engineering mechanics problem
DESCRIPTION
engineering problemTRANSCRIPT
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Problem 309 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 23, 2011 - 5:21pm
Problem 309A cylinder weighing 400 lb is held against a smooth incline by means of the weightless rod AB inFig. P-
309. Determine the forces P and N exerted on the cylinder by the rod and the incline.
Solution 309
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answer
answer
Problem 310 - 311 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 23, 2011 - 10:35pm
Problem 310A 300-lb box is held at rest on a smooth plane by a force P inclined at an angle θ with the plane as shown
in Fig. P-310. If θ = 45°, determine the value of P and the normal pressure N exerted by the plane.
Solution 310
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answer
answer
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Problem 311If the value of P in Fig. P-310 is 180 lb, determine the angle θ at which it must be inclined with the smooth plane to hold 300-lb box in equilibrium.
Solution 311
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answer
Problem 312 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 25, 2011 - 7:13am
Problem 312Determine the magnitude of P and F necessary to keep the concurrent force system in Fig. P-312 in
equilibrium.
Solution 312
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answer
answer
Problem 313 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 25, 2011 - 7:26am
Problem 313Figure P-313 represents the concurrent force system acting at a joint of a bridge truss. Determine the
value of P and E to maintain equilibrium of the forces.
Solution 313
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answer
answer
Problem 314 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 25, 2011 - 7:41am
Problem 314The five forces shown in Fig. P-314 are in equilibrium. Compute the values of P and F.
Solution 314
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answer
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answer
Problem 315 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 25, 2011 - 7:55am
Problem 315The 300-lb force and the 400-lb force shown in Fig. P-315 are to be held in equilibrium by a third force F
acting at an unknown angle θ with the horizontal. Determine the values of F and θ.
Solution 315
Click here to show or hide the solutionBy Cosine Law
answer
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answer
The correct position of F would be as shown below.
Problem 316 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 25, 2011 - 8:05am
Problem 316Determine the values of α and θ so that the forces shown in Fig. P-316 will be in equilibrium.
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Solution 316
Click here to show or hide the solutionBy Cosine Law
answer
answer
Problem 317 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 27, 2011 - 8:56pm
Problem 317The system of knotted cords shown in Fig. P-317 support the indicated weights. Compute the tensile
force in each cord.
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Solution 317
Click here to show or hide the solutionFrom the knot where 400-lb load is hanging
answer
answer
From the knot where 300-lb load is hanging
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answer
answer
Problem 318 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 27, 2011 - 9:19pm
Problem 318Three bars, hinged at A and D and pinned at B and C as shown in Fig. P-318, form a four-link
mechanism. Determine the value of P that will prevent motion.
Solution 318
Click here to show or hide the solutionAt joint B
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At joint C
answer
Problem 319 | Equilibrium of Concurrent Force SystemSubmitted by Romel Verterra on May 27, 2011 - 9:40pm
Problem 319Cords are loop around a small spacer separating two cylinders each weighing 400 lb and pass, as shown
in Fig. P-319 over a frictionless pulleys to weights of 200 lb and 400 lb . Determine the angle θ and the normal pressure N between the cylinders and the smooth horizontal surface.
Solution 319
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Click here to show or hide the solution
answer
answer
Problem 322 | Equilibrium of Force SystemSubmitted by Romel Verterra on May 31, 2011 - 9:57pm
Problem 322The Fink truss shown in Fig. P-322 is supported by a roller at A and a hinge at B. The given loads are normal to the inclined member. Determine the reactions at A and B. Hint: Replace the loads by their
resultant.
Solution 322
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answer
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Thus,RB = 4618.80 lb at 30° with horizontal answer
Problem 323 | Equilibrium of Force SystemSubmitted by Romel Verterra on May 31, 2011 - 10:40pm
Problem 323The truss shown in Fig. P-323 is supported by a hinge at A and a roller at B. A load of 20 kN is applied at
C. Determine the reactions at A and B.
Solution 323
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answer
Thus,RA = 21.06 kN down to the left at 34.7° with the horizontal. answer
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Another Solution
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(okay!)
(okay!)
(okay!)
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Problem 324 | Equilibrium of Three-force SystemSubmitted by Romel Verterra on June 2, 2011 - 11:23pm
Problem 324A wheel of 10-in radius carries a load of 1000 lb, as shown in Fig. P-324. (a) Determine the horizontal
force P applied at the center which is necessary to start the wheel over a 5-in. block. Also find the reaction at the block. (b) If the force P may be inclined at any angle with the horizontal, determine the
minimum value of P to start the wheel over the block; the angle P makes with the horizontal; and the reaction at the block.
Solution 324
Click here to show or hide the solutionPart (a)
answer
answer
Part (b)
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answer
answer
answer
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Problem 325 | Equilibrium of Three-force SystemSubmitted by Romel Verterra on June 2, 2011 - 11:58pm
Problem 325Determine the amount and direction of the smallest force P required to start the wheel in Fig. P-325 over
the block. What is the reaction at the block?
Solution 325
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answer
answer
answer
Problem 326 | Equilibrium of Force SystemSubmitted by Romel Verterra on June 3, 2011 - 11:07am
Problem 326The cylinders in Fig. P-326 have the indicated weights and dimensions. Assuming smooth contact
surfaces, determine the reactions at A, B, C, and D on the cylinders.
Solution 326
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From the FBD of 200 kN cylinder
answer
answer
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From the FBD of 400 kN cylinder
answer
answer
Problem 327 | Equilibrium of Force SystemSubmitted by Romel Verterra on June 4, 2011 - 1:02pm
Problem 327Forces P and F acting along the bars shown in Fig. P-327 maintain equilibrium of pin A. Determine
the values of P and F.
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Solution 327
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→ Equation (1)
Substitute F of Equation (1)
answer
From Equation (1)
answer
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Problem 328 | Equilibrium of Force SystemSubmitted by Romel Verterra on June 4, 2011 - 1:14pm
Problem 328Two weightless bars pinned together as shown in Fig. P-328 support a load of 35 kN. Determine the
forces P and F acting respectively along bars AB and AC that maintain equilibrium of pin A.
Solution 328
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answer
answer
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Problem 329 | Equilibrium of Force SystemSubmitted by Romel Verterra on June 4, 2011 - 1:29pm
Problem 329Two cylinders A and B, weighing 100 lb and 200 lb respectively, are connected by a rigid rod curved
parallel to the smooth cylindrical surface shown in Fig. P-329. Determine the angles α andβ that define the position of equilibrium.
Solution 329
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From the figure
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Thus,
answer
answer
Problem 332 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 6, 2011 - 10:21pm
Problem 332Determine the reactions for the beam shown in Fig. P-332.
Solution 332
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answer
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answer
Problem 333 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 6, 2011 - 10:34pm
Problem 333Determine the reactions R1 and R2 of the beam in Fig. P-333 loaded with a concentrated load of 1600 lb
and a load varying from zero to an intensity of 400 lb per ft.
Solution 333
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answer
answer
Problem 334 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 6, 2011 - 10:47pm
Problem 334Determine the reactions for the beam loaded as shown in Fig. P-334.
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Solution 334
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answer
answer
Problem 335 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 6, 2011 - 10:57pm
Problem 335The roof truss in Fig. P-335 is supported by a roller at A and a hinge at B. Find the values of the
reactions.
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Solution 335
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answer
answer
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Problem 336 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 6, 2011 - 11:05pm
Problem 336The cantilever beam shown in Fig. P-336 is built into a wall 2 ft thick so that it rests against points A and
B. The beam is 12 ft long and weighs 100 lb per ft.
Solution 336
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answer
answer
Problem 337 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 6, 2011 - 11:13pm
Problem 337The upper beam in Fig. P-337 is supported at D and a roller at C which separates the upper and lower
beams. Determine the values of the reactions at A, B, C, and D. Neglect the weight of the beams.
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Solution 337
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answer
answer
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answer
answer
Problem 338 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 6, 2011 - 11:28pm
Problem 338The two 12-ft beams shown in Fig. 3-16 are to be moved horizontally with respect to each other and load P shifted to a new position on CD so that all three reactions are equal. How far apart will R2 and R3 then
be? How far will P be from D?
Solution 338
Click here to show or hide the solutionFrom FBD of beam CD
answer
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Thus, P is 8 ft to the left of D. answer
From the figure above, Rc is at the midspan of AB to produce equal reactions R1 and R2. Thus, R2 and R3 are 6 ft apart. answer
From FBD of beam AB answer
answer
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Problem 339 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 12, 2011 - 11:12pm
Problem 339The differential chain hoist shown in Fig. P-339 consists of two concentric pulleys rigidly fastened
together. The pulleys form two sprockets for an endless chain looped over them in two loops. In one loop is mounted a movable pulley supporting a load W. Neglecting friction, determine the maximum load W
that can just be raised by a pull P supplied as shown.
Solution 339
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answer
Problem 340 - 341 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 13, 2011 - 3:52pm
Problem 340For the system of pulleys shown in Fig. P-340, determine the ratio of W to P to maintain equilibrium.
Neglect axle friction and the weights of the pulleys.
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Solution 340
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Problem 341If each pulley shown in Fig. P-340 weighs 36 kg and W = 720 kg, find P to maintain equilibrium.
Solution 341
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From pulley A
Problem 342 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 23, 2011 - 2:36pm
Problem 342The wheel loads on a jeep are given in Fig. P-342. Determine the distance x so that the reaction of the
beam at A is twice as great as the reaction at B.
Solution 342
Click here to show or hide the solutionThe reaction at A is twice as the reaction at B
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answer
Problem 343 | Equilibrium of Parallel Force SystemSubmitted by Romel Verterra on June 23, 2011 - 2:51pm
Problem 343The weight W of a traveling crane is 20 tons acting as shown in Fig. P-343. To prevent the crane from
tipping to the right when carrying a load P of 20 tons, a counterweight Q is used. Determine the value and position of Q so that the crane will remain in equilibrium both when the maximum load P is applied and
when the load P is removed.
Solution 343
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When load P is removed
→ Equation (1)
When load P is applied
From Equation (1), Qx = 120, thus,
answer
Substitute Q = 20 tons to Equation (1)
answer
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From pulley B
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From pulley C
Thus, answer
Problem 346 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on June 30, 2011 - 11:45pm
Problem 346A boom AB is supported in a horizontal position by a hinge A and a cable which runs from C over a small
pulley at D as shown in Fig. P-346. Compute the tension T in the cable and the horizontal and vertical components of the reaction at A. Neglect the size of the pulley at D.
Solution 346
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Click here to show or hide the solution
answer
answer
answer
Problem 347 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 1, 2011 - 12:00am
Problem 347Repeat Problem 346 if the cable pulls the boom AB into a position at which it is inclined at 30° above the
horizontal. The loads remain vertical.
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Solution 347
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Because θ = 60°, T is perpendicular to AB.
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answer
answer
answer
Problem 348 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 5, 2011 - 10:00pm
Problem 348The frame shown in Fig. P-348 is supported in pivots at A and B. Each member weighs 5 kN/m. Compute
the horizontal reaction at A and the horizontal and vertical components of the reaction at B.
Solution 348
Click here to show or hide the solutionLength of DF
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Weights of members
answer
answer
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answer
Problem 349 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 6, 2011 - 4:26pm
Problem 349The truss shown in Fig. P-349 is supported on roller at A and hinge at B. Solve for the components of the
reactions.
Solution 349
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answer
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answer
answer
Problem 350 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 7, 2011 - 3:30pm
Problem 350Compute the total reactions at A and B for the truss shown in Fig. P-350.
Solution 350
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Click here to show or hide the solution
answer
Thus, up to the left at from horizontal. answer
Problem 351 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 7, 2011 - 4:31pm
Problem 351The beam shown in Fig. P-351 is supported by a hinge at A and a roller on a 1 to 2 slope at B. Determine
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the resultant reactions at A and B.
Solution 351
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Thus, up to the right at from horizontal. answer
Another Solution
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From Equilibrium of Concurrent Force System, three coplanar forces in equilibrium are concurrent.
okay
okay
okay
Problem 352 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 10, 2011 - 11:19am
Problem 352A pulley 4 ft in diameter and supporting a load 200 lb is mounted at B on a horizontal beam as shown
in Fig. P-352. The beam is supported by a hinge at A and rollers at C. Neglecting the weight of the beam, determine the reactions at A and C.
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Solution 352
Click here to show or hide the solutionFrom FBD of pulley
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From FBD of beam
answer
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Thus, up to the right at from horizontal. answer
Problem 354 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 10, 2011 - 8:56pm
Problem 354Compute the total reactions at A and B on the truss shown in Fig. P-354.
Solution 354
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answer
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Thus, up to the right at from horizontal. answer
Problem 355 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 11, 2011 - 9:50pm
Problem 355Determine the reactions at A and B on the Fink truss shown in Fig. P-355. Members CD and FG are
respectively perpendicular to AE and BE at their midpoints.
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Solution 355
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answer
answer
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answer
Problem 356 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 14, 2011 - 4:30pm
Problem 356The cantilever truss shown in Fig. P-356 is supported by a hinge at A and a strut BC. Determine the
reactions at A and B.
Solution 356
Click here to show or hide the solutionFrom right triangles ACD and ACB.
Notice also that triangle ABD is an equilateral triangle of sides 6 m.
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answer
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Thus, up to the right at from horizontal. answer
Problem 357 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 15, 2011 - 4:57pm
Problem 357The uniform rod in Fig. P-357 weighs 420 lb and has its center of gravity at G. Determine the tension in
the cable and the reactions at the smooth surfaces at A and B.
Solution 357
Click here to show or hide the solutionDistance AB
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answer
answer
answer
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Problem 358 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 19, 2011 - 4:04pm
Problem 358A bar AE is in equilibrium under the action of the five forces shown in Fig. P-358. Determine P, R, and T.
Solution 358
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answer
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Problem 359 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 19, 2011 - 7:30pm
Problem 359A 4-m bar of negligible weight rests in a horizontal position on the smooth planes shown in Fig. P-359.
Compute the distance x at which load T = 10 kN should be placed from point B to keep the bar horizontal.
Solution 359
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From the Force Polygon
From the Free Body Diagram
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Problem 360 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 19, 2011 - 7:51pm
Problem 360Referring to Problem 359, what value of T acting at x = 1 m from B will keep the bar horizontal.
Solution 360
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From the Force Polygon
From the Free Body Diagram
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Problem 361 | Equilibrium of Non-Concurrent Force SystemSubmitted by Romel Verterra on July 19, 2011 - 8:35pm
Problem 361Referring to Problem 359, if T = 30 kN and x = 1 m, determine the angle θ at which the bar will be inclined
to the horizontal when it is in a position of equilibrium.
Solution 361
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From the Force Polygon
From the Free Body Diagram
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