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YZ
Numerade Educator

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Problem 36 Hard Difficulty

Center of mass of wire with variable density Find the center of mass of a thin wire lying along the curve $\mathbf { r } ( t ) = t \mathbf { i } + 2 t \mathbf { j } +$ $( 2 / 3 ) t ^ { 3 / 2 } \mathbf { k } , 0 \leq t \leq 2 ,$ if the density is $\delta = 3 \sqrt { 5 } + t$

Answer

Center of Mass $=(19 / 18,19 / 9,(4 \text { root }(2)) 7)$

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Video Transcript

no handle or eagles to t to t 2/3 comes t to the three f's 41 0 to 2. So now the derivative Ask the marshal swear with one plus four plus t which is t plus five. What? So the mess will be this Is he on the line? It's rule which is 0 to 2, three times why plus t did see which is 36 and for a TSH first moments and we have and was he is extra zero tips Tell Adi s and I see is why Timestony s oversee and I'm that's wise Z come study s oversee. It's uploading the data We have 38 76 in one 44 was seven times for two respectively. So now we know this is a mass equals two And this, um c y over and em if x c over m and Abbott X Y over and was just equal to formula data unseen over. It's in unseen over noni and, uh, for transport yourself. That's it

YZ
University of Illinois at Urbana-Champaign
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