MOMENT OF FORCE
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.
Solution 226
Moment of force F about points A, B, C, and D:
answer
answer
answer
answer
Moment of force P about points A, B, C, and D:
(this means that point A is on the line of action of force P)
answer
answer
answer
You can also resolve P to horizontal and vertical components at point E then take the moment of
these components at point C. The answer would be the same. Try it.
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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 a moment center O.
Force P is 890 N directed up to the left 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.
Solution 227
(to the right)
(upward)
(counterclockwise)
answer
The moment of resultant about O can be solved actually without the use of Rx and Ry. The moment effect
of the components of R is the same as the combined moment effect of the components P and Q.
Thus,
. Try it.
You can also find Mo by finding the magnitude of R and its moment arm about point O. Moment arm is
the perpendicular distance between the line of action of R and point O.
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.
Solution 228
to the right
upward
to the right
downward
clockwise
to the right
upward
x-intercept of the resultant
to the left of point O
answer
y-intercept of the resultant
above point O
answer
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.
Solution 229
answer
Y-intercept of the line of action of force F
answer
X-intercept of the line of action of force F
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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.
Solution 230
Let
d = length of member BD
dx = 12 ft
dy = 16 - 12 = 4 ft
Moment about point E
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Moment about point G
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Checking (by Geometry):
(okay!)
(okay!)
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.
Solution 231
Ratio and proportion
Moment at point O
down to the right from A to B
answer
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 ftlb clockwise about O and 90 ftlb
counterclockwise about B. If its moment about A is zero, determine the force.
Solution 232
Moment about O
Moment about B
Substitute xFy = 180 to the above equation
Thus, F = 75 lb downward to the right at x = 36.87 and x-intercept at (4, 0).
answer
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 ftlb
counterclockwise and its moment about B is 40 ftlb clockwise, determine its y intercept.
Solution 233
Resolve force P into components at its x-intercept
Resolve force P into components at its y-intercept
Thus, y intercept of force P is (0, -8/3).
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