to x=L, with L= 0.830 m. The mass per unit length, $\lambda$ (in kg/m) varies according to the equation $ \lambda = \lambda_0 (1+1.110x^3). The value of $\lambda_0$ is 0.200 kg/m and x is in meters. Calculate the total mass of the rod.

- So I tried:

lambda = m/x
m = (lambda)(x)
= (0.200kg/m)(0.830m)
= 0.166kg

...which was apparently wrong so then I retried this time using the given equation:

$ \lambda = \lambda_0 (1+1.110x^3).
= (0.200kg/m)(1+(1.110)(0.830m)^3)
= 0.271kg

But that is also incorrect and I don't know what else to do.

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  1. this is integral calculus

    the mass of a segment of the rod is
    ... segment length * lambda

    lambda = .200 (1 + 1.110 x^3)
    ... = .200 + .222 x^3

    segment length is dx

    integrate from x = 0 to .83

    .200 dx + .222 x^3 dx ... sum the two integrals

    .166 + .026

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  2. I have no idea because I'm not in your grade. SORRY!

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  3. dM=dx(0.200*(1+1.110x^3))
    taking integral on both sides,
    M=0.200(L+1.110*x^4/4)
    put L=0.830
    M=0.19234

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