2-94. x y 30Њ 30Њ 45Њ F1 ϭ 80 N F2 ϭ 75 N F3 ϭ 50 N 2–147. Determine the magnitude of the projected component of F1 along the line of action of F2, if the cables each exert a force of 410 N on the post. 2-125: Determine the projected component of force FAC along the into components along the u and v axes and determine the magnitudes of these components. 2–124 Determine the magnitude of the projected component of the force F = {400i – 200j + 500k} N acting along the cable CA and perpendicular to it. 1) Find the forces along AB and AC in the Cartesian vector form. [α = 76. 66 kN T ตัวอย่างที่ 2. So when applying the condition of net force to be zero in the y direction, we get FAB cos30 = (2/3)*900. Determine the magnitude of the projected component of force FAC acting along the Z axis. Clarification: As the system is in equilibrium so we need to balance the forces. This gives us force along AB be 693N. 2-125: Determine the projected component of force FAC along the Resolve the force F acting at C into two components acting along members AC and BC , if θ= 20o. R. What is the buoyant force (N), γ is the specific weight of fluid (N/m3), and ∀ is the volume of the body (m3) The direction of the buoyant force, which is the force of the fluid on the body, is opposite to that shown on the freebody diagram. Determine the magnitude of the projected component of force FAB acting along the z axis. The coefficient of kinetic friction between the crate and the ground is m k = 0. Suppose that a = 2 m and b = 5 m. , S. 5650 tan 13 tan Determine the projection of this force on a line which originates from (2 , -5, 3) and passes through point (5 ,2,-4) 54. 25. Suppose a= 3 m, and b= 4 m By signing up, you'll get 1 Answer to the final answer should be 52. 4. Ahmed A. 5 N, 27. Geometry Method •The magnitude of the resultant force is equivalent to the area under the curve of the distributed load 10 kN/m 1 m 3 m 2 m ตัวอย่างที่ 2. to/2h3hcFq Determine the magnitude of the projection of the force F1 along cable AC. The unit vector uAC must be determined first. 2 m)cos9k P = —P sin "j + P cos 4k 0. 2-122: Determine the angle u between cables AB and AC . (Figure 1) Part B: Determine the magnitude of the projection of the force F1 along cable AC. ) 20 Engineering Mechanics for Preparatory Year Part (i): statics Prepared by: Dr. 5 m and b = 4 m. f*2–116. 57ft•lb 34 Moments Along an Axis Q: Determine the magnitude of the projection of the force F1 along cable AC. Using this result to apply the sines law, Fig. 2-124: Determine the projected component of force FAB along the axis of st 2. Cable AB exerts a force of 80 N on the end of the 3-m-long boom OA. 8 kN) 2(3 kN)(4. Get the book: http://amzn. 18 (Merium & Kraige) A force 𝐹 with a magnitude of 100 N is applied at the origin O of the axes x-y-z as shown. Determine the magnitude and The 20-kg crate is subjected to a force having a constant direction and a magnitude F = 100 N. Determine the magnitude of the projection of the force Fl along cable AC 2. Homework Equations Vector properties The Attempt at a Solution My first course of action was to find the component form of vectors AB, AC, and AD (representing the three cables). If cable AB is subjected to a tension of 700 N, determine the tension in cables AC and AD and the magnitude of the vertical force F. The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the guy wires AC and AD. Respectively, my results were <-45, 0, 115>, <-105, -70, 115>, and <0, -135, 115>. Using the eye hook example, let's see how we would find the projection of force vector along line CD as depicted in the figure below. 48 8=1800 - (600+550) = = (30 1b) - = 1b M=4901b The equi'nlent force-couple s»tem at is Determine the magnitude and direction of the couple M which will replace the two given couples and still produce the same external effect on the block. 2–115. Knowing that P must have a 350-lb vertical component, determine (a) The magnitude of the force P, (b) Its horizontal component. Determine the magnitude of the projection of the force F1 along cable AC. Force Triangle 00 2(1200 N)cos 850 SOLUTION (a) Free - Body Diagram Law Of cosines: P-1294. 7 lb-in. 8 m By signing up, you'll get Answer to: Determine the magnitude of the projection of the force F 1 along cable aAC. ABE: 4. 18 . a) 23. Waseem 'Younis O, o J 36) C , - qs k F = 6001b 36 ft - 7001b 12 ft 12ftc Q. Determine the projection of this force along the z axis of the pole. 7° above the horizontal, and it is the force that tends to shear the pin in joint A. F. (Figure 1) Express your answer to three significant figures and include Solution for • Determine the angle between cable AC and strut AO. Force: Vector with magnitude and direction Magnitude – a positive numerical value representing the size or amount of the force Directions – the slope and the sense of a line segment used to represent the force – Described by angles or dimensions – A negative sign usually represents opposite direction Point of application If cable AB is subjected to a tension. For example, in Fig. Instructor Solutions Manual (Download only) for Engineering Mechanics: Statics, 13th Edition. 2 m)sin ej+ (0. Determine the required tension T in cable AB such that the net effect of the two cable tension is a downward force at point A. Essam Mohammed 7. 8-kN force directed along the axis of the automobile. the maximum allowable tension is 1200 N in cable AC and N in cable BC, determine (a) the magnitude Of the largest force P that can be applied at C, (b) the cœresrx'nding value of a. Solution Write the position vectors to the points A, B, and C. 226. 2 m . Knowing that the tension is 500 N in AB and 160 N in AD, determine graphically the magnitude and direction of the resultant of the forces exerted by the stays at A using Force is a Fixed Vector In case of rigid bodies, line of action of force is important (not its point of application if we are interested in only the resultant external effects of the force), we will treat most forces as Cable Tension P External effect: Forces applied (applied force); Forces exerted by bracket, bolts, Foundation (reactive force) Find step-by-step Physics solutions and your answer to the following textbook question: If $\theta=60^{\circ}$ and F=450 N determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. to/2h3hcFq Answer to: Determine the magnitude of the projection of the force F_1 along cable AC. 2 F2 = 40 N 4 m e F1-70 N 2 m 3 m 2 m 3 m Probs. AsmahanAl-¶u6eÆ T. Determine the magnitude of the projected component of z force FAB acting along the z axis. Plan: 1) Using the geometry and trigonometry, write F 1 and F 2 in the Cartesian vector form. 25 0. 6 m . Therefore, the buoyant force has a magnitude equal to the weight of the fluid displaced by the body and is 2–14 . SOLUTION Free-Body Diagram of Rod AB: — (650 — 250) 115. Determine (a) the moment of the 300-N force about D, (b) the magnitude and sense of the horizontal force applied at C that creates the same moment about D, (c) the smallest force applied at C that creates the same moment about D. Determine the magnitude R of this downward force. 115. Equating the force components along the x and y axes algebraically by referring to Fig. more_vert Determine the magnitude of the projection of the force F1 along cable AC. Suppose that α = 3. 3. Determine the magnitude T of the tension in the supporting cable and the magnitude of the force on the pin at A for the jib crane shown. The line of action of F passes through a point A whose coordinates are 3m, 4m and 5m. A force of 50 N is applied to the handle of the door as shown. Therefore, the buoyant force has a magnitude equal to the weight of the fluid displaced by the body and is Determine the magnitude and the coordinate direction angles of the resultant force acting on the ring. The magnitude of force IF2I=40 N. Member AC is therefore in pure tension. If the magnitude of the resultant force acting on the bracket is to be 450 N directed along the positive u axis, determine the magnitude of F1 and its angle φ from y axis. Determine the magnitude of the projection of this force along the boom. If 700N, and 560N, determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole. 41. 2-114/115 This problem has been solved! See the answer See the answer See the answer done loading Mechanical Engineering INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit) Determine the magnitude of the projection of the force F1 along cable AC. Specify the two force F and –F, applied in the two faces of the block parallel to the y-z plane, which may replace the four given forces. A model is placed in a test channel and three cables are used to align its bow on the channel centerline. Suppose that a = 3. rc = (0. 125 m a a SOLutiOn If cable AB is subjected to a tension of 700 N, determine the tension in cables AC and AD and the magnitude of the vertical force F. Knowing that Mx = +20 N m and M = —8. Determine the angle between the force and the line AO, and the magnitude of the projection of force along the line AO Step 1 Step 2 Established dot product F •r AO Step 3 Magnitude of the projection of force, F AO r AO Established position vector = cos-1{(F •r AO)/(F r AO)} F AO = F •u AO or F cos For the frame and loading shown, determine the reactions at C and D. Determine (a) the x, y and z scalar components of F, (b) the projection F xy of F on the x-y plane, and (c) the projection F OB of F along the line OB. Part A Determine the magnitude of the projection of the force F1 along cable AC. 4, 1. Therefore, the buoyant force has a magnitude equal to the weight of the fluid displaced by the body and is The magnitude of a vector projection is a scalar projection. pliers, determine the clamping force exerted on the smooth pipe B and the magnitude of the resultant force that one of the members exerts on pin A . 3o] 35o F=100N θ B A force F with a magnitude of 100 N is applied at the origin O of the axes x-y-z as shown. For a given speed, the tension is 40 lb in cable AB and 60 lb in cable AE. Determine θ, so that the component F AC is directed toward C and has a magnitude of 150N. 2sine o. Knowing that the length of the rod is 9 in. determine (a) the vertical component of the force exerted on the shearing blade at D, (b) the reaction at C . The cable stays AB and AD help support pole AC. 3) Determine the magnitude and the coordinate angles of . 10- The component of force F acting along line aa is required to be 30 lb. By signing up, you'll If the resultant of the four forces is FR = 5-360k6lb, determine the tension developed in each cable. Determine the projection of the moment of this force about the hinged axis z. A single force P acts at C in a direction perpendicular to the handle BC of the crank shown. 2 m C D 0. The line of acting of 𝐹 passes through a point A whose coordinates are 3 m, 4 m, and 5 m. 2) Add the two forces to get the resultant force, F. along cable AC. Determine the drag force exerted on the hull and the tension in cable AC Department of Engineering. Determine the magnitude and direction θ of force F and the couple moment M such that the loading system is equivalent to a resultant force of 600N, acting vertically downward at O, and a clockwise moment of 400 N-m. 6643 kN AC AC T T =+ - = Using the law of sines: sin sin30 3 kN 2. 33 Moments Along an Axis, Couples Monday, September 24, 2012 r OA r OB B C Example ! The magnitude of the moment produced by F along a-a is then − 3 7 − 2 7 6 7 0ft4ft0ft −400lb400lb200lb − 3 7 0ft −400lb − 2 7 4ft 400lb − 3 7 (800ft•lb)− 2 7 (0)+ 6 7 (1600ft•lb) = 7200ft•lb 7 =1028. F 1. For example, if a child is pulling the handle of a wagon at a 55° angle, we can use projections to determine how much of the force on the handle is actually moving the wagon forward (). Ans: F=50i−40j+180klb, F = 191 lb, α = 74. Fan, Kai Beng. 4 N , θ= 4. For the frame and loading shown, determine the reactions at C and D. 523 kN Ans. A force of magnitude 750N is directed along AB where A is (0 . Suggestion: Use a scaler analysis. (Figure 1) Express your answer to three significant figures and include the appropriate units. Express the result as a Cartesian vector. II. 9 kN. C = 560 N. Forces in a Space Forces on a This force acts along the strut AC, at an angle of 33. Determine the magnitude of the projection of the force F_1 along cable AC. 598 Submit Previous Answers Request Answer Figure < 1of1 > X Incorrect; Try Again; 3 attempts remaining Provide Feedback The 500-N weight is supported by two cables, the cable forces being F1 and F2. 1294 N Law Of sin 1200 N sin is the buoyant force (N), γ is the specific weight of fluid (N/m3), and ∀ is the volume of the body (m3) The direction of the buoyant force, which is the force of the fluid on the body, is opposite to that shown on the freebody diagram. Determine the angle between the force and the line AO, and the magnitude of the projection of force along the line AO Step 1 Step 2 Established dot product F •r AO Step 3 Magnitude of the projection of force, F AO r AO Established position vector = cos-1{(F •r AO)/(F r AO)} F AO = F •u AO or F cos into components along the u and v axes and determine the magnitudes of these components. 2. If you like to add another force F4 so the total resultant force of four forces will be in the positive y direction, determine the direction ɵ of the force F4. Engineering Mechanics: Statics. The beam AB is a standard 0. )hC rac (JA c 18 ft 27 100-lb force acting along the axis BC of the pipe and perpendicular to it. Dr. Hibbeler Pearson Education, Inc. 2-132. weight In equilibrium. Determine the vector expression for the tension T as a force acting on member AD. Due to symmetry, the tension in the four cables is the same. 3) Determine the magnitude and α, β, γ. F net ma (5. 8 N , F AC = 168. Also find the magnitude of the projection of T along the line AC. View Answer. O A 80 N 3 m B z y x 4 m 60Њ 6 . Determine the magnitude of F and its component along line bb. A: Eng. 6 N but i need the steps how. 5 2 1. 𝐀; 3. The coordinate direction angles for F2 are F2x Determine the x and y components of F1 and F2. Determine the magnitude of the pro 2-124. Determine the angle u between the two cables. Three forces act on the bracket. 5 m and b = 5 m . ) MB 9 Zo 1b (20 1b) cos 500 Part A Determine the magnitude of the projection of the force F1 along cable AC. Given the vectors A = 8i + 4j -2k N B = 2j + 6k m C = 3i -2j + 4k m Calculate the following: a. 2,0) m. Upper Saddle River, New Jersey. 1) F net,x ma x, F net,y ma y, F net,z ma z (5. If the resultant force acting on the bracket is directed along the positive y axis, determine the magnitude of the resultant force and the coordinate direction angles of F so that b 6 90 . 2—113. 5 m and b = 4. 6 m. Determine the magnitude of the projected component of F1 along the line of 2-133. 2-123. The turnbuckle is tightened until the tension in the cable AB equals 2. When s = 15 m, the crate is moving to the right with a speed of 8 m/s. 2-134 Instructor’s Solutions Manual ENGINEERING MECHANICS STATICS TENTH EDITION R. (Figure 1) Express your answer to three significant figures and include the 2-131. 5 ft 56. ass. The force at C on the strut AC is also 48. 2 Determine the angle θ between them. Cable AB exerts a force of 80 N on the end of the 3 m long boom OA. A FAC 600 lb 36 ft FAB 700 lb SOLUTION Unit Vector: The unit vector uAB must be determined point along the bar . (Figure 1) Hibbeler Statics 14e: Problem 2-115 Page 1 of 1 Problem 2-115 Determine the magnitude of the projection of the force F 1 along cable AC. Knowing that the resu; 2. 2)m and B is (1 . 07 kN acting upward to the right to balance RA on the two-force member as shown in Figure 3–3. 598 Submit Previous Answers Request Answer Figure < 1of1 > X Incorrect; Try Again; 3 attempts remaining Provide Feedback Part A Determine the magnitude of the projection of the force F1 along cable AC. Abu-foul Eng. Homework Equations The Attempt at a Solution I was able to find the vector expression for T without any real trouble: Find the magnitude of the projected component ofthe force along the pipe AO. 100 N 50 mm 450 250 mm 100 N Prob. SOLUTION Using the law of cosines: 22 2(3 kN) (4. 2-125: Determine the projected component of force FAC along the The force are acting on the hook at point A. НА Figure 1 of 1 Value Units |(F1)Ac| = Request Answer Submit F = 40 N ( Return to Assignment F = 70 N Provide Feedback 2 m B 2 m Determine the angle θ between the two cables. 9- The force acting on the gear tooth is F = 20 lb. determine by trigonometry the tension in rope AC and the value of α so that the resultant force exerted at A is a 4. 598 Submit Previous Answers Request Answer Figure < 1of1 > X Incorrect; Try Again; 3 attempts remaining Provide Feedback Physics 3-D Force Vector Question. of the force F acting in the Q: Determine the magnitude of the projection of the force F1 along cable AC. 2) Add F 1 and F 2 to get F R . 2-125. In order to determine the magnitude of each component, a A 20-1b force is applied to the control rod AB as shown. Determine the magnitude of the projection of theforce F1 along cable AC. 6N b) 55N c) 89N d) -29N Answer: a 2–61. The systems of four forces acts on the roof truss determine the resultant force and specify its Determine the force P needed to hold F6-13. 598 Submit Previous Answers Request Answer Figure < 1of1 > X Incorrect; Try Again; 3 attempts remaining Provide Feedback It is desired to determine the drag force at a given speed on a prototype sailboat hull. the final answer should be 52. 5650 tan 13 tan • Determine the reactions at the wheels by solving equations for the sum of moments about points above each axle. A: Given Data: The magnitude of force IF1I=70 N. (i) A simplified sketch of the crate, ramp and the tensile force (T) in the cable is shown at the point of the crate sliding up the ramp. Suppose that a = 2. 25 m)i + (0. Cable AC exerts on beam AB a force P directed along line AC. Neglect the size of the doorknob. 6643 kN 34. 3) Determine the magnitude and the coordinate angles of F R . SOLUTION Since BD is a two-force member, the reaction at D must pass through Points B and D. Determine the magnitude of force F so that the resultant force of the three forces is as small as possible. 02—121. Find: The magnitude and the coordinate direction angles of the Force Projection: In some problems, we are interested in finding the projection (component) of a force in a specified direction. 7 m>s Determine the magnitude of the projection of the force F1 along the cable AC. 2cos9 —PsinØ P cose is the buoyant force (N), γ is the specific weight of fluid (N/m3), and ∀ is the volume of the body (m3) The direction of the buoyant force, which is the force of the fluid on the body, is opposite to that shown on the freebody diagram. 4°] 3 Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the positive u axis. Ālso determine the projected component of force FAC along the axis of strut AO. Engineering Mechanics (14th Edition) Edit edition Solutions for Chapter 2 Problem 115P: Determine the magnitude of the projection of the force F1 along cable AC. Determine the angles θ and ? made between the axes OA of the flag pole and AB and AC, respectively, of each cable. Question: Determine the magnitude of the projection of the force. We return to this example and learn how to solve it after we see how to calculate projections. 8 kN)cos 30° 2. and that = 250, determine the moment of the force about Point B by resolving the force into components along AB and in a direction perpendicular to AB. x Fy = 2. The force are acting on the hook at point A. (Ans. Prob. Suppose thata = 3. Given a flow network G = (V, E), let f1 and f2 be functions from V × V to R. 2–122 Determine the angle θ between the cables AB and AC. 3 a a = = 2. 2–8a, F is to be resolved into two components along the two members, defined by the u and v axes. The guy cables AB and AC are attached to the top of the transmission tower. Determine (a) the x,y and z scalar components of 𝐹 , (b) the projection 𝐹 of 𝐹 on the x-y Question: Determine the magnitude of the projection of the force. Determine the projection of force F = 400 N, acting along line AC of the pipe assembly. Knowing that the tension in wire AC is 120 N, determine (a) the components of the force exerted by this wire on the pole, (b) the angles θx, θy, and θz that the force forms with the coordinate axes. Determine (a) the x,y and z scalar components of 𝐹 , (b) the projection 𝐹 of 𝐹 on the x-y Determine the magnitude of the resultant force and its y direction, measured clockwise from the positive x axis. • Check the values obtained by verifying that the sum of force components perpendicular to the track are zero. 2-123: Determine the angle f between cable AC and strut AO . Suppose that a = 2 m and b = 4. Add labelled arrows to the sketch to indicate the following forces: Calculate the tension force of EACH of the three cables. A 300-N force is applied at A as shown. 8, 0, 1. Free-Body Diagram: (Th/te-force body) Reaction at C must pass through E, where the reaction at D and the 150-1b load intersect. Statics: Mechanics for Engineers. 02 N Since P 1200 N, the solution is correct. Also, what are the projections of F1 and F2 along the y 2-122. Cable Crate Winch The winch cable is parallel to the ramp. 4 m . Ans: v = 10. Determine the magnitudes of the components of F 600 N acting along and perpendicular to segment DE of the pipe assembly. The unit vector uCB must be determined first. 02 cos 75° = 0. 3100 26. 5 ⎠ The magnitude of the projection of r1 along r2. 75 N m, and Mz = —30 N m, determine the magnitude of P and the values of and 9. Determine the magnitude and direction of the couple M which will replace the two given couples and still produce the same external effect on the block. Write the vector form of the force. 25 2 a b + cos2 75° + a b = 1 Fx F F F = 2. Yap, and Peter Schiavone. PROBLEM SET NO. The 30-N forces act parallel to the y-z plane. { F }_ { 1 } F 1. 19 . 2-121: Determine the magnitude of the projection of force F = 600 N along 2. 5. Posted in Uncategorized Post navigation. 02 kN Ans. The coordinates for points A, B and C are 0, – 0. 600 N 2—115. C. 2- Water pressure in the supply system exerts a downward force of 135 N on the vertical plug at A . 2) Add the two forces to get the resultant force, F R . Determine the angle θ between the two cables attached to the post. Homework Problem Sets Set #1. Ans: 450. Compute the magnitude of the moment of the force P about point A Fz g F SOLUTION b Fy y cos2 a + cos2 b + cos2 g = 1 a 1. Singapore: Pearson, 2013. Calculate the moment of the forces about the origin. Find: The magnitude and the coordinate direction angles of the resultant force. Determine the magnitudes of the components of force F = 400 N acting parallel and perpendicular to segment BC of the pipe assembly. 2-124. Find the tension in the cable AC. Suppose that a=3. 4O, 1714 N m. ENGN 36. 2 The force F of magnitude 1500 N is to be resolved into two components along line a-a and b-b. 0. Determine its speed when s = 25 m. z C to resolve a force into two components in order to study its pulling or pushing effect in two specific directions. 8°, β = 102°, 𝛾= 19. (Figure 1) Express your answer to three significant figures and include the appropriate units I(FI)AC 623. Answer to: Determine the magnitude of the projection of the force F_1 along cable AC. The cables each exert a force of 400 N on the post. F6-13 the 60-1b If a 100-N force is applied to the handles of the F6-15. Image from: Hibbeler, R. F6-15 equivalent force-couple s»tem at R (b) Determine the single force that is equivalent to the force-couple s;stem obtained in Part a, and sFecifyits Eoint of applicafion on the lever First note that the tun 20-1b forces fonnA couple Then where F -481b . Newton’s second law: The net force on a body is equal to the product of the body’s mass and its acceleration. 5-m I-beam with a mass of 95 kg per meter of length The guy cables AB and AC are attached to the top of the transmission tower. 5 m and b = 4 m . . Question: Determine the magnitude of the projection of the force F1 along cable AC. The tension in cable AB is 8 kN. 5m and b=5m. • Determine the cable tension by solving the equation for the sum of force components parallel to the track. Determine the required tension T in cable AC such that the net effect of the two cable tensions is a downward force at point A Determine the magnitude R of this downward force. … Solutions for problems in chapter 2 Determine the magnitude of the projection of the force F1 along cable AC. 2) - The acceleration component along a given axis is caused only by the sum of the force components along the same axis, and not by force components along any other axis. Determine the magnitude of the projection of the force F1 z along cable AC. Determine the magnitude of the projection of the moment cause by the force about the aa axis. 6° 2. I know how to figure out F2x, F2y, and F2z, but I have no idea how to find F1y and F1x. B = 700 N and F. Determine the magnitude of the projection of the force F{eq}_1 {/eq} along cable AC. Determine the angle α, knowing that the components of F along line a-a to be 1200 N. Please show The tension in cable AC is 8 kN. A C [Answer : F CB = 163. Resolve this force into two components acting along the lines aa and bb. . Given: Two forces are acting on a flag pole as shown in the figure. Determine the angle u between the cables AB and AC.