Engineering Mathematics

moment

246 - System with couples and forces on it

Problem 246
Determine the resultant moment about point A of the system of forces shown in Fig. P-246. Each square is 1 ft on a side.
 

246-resultant-of-system-with-couples.gif

 

Couples

Couple is a system of forces whose magnitude of the resultant is zero and yet has a moment sum. Geometrically, couple is composed of two equal forces that are parallel to each other and acting in opposite direction. The magnitude of the couple is given by
 

$C = Fd$

 
Where $F$ are the two forces and $d$ is the moment arm, or the perpendicular distance between the forces.
 

233 A force creating counterclockwise and clockwise moments

Problem 233
In Fig. P-231, a force P intersects the X axis at 4 ft to the right of O. If its moment about A is 170 ft·lb counterclockwise and its moment about B is 40 ft·lb clockwise, determine its y intercept.
 

Three points in XY plane (A, B, and O)

 

232 Moment of a force about points O and B

Problem 232
In Fig. P-231, the moment of a certain force F is 180 ft·lb clockwise about O and 90 ft·lb counterclockwise about B. If its moment about A is zero, determine the force.
 

Three points in XY plane (A, B, and O)

 

231 Force P producing a clockwise moment about the origin

Problem 231
A force P passing through points A and B in Fig. P-231 has a clockwise moment of 300 ft-lb about O. Compute the value of P.
 

Three points in XY plane (A, B, and O)

 

230 Distance from truss member to truss joint

Problem 230
For the truss shown in Fig. P-230, compute the perpendicular distance from E and from G to the line BD. Hint: Imagine a force F directed along BD and compute its moment in terms of its components about E and about G. Then equate these results to the definition of moment M = Fd to compute the required perpendicular distances.
 

Symmetrical Truss

 

229 Y-coordinate of the point of application of the force

Problem 229
In Fig. P-229, find the y-coordinate of point A so that the 361-lb force will have a clockwise moment of 400 ft-lb about O. Also determine the X and Y intercepts of the line of action of the force.
 

Point of application of a force

 

228 Intercepts of the resultant force

Problem 228
Without computing the magnitude of the resultant, compute where the resultant of the forces shown in Fig. P-228 intersects the x and y axes.
 

Two concurrent forces in rectangular grid

 

227 - Moment of resultant force about a point

Problem 227
Two forces P and Q pass through a point A which is 4 m to the right of and 3 m above a moment center O. Force P is 890 N directed up to the right at 30° with the horizontal and force Q is 445 N directed up to the left at 60° with the horizontal. Determine the moment of the resultant of these two forces with respect to O.
 

226 - Moment of force about different points

Problem 226
In Fig. P-226 assuming clockwise moments as positive, compute the moment of force F = 200 kg and force P = 165 kg about points A, B, C, and D.
 

Forces in rectangular grid

 

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