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ID: 4bbmpxc69k
Problem: \(\mathbf{F}_1 = \{100\,\mathbf{i} + 300\,\mathbf{j} - 200\,\mathbf{k}\}\,\text{N}\). A second force of 500 N has \(\phi = 60^\circ\), and its angle \(\theta\) in the \(xy\) plane can be chosen. Find both values of \(\theta\) (between \(0^\circ\) and \(360^\circ\)) for which the resultant has no \(y\) component, and the resultant in each case. Give the smaller angle first.
Reference materials
Engineering Mechanics: Statics
Vector Mechanics for Engineers: Statics
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Engineering Statics: Open and Interactive
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Notes, problems and apps on the same topics
Add concurrent forces in space component by component and find the magnitude and direction angles of the resultant.
Add any number of coplanar forces by summing x and y components, and find an unknown force from a known resultant.
Describe a force in 3D with i, j, k components, its magnitude, coordinate direction angles and unit vector.
Find the resultant of two or more forces with the parallelogram law, the triangle rule and the laws of sines and cosines.
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Add any number of forces in a plane with a clear component table and a force polygon, or find the force that is missing, that balances the others or that turns the resultant to a wanted direction.
Drag two or more forces and watch their resultant appear by the parallelogram, triangle or polygon rule, with the magnitude and direction worked out live.
See what the dot product means: the angle between two directions and the part of a force along a line, drawn in 3D with its perpendicular part and a right-angle mark.
Start statics here: its basic models and principles, SI and U.S. units, and a five-step method for solving problems, with practice problems and unit converters.
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