Consider the force system acting on particle P as shown. 50 Ν 2F P 135° F 1.1 Determine F so that the resultant of the three forces is as small as possible. Also find the corresponding magnitude, direction and sense of the resultant force and depict the resultant with respect to the vectors in the given sketch. There are different approaches to the problem. Two approaches are to (i) use a combination of algebra and calculus or (ii) to proceed with a geometrical interpretation. Both approaches are described below. (i) Algebra and calculus Start with a rectangular system of axes and express all the forces in cartesian vector format. Use calculus results or graphs to find the minimum. (ii) Geometry Start with finding the resultant P of the two forces with magnitudes F and 2F. Now add P to the 50 N force.

Consider the force system acting on particle P as shown. 50 Ν 2F P 135° F 1.1 Determine F so that the resultant of the three forces is as small as possible. Also find the corresponding magnitude, direction and sense of the resultant force and depict the resultant with respect to the vectors in the given sketch. There are different approaches to the problem. Two approaches are to (i) use a combination of algebra and calculus or (ii) to proceed with a geometrical interpretation. Both approaches are described below. (i) Algebra and calculus Start with a rectangular system of axes and express all the forces in cartesian vector format. Use calculus results or graphs to find the minimum. (ii) Geometry Start with finding the resultant P of the two forces with magnitudes F and 2F. Now add P to the 50 N force.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 5CQ: Suppose you add two vectors A and B . What relative direction between them produces the resultant...

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