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YZ
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Problem 34 Hard Difficulty

Center of mass of a curved wire $A$ wire of density $\delta ( x , y , z ) = 15 \sqrt { y + 2 }$ lies along the curve $\mathbf { r } ( t ) = \left( t ^ { 2 } - 1 \right) \mathbf { j } +$ $2 t \mathbf { k } , - 1 \leq t \leq 1 .$ Find its center of mass. Then sketch the curve and center of mass together.

Answer

40

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Video Transcript

over or is equals two t squared. Nice one to t zero Disagreements went to tea 40 from nothing 1 to 1. So the model the derivative will be to Times Square and keep us this worthless world Know about this London's girl Everything's to see we have functioned Delta X y z Yes, flooding all the data It is it is. It equals to zero of making 1 to 1 15 times square with t minus one squared plus two comes to Tom's School squirt thescore close one The tea which is 80 and for m x z. So the first moment we have why tons density function the S Forget the data. We have like a 1 to 1. This word plus minus one turns 30 times Things were possible. Did see which is that 48 suing though the average for why or the sins were a mess on Lee Y Coordinates has the value an X Z over M, which is like three or flight. And for the center of mass on the X axis, we're gonna find X is able to have a y Z over end. But since our ex Cornet zero from this trajectory. So this is Cyril. And my symmetry. The valuables ease off zero because that the other function this independent of Z. So finally, l listen, the masses okay to add zero making through if it zero is it.

YZ
University of Illinois at Urbana-Champaign
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