An icicle is modelled as a cone of length

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Calculus of change and accumulation · Calculus of change and accumulation

Mathematical Methods for Physics, Ch Accumulation: integration and the techniques that make it possible

Problem

An icicle is modelled as a cone of length L=0.30 mL = 0.30\,\mathrm{m}, hanging with its wide end at x=0x=0 and its point at x=Lx=L. Its radius narrows linearly, r(x)=r0(1−xL)r(x) = r_0\left(1 - \dfrac{x}{L}\right), with r0=0.012 mr_0 = 0.012\,\mathrm{m}. The ice has uniform density ρ=917 kg m−3\rho = 917\,\mathrm{kg\,m^{-3}}. (a) Describe the slice at position xx that you will add up, giving its shape, its thickness and the volume it contributes. (b) Write the integral for the total mass MM of the icicle and evaluate it.

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