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I'm having trouble with the following example problem and would appreciate if I could get a walkthrough
of how to do it.
Forces with magnitudes of v = 160 newtons and u = 280 newtons act on a hook.
The angle between the two forces is 45°. Find the magnitude of the resultant of this force.
Thank you.
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Do it exactly in accordance with the rule.
The rule of adding forces (vectors) is the parallelogram rule.
In this case you have one vector with the magnitude 160 N
and another vector with the magnitude 280 N.
When you apply the parallelogram rule, the angle between the vectors is 135°.
To find the resultant, use the Law of Cosine
R^2 = 160^2 + 280^2 - 2*160*280*cos(135°) = = 167356.7676.
Hence, R = = 409.1 N (rounded).
Solved.
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For introduction to vectors on a plane, see the lessons
- Vectors in a plane
- Sum of vectors that are coherently oriented sides of a convex closed polygon
- Sum of vectors that are coherently oriented sides of an unclosed polygon
- Sum of vectors that connect the center of a parallelogram with its vertices
- Vectors in a coordinate plane
- Addition, Subtraction and Multiplication by a number of vectors in a coordinate plane
- Summing vectors that are coherently oriented sides of a convex closed polygon
- Summing vectors that are coherently oriented sides of an unclosed polygon
- The Centroid of a triangle is the Intersection point of its medians
- The Centroid of a parallelogram is the Intersection point of its diagonals
- Sum of vectors connecting the center of mass of a triangle with its vertices
- Sum of vectors connecting the center of mass of a quadrilateral with its vertices
- Sum of vectors connecting the center of mass of a n-sided polygon with its vertices
- Sum of vectors connecting the center of a regular n-sided polygon with its vertices
- Solved problems on vectors in a plane
- Solved problems on vectors in a coordinate plane
- HOW TO find the length of the vector in a coordinate plane
in this site.