Consider the force system acting on particle P as shown. 50 N 2F 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. ANSWER THIS QUESTION USING BOTH METHODS. 1.2 For which values of F will the resultant R not exceed 50 N?

Consider the force system acting on particle P as shown. 50 N 2F 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. ANSWER THIS QUESTION USING BOTH METHODS. 1.2 For which values of F will the resultant R not exceed 50 N?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

Consider the force system acting on particle P as shown.
50 N
2F
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.
ANSWER THIS QUESTION USING BOTH METHODS.
1.2 For which values of F will the resultant R not exceed 50 N?

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