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(a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line.

(a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line.

Elements Of Electromagnetics
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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Answer true or false in response to the following questions: (a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line. (d) The moment about a point P of the sum of a set of concurrent forces, placed at the point of concurrency (point P), equals the sum of the moments about P of the separate forces. (e) A couple has the same moment about any point. (f) If we know the moment of a couple about a point A, then we can find the moment of the couple about a specified line BC even if A does not lie on BC. (g) Two force and couple systems are equipollent if they have either the same resul- tant force or if the moments about some point P are the same for both systems. (h) It is possible for a system consisting of a single couple to be equipollent to a system of one force and 99 couples. (i) Given any system of forces and couples, and any point P, the system may be reduced to an equipollent system comprising of a force at P and a couple (where either or both might be zero). (j) If a system S₁ of forces and couples has a "force-alone" (single force resultant) equipollent system S2, then S₁ must be a coplanar force system. (k) The simplest resultant of a general system of forces and couples is a "wrench" or "screwdriver," that is, a collinear force and a couple along a specific axis in space. (1) Let a general system of forces and couples be resolved into a resultant force at P and an accompanying couple. If the couple is normal to the force, then the equipollent wrench consists of a single force. (m) If a body is in equilibrium under the action of three forces, and two of these intersect at a point P, then the line of action of the third also passes through P. (n) If a body equilibrium und four forces, two of which for a couple, then the other two also form a couple. (o) If a body is in equilibrium under the action of three forces, the forces need not be coplanar. (p) It is possible for a body acted on by a single couple to be in mechanical equilib- rium. (q) If the external forces acting on a body satisfy ΣF = 0 and ΣMk = 0; then the body must be at rest. (r) The tensions in a cable passing over a pulley in equilibrium are always equal. (s) It is possible for a body to be in equilibrium with two separate parts comprising the body not being in equilibrium separately. (t) The action-reaction principle (Newton's 3rd law) plays no role when constructing free-body diagrams of various parts of a rigid structure subjected to external forces.
Transcribed Image Text:Answer true or false in response to the following questions: (a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line. (d) The moment about a point P of the sum of a set of concurrent forces, placed at the point of concurrency (point P), equals the sum of the moments about P of the separate forces. (e) A couple has the same moment about any point. (f) If we know the moment of a couple about a point A, then we can find the moment of the couple about a specified line BC even if A does not lie on BC. (g) Two force and couple systems are equipollent if they have either the same resul- tant force or if the moments about some point P are the same for both systems. (h) It is possible for a system consisting of a single couple to be equipollent to a system of one force and 99 couples. (i) Given any system of forces and couples, and any point P, the system may be reduced to an equipollent system comprising of a force at P and a couple (where either or both might be zero). (j) If a system S₁ of forces and couples has a "force-alone" (single force resultant) equipollent system S2, then S₁ must be a coplanar force system. (k) The simplest resultant of a general system of forces and couples is a "wrench" or "screwdriver," that is, a collinear force and a couple along a specific axis in space. (1) Let a general system of forces and couples be resolved into a resultant force at P and an accompanying couple. If the couple is normal to the force, then the equipollent wrench consists of a single force. (m) If a body is in equilibrium under the action of three forces, and two of these intersect at a point P, then the line of action of the third also passes through P. (n) If a body equilibrium und four forces, two of which for a couple, then the other two also form a couple. (o) If a body is in equilibrium under the action of three forces, the forces need not be coplanar. (p) It is possible for a body acted on by a single couple to be in mechanical equilib- rium. (q) If the external forces acting on a body satisfy ΣF = 0 and ΣMk = 0; then the body must be at rest. (r) The tensions in a cable passing over a pulley in equilibrium are always equal. (s) It is possible for a body to be in equilibrium with two separate parts comprising the body not being in equilibrium separately. (t) The action-reaction principle (Newton's 3rd law) plays no role when constructing free-body diagrams of various parts of a rigid structure subjected to external forces.
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