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e Find the mass of a wire t Dj + 2rk, 0

e Find the mass of a wire t Dj + 2rk, 0

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Masses and Moments 33. Mass of a wire Find the mass of a wire that lies along the curve r(t) = (1- 1)j + 2tk, 0 < t < 1, if the density is & = (3/2)t. | 34. Center of mass of a curved wire A wire of density 8(x, y, z) = 15Vy + 2 lies along the curve r(t) = (t² – 1)j + 2tk,-1 < t< 1. Find its center of mass. Then sketch the curve and center of mass together. - 35. Mass of wire with variable density Find the mass of a thin wire lying along the curve r(t) 0<t< 1, if the density is (a) 8 = 3t and (b) 8 = 1. V2ri + V2tj + (4 )k, %3D 36. Center of mass of wire with variable density Find the center of mass of a thin wire lying along the curve r(t) = ti + 2tj + (2/3)t3/2k, 0 <IS 2, if the density is 8 = 3 V5 + t. 37. Moment of inertia of wire hoop A circular wire hoop of con- ENG
Transcribed Image Text:Masses and Moments 33. Mass of a wire Find the mass of a wire that lies along the curve r(t) = (1- 1)j + 2tk, 0 < t < 1, if the density is & = (3/2)t. | 34. Center of mass of a curved wire A wire of density 8(x, y, z) = 15Vy + 2 lies along the curve r(t) = (t² – 1)j + 2tk,-1 < t< 1. Find its center of mass. Then sketch the curve and center of mass together. - 35. Mass of wire with variable density Find the mass of a thin wire lying along the curve r(t) 0<t< 1, if the density is (a) 8 = 3t and (b) 8 = 1. V2ri + V2tj + (4 )k, %3D 36. Center of mass of wire with variable density Find the center of mass of a thin wire lying along the curve r(t) = ti + 2tj + (2/3)t3/2k, 0 <IS 2, if the density is 8 = 3 V5 + t. 37. Moment of inertia of wire hoop A circular wire hoop of con- ENG
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