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Both the Magnitude and Direction of the Force on a Crankshaft

question 167

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Both the magnitude and direction of the force on a crankshaft change as the crankshaft rotates.Vectors representing the position of the crank and the force are V=0.16(cos30jsin30k) \mathbf { V } = 0.16 \left( - \cos 30 ^ { \circ } \mathbf { j } - \sin 30 ^ { \circ } \mathbf { k } \right) and F=2000k\mathbf { F } = - 2000 \mathrm { k } respectively.The magnitude of the torque on the crank is given by V×F\| \mathbf { V } \times \mathbf { F } \| ,find the magnitude of the torque on the crank shaft using the position and data shown in the figure.  Both the magnitude and direction of the force on a crankshaft change as the crankshaft rotates.Vectors representing the position of the crank and the force are  \mathbf { V } = 0.16 \left( - \cos 30 ^ { \circ } \mathbf { j } - \sin 30 ^ { \circ } \mathbf { k } \right)   and  \mathbf { F } = - 2000 \mathrm { k }  respectively.The magnitude of the torque on the crank is given by  \| \mathbf { V } \times \mathbf { F } \|  ,find the magnitude of the torque on the crank shaft using the position and data shown in the figure.      \mathbf { a } = 2000 , \mathbf { b } = 0.16   A)   320 \sqrt { 3 } \mathrm { lt } - \mathrm { fb }  B)   160 \mathrm { lt } - \mathrm { fb }  C)   3201 \mathrm { t } - \mathrm { fb }  D)   160 \sqrt { 3 } \mathrm { lt } - \mathrm { fb }  E)   2000 \sqrt { 3 } \mathrm { lt } - \mathrm { fb } a=2000,b=0.16\mathbf { a } = 2000 , \mathbf { b } = 0.16


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