Explanation The vector diagrams corresponding to Fig P3.112 is given below. Write the formula to calculate the single equivalent force at point A. R A = − F a 1 − F a 2 (I) Here, R A is the single equivalent force at point A, F a 1 is the force on left side of pulley A, and F a 2 is the force on right side of pulley A. Write the expression to calculate the moment of couple about point A. M A = ( F a 1 − F a 2 ) r a (II) Here, M A is the moment of couple about point A, and r a is the radius of pulley A. Write the formula to calculate the resultant force about point B. R B = F b 1 + F b 2 (III) Here, R B is the resultant force about point B, F b 1 is the force above point B on pulley B, and F b 2 is the force below point B on pulley B. Write the expression to calculate the moment of couple about point B. M B = ( F b 1 − F b 2 ) r b (IV) Here, M B is the moment of couple about point B, and r b is the radius of pulley B. Write the formula to calculate the equivalent force couple at F . R → F = R A j ^ + ( R B cos θ i ^ + R B sin θ j ^ ) (V) Here, R F is the equivalent force couple at F, θ is the angle made by F b 1 and F b 2 with horizontal. Write the formula to calculate the magnitude of R → F . R F = R F x 2 + R F y 2 (VI) Here, R F x is the is the x-component of R → F and R F y is the y-component of R → F . Write the expression to calculate the direction of R → F . ϕ = tan − 1 ( R F y R F x ) (VII) Here, ϕ is the angle made by R → F with positive x-direction. Write the expression to calculate the resultant moment of couple about point B. M F = R A l 1 + M A − ( R B cos θ ) l 2 + ( R B sin θ ) l 3 + M B (VIII) Here, M F is the is the resultant moment of couple at point F, l 1 is the length from line CF to force F a 1 , l 2 is the length perpendicular to horizontal component of R B , and l 3 is the length perpendicular to vertical component of R B . Write the formula to calculate the distance from F to point of intersection of line of action of equivalent with bottom edge FE. d = M F R F y (IX) Here, d is the distance from F to point of intersection of line of action of equivalent with bottom edge FE. Conclusion: Substitute 120 lb for F a 1 and 160 lb for F a 2 in equation (I) to find R A . R A = − 120 lb − 160 lb = − 280 lb Substitute 120 lb for F a 1 , 160 lb for F a 2 , and 2 in for r a in equation (II) to find M A . M A = ( 120 lb − 160 lb ) ( 2 in ) = − 80 lb ⋅ in Substitute 210 lb for F b 1 and 150 lb for F b 2 in equation (III) to find R B

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 3.4, Problem 3.112P

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The resultant force and the point at which line of action of resultant intersects the bottom edge of the bracket.

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Chapter 3.4, Problem 3.111P

Chapter 3.4, Problem 3.113P

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Chapter 3 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 3.1 - A foot valve for a pneumatic system is hinged at...Ch. 3.1 - 3.2A foot valve for a pneumatic system is hinged...Ch. 3.1 - It is known that a vertical force of 200 lb is...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - An 8-lb force P is applied to a shift lever....Ch. 3.1 - For the shift lever shown, determine the magnitude...Ch. 3.1 - An 11-lb force P is applied to a shift lever. The...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...

Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - Form the vector product P1 P2 and use the result...Ch. 3.1 - The vectors P and Q are two adjacent sides of a...Ch. 3.1 - A plane contains the vectors A and B. Determine...Ch. 3.1 - A line passes through the points (4 m, 3 m) and (2...Ch. 3.1 - Prob. 3.19P Ch. 3.1 - Determine the moment about the origin O of the...Ch. 3.1 - Before the trunk of a large tree is felled, cables...Ch. 3.1 - The 12-ft boom AB has a fixed end A. A steel cable...Ch. 3.1 - A 200-N force is applied as shown to the bracket...Ch. 3.1 - A force P of magnitude 200 N acts along the...Ch. 3.1 - A 6-ft-long fishing rod AB is securely anchored in...Ch. 3.1 - A precast concrete wall section is temporarily...Ch. 3.1 - In Prob. 3.22, determine the perpendicular...Ch. 3.1 - In Prob. 3.23, determine the perpendicular...Ch. 3.1 - In Prob. 3.24, determine the perpendicular...Ch. 3.1 - In Prob. 3.25, determine the perpendicular...Ch. 3.1 - In Prob. 3.25, determine the perpendicular...Ch. 3.1 - In Prob. 3.26, determine the perpendicular...Ch. 3.1 - In Prob. 3.26, determine the perpendicular...Ch. 3.1 - Determine the value of a that minimizes the...Ch. 3.2 - Given the vectors P = 2i + j + 2k, Q = 3i + 4j ...Ch. 3.2 - Form the scalar product B C and use the result...Ch. 3.2 - Three cables are attached to the top of the tower...Ch. 3.2 - Three cables are attached to the top of the tower...Ch. 3.2 - Knowing that the tension in cable AC is 280 lb,...Ch. 3.2 - Prob. 3.40P Ch. 3.2 - Ropes AB and BC are two of the ropes used to...Ch. 3.2 - Prob. 3.42P Ch. 3.2 - The 20-in. tube AB can slide along a horizontal...Ch. 3.2 - Solve Prob. 3.43 for the position corresponding to...Ch. 3.2 - Determine the volume of the parallelepiped of Fig....Ch. 3.2 - Given the vectors P = 3i + 2j + k, Q = 5i + j 2k,...Ch. 3.2 - A crane is oriented so that the end of the 25-m...Ch. 3.2 - 3.48The 25-m crane boom AO lies in the yz plane....Ch. 3.2 - To loosen a frozen valve, a force F with a...Ch. 3.2 - 3.50When a force F is applied to the handle of the...Ch. 3.2 - The 0.61 1.00-m lid ABCD of a storage bin is...Ch. 3.2 - 3.52The 0.61 1.00-m lid ABCD of a storage bin is...Ch. 3.2 - A farmer uses cables and winch pullers B and E to...Ch. 3.2 - Solve Prob. 3.53 when the tension in cable AB is...Ch. 3.2 - A force P of magnitude 520 lb acts on the frame...Ch. 3.2 - 3.56A force P acts on the frame shown at point E....Ch. 3.2 - The frame ACD is hinged at A and D and is...Ch. 3.2 - In Prob. 3.57, determine the moment about the...Ch. 3.2 - The triangular plate ABC is supported by...Ch. 3.2 - 3.60The triangular plate ABC is supported by...Ch. 3.2 - A regular tetrahedron has six edges of length a. A...Ch. 3.2 - Prob. 3.62P Ch. 3.2 - Prob. 3.63P Ch. 3.2 - In Prob. 3.55, determine the perpendicular...Ch. 3.2 - In Prob. 3.56, determine the perpendicular...Ch. 3.2 - In Prob. 3.57, determine the perpendicular...Ch. 3.2 - In Prob. 3.58, determine the perpendicular...Ch. 3.2 - In Prob. 3.59, determine the perpendicular...Ch. 3.2 - In Prob. 3.60, determine the perpendicular...Ch. 3.3 - Two 80-N forces are applied as shown to the...Ch. 3.3 - Two parallel 60-N forces are applied as shown to...Ch. 3.3 - A multiple-drilling machine is used to drill...Ch. 3.3 - Four pegs of the same diameter are attached to a...Ch. 3.3 - Prob. 3.74P Ch. 3.3 - The shafts of an angle drive are acted upon by the...Ch. 3.3 - If P = 0 in the figure, replace the two remaining...Ch. 3.3 - 3.77If P = 20 lb in the figure, replace the three...Ch. 3.3 - The two couples shown are to be replaced with a...Ch. 3.3 - Solve part a of Prob. 3.78, assuming that two 15-N...Ch. 3.3 - Shafts A and B connect the gear box to the wheel...Ch. 3.3 - A 500-N force is applied to a bent plate as shown....Ch. 3.3 - Prob. 3.82P Ch. 3.3 - Prob. 3.83P Ch. 3.3 - A 30-lb vertical force P is applied at A to the...Ch. 3.3 - A worker tries to move a rock by applying a 360-N...Ch. 3.3 - A worker tries to move a rock by applying a 360-N...Ch. 3.3 - The shearing forces exerted on the cross section...Ch. 3.3 - Knowing that = 60, replace the force and couple...Ch. 3.3 - Three control rods attached to a lever ABC exert...Ch. 3.3 - A rectangular plate is acted upon by the force and...Ch. 3.3 - While tapping a hole, a machinist applies the...Ch. 3.3 - Prob. 3.92P Ch. 3.3 - Replace the 250-kN force P with an equivalent...Ch. 3.3 - A 2.6-kip force is applied at point D of the...Ch. 3.3 - Prob. 3.95P Ch. 3.3 - To keep a door closed, a wooden stick is wedged...Ch. 3.3 - A 46-lb force F and a 2120-lbin. couple M are...Ch. 3.3 - Prob. 3.98P Ch. 3.3 - Prob. 3.99P Ch. 3.3 - Prob. 3.100P Ch. 3.4 - 3.101A 4-m-long beam is subjected to a variety of...Ch. 3.4 - A 4-m-long beam is loaded as shown. Determine the...Ch. 3.4 - Determine the single equivalent force and the...Ch. 3.4 - Five separate force-couple systems act at the...Ch. 3.4 - The weights of two children sitting at ends A and...Ch. 3.4 - Three stage lights are mounted on a pipe as shown....Ch. 3.4 - A beam supports three loads of given magnitude and...Ch. 3.4 - A 6 12-in. plate is subjected to four loads as...Ch. 3.4 - Gear C is rigidly attached to arm AB. If the...Ch. 3.4 - To test the strength of a 625 500-mm suitcase,...Ch. 3.4 - Prob. 3.111P Ch. 3.4 - Prob. 3.112P Ch. 3.4 - The roof of a building frame is subjected to the...Ch. 3.4 - Prob. 3.114P Ch. 3.4 - A couple M and the three forces shown are applied...Ch. 3.4 - A machine component is subjected to the forces and...Ch. 3.4 - Prob. 3.117P Ch. 3.4 - As follower AB rolls along the surface of member...Ch. 3.4 - A machine component is subjected to the forces...Ch. 3.4 - Two 150-mm-diameter pulleys are mounted on line...Ch. 3.4 - As an adjustable brace BC is used to bring a wall...Ch. 3.4 - In order to unscrew the tapped faucet A, a plumber...Ch. 3.4 - Prob. 3.123P Ch. 3.4 - Four forces are applied to the machine component...Ch. 3.4 - A blade held in a brace is used to tighten a screw...Ch. 3.4 - A mechanic uses a crowfoot wrench to loosen a bolt...Ch. 3.4 - Four horizontal forces act on a vertical...Ch. 3.4 - Determine the magnitude of the force P for which...Ch. 3.4 - Prob. 3.129P Ch. 3.4 - Prob. 3.130P Ch. 3.4 - A concrete foundation mat of 5-m radius supports...Ch. 3.4 - Prob. 3.132P Ch. 3.4 - Three forces of the same magnitude P act on a cube...Ch. 3.4 - A piece of sheet metal is bent into the shape...Ch. 3.4 - Prob. 3.135P Ch. 3.4 - Prob. 3.136P Ch. 3.4 - Two bolts at A and B are tightened by applying the...Ch. 3.4 - Two bolts at A and B are tightened by applying the...Ch. 3.4 - Prob. 3.139P Ch. 3.4 - Prob. 3.140P Ch. 3.4 - Prob. 3.141P Ch. 3.4 - Prob. 3.142P Ch. 3.4 - Replace the wrench shown with an equivalent system...Ch. 3.4 - Prob. 3.144P Ch. 3.4 - Show that a wrench can be replaced with two...Ch. 3.4 - Show that a wrench can be replaced with two...Ch. 3 - A 300-N force P is applied at point A of the bell...Ch. 3 - A winch puller AB is used to straighten a fence...Ch. 3 - A small boat hangs from two davits, one of which...Ch. 3 - Prob. 3.150RP Ch. 3 - A single force P acts at C in a direction...Ch. 3 - The 23-in. vertical rod CD is welded to the...Ch. 3 - In a manufacturing operation, three holes are...Ch. 3 - A 260-lb force is applied at A to the rolled-steel...Ch. 3 - The force and couple shown are to be replaced by...Ch. 3 - Prob. 3.156RP Ch. 3 - Prob. 3.157RP Ch. 3 - While using a pencil sharpener, a student applies...

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The resultant force and the point at which line of action of resultant intersects the bottom edge of the bracket.

Solution Summary: The author explains the resultant force and the point at which line of action intersects the bottom edge of the bracket. The vector diagrams corresponding to Fig.

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The resultant force and the point at which line of action of resultant intersects the bottom edge of the bracket.

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Chapter 3 Solutions