VECTOR MECHANICS FOR ENGINEERS: STATICS
12th Edition
ISBN: 9781260912814
Author: BEER
Publisher: MCG
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Chapter 3.3, Problem 3.73P
Four pegs of the same diameter are attached to a board as shown. Two strings are passed around the pegs and pulled with the forces indicated. Determine the diameter of the pegs knowing that the resultant couple applied to the board is 1132.5 lb·in. counterclockwise.
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The force-couple system shown acts on a trapezoidal plate.
a. Determine the value of M1 if the system shown is equivalent to a single force acting at point C.
b. The system shown is equivalent to a force-couple system consisting of R and M2 = 3000 kip-in clockwise. If M1 in this case is 120 kip-in counterclockwise, determine the point of action of the resultant force R along line CD.
M6
2)The forces and couples shown are applied to two screws as a piece of sheet metal is
fastened to a block of wood. Reduce the forces and the couples to an equivalent wrench and
determine (a) the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of
the wrench intersects the xz-plane.
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20 in.
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Chapter 3 Solutions
VECTOR MECHANICS FOR ENGINEERS: STATICS
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 - Prob. 3.7PCh. 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 - Prob. 3.17PCh. 3.1 - Prob. 3.18PCh. 3.1 - Prob. 3.19PCh. 3.1 - Prob. 3.20PCh. 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 - Prob. 3.38PCh. 3.2 - Knowing that the tension in cable AC is 280 lb,...Ch. 3.2 - Knowing that the tension in cable AD is 180 lb,...Ch. 3.2 - Ropes AB and BC are two of the ropes used to...Ch. 3.2 - Ropes AB and BC are two of the ropes used to...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 - Prob. 3.46PCh. 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 - Prob. 3.52PCh. 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 - Prob. 3.61PCh. 3.2 - Prob. 3.62PCh. 3.2 - Two forces F1 and F2 in space have the same...Ch. 3.2 - Prob. 3.64PCh. 3.2 - Prob. 3.65PCh. 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 - A piece of plywood in which several holes are...Ch. 3.3 - The shafts of an angle drive are acted upon by the...Ch. 3.3 - Prob. 3.76PCh. 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 - A crane column supports a 16-kip load as shown....Ch. 3.3 - A dirigible is tethered by a cable attached to its...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 - A hexagonal plate is acted upon by the force P and...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 - Replace the 150-N force with an equivalent...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 - A 110-N force acting in a vertical plane parallel...Ch. 3.3 - The 12-ft boom AB has a fixed end A, and the...Ch. 3.3 - The jib crane shown is oriented so that its boom...Ch. 3.4 - 3.101A 4-m-long beam is subjected to a variety of...Ch. 3.4 - Prob. 3.102PCh. 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 - Two cables exert forces of 90 kN each on a truss...Ch. 3.4 - Pulleys A and B are mounted on bracket CDEF. The...Ch. 3.4 - The roof of a building frame is subjected to the...Ch. 3.4 - A couple of magnitude M = 80 lbin. and the three...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 - Solve Prob. 3.116, assuming that P = 60 N.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 - Assuming = 60 in Prob. 3.122, replace the two...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 - Prob. 3.127PCh. 3.4 - Prob. 3.128PCh. 3.4 - Four signs are mounted on a frame spanning a...Ch. 3.4 - Prob. 3.130PCh. 3.4 - A concrete foundation mat of 5-m radius supports...Ch. 3.4 - Determine the magnitude and the point of...Ch. 3.4 - Prob. 3.133PCh. 3.4 - A piece of sheet metal is bent into the shape...Ch. 3.4 - Prob. 3.135PCh. 3.4 - Prob. 3.136PCh. 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. 3.139PCh. 3.4 - A flagpole is guyed by three cables. If the...Ch. 3.4 - 3.141 and 3.142Determine whether the...Ch. 3.4 - 3.141 and 3.142Determine whether the...Ch. 3.4 - Replace the wrench shown with an equivalent system...Ch. 3.4 - Show that, in general, a wrench can be replaced...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. 3.150RPCh. 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 - Prob. 3.155RPCh. 3 - A 77-N force F1 and a 31-Nm couple M1 are applied...Ch. 3 - Three horizontal forces are applied as shown to a...Ch. 3 - While using a pencil sharpener, a student applies...
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- Two bolts at A and B are tightened by applying the forces and couples shown. Replace the two wrenches with a single equivalent wrench and determine (a) the resultant R, (b) the pitch of the single equivalent wrench, (c) the point where the axis of the wrench intersects the xz plane.arrow_forwardFour pegs of the same diameter are attached to a board as shown. Two strings are passed around the pegs and pulled with the forces indicated. Determine the diameter of the pegs knowing that the resultant couple applied to the board is 1132.5 lb·in. counterclockwise.arrow_forward60 lb 9 in. 40 lb -12 in.- BI 40 lb 60 lb PROBLEM 3.73 Four pegs of the same diameter are attached to a board as shown. Two strings are passed around the pegs and pulled with the forces indicated. Determine the diameter of the pegs knowing that the resultant couple applied to the board is 1132.5 lb-in. counterclockwise.arrow_forward
- Jatapraarrow_forwardThe overhead electric hoist C rides along a track on the horizontal beam AB. In addition to the 500-KN vertical force carried by the hoist, the beam also supports the three vertical forces shown. (a) If x=5m determine the resultant of the four forces carried by the beam. (b) Determine the distance x for which the resultant of the four forces would act at the center of the span AB.arrow_forwardThe pipe ABCDE is supported by ball-and-socket joints at A and D and by cable ECF that passes through a ring C with negligible friction and is attached to hooks at E and F. Knowing that the frame supports a uniformly distributed load of 1500 N/m along segment AB, do the following.1) Shows the correct vector representation of the resultant of the two tension forces acting at ring C. Note that T_CF = T_CE = T2) Explain along which line/axis you can sum moments to generate an equilibrium equation with only the magnitude of the tension force as the unknown. Explain your choice.3) Find the magnitude of the tension force.arrow_forward
- Two bolts at A and B are used to move the trunk of a fallen tree. Replace the forces exerted by the ropes with an equivalent wrench and determine (a) the resultant force , (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the yz plane.arrow_forwardPROBLEM 3 The force-couple system shown acts on a trapezoidal plate. a. Determine the value of M, if the system shown is equivalent to a single force acting at point C. b. The system shown is equivalent to a force-couple system consisting of R and M2 = 3000 kip-in clockwise. If M, in this case is 120 kip-in counterclockwise, determine the point of action of the resultant force Ralong line CD. 50° 1YZ kips 10 in 1X in 10 in A |20 kips 35 kips 8x kips 2Y in M, 50° 1YZ kips C D Parameters X = 4, Y = 8, Z = 7 1X in 13 in 2Y in 24 in 8X kips 83 kips 145 kips 1YZ kips 18 inarrow_forwardQ: Determine the resultant of the force system shown in Fig. (1) and locate it with respect to point A 40 KN 6 80 kN.m 8 6. 10 m 6 m 7 kN Fig. (1)arrow_forward
- 125 N 90 mm 240 N x30mm, BY 75 mm 60 mm 150 N 50 mm 300 N A machine component is subjected to the forces shown, each of which is parallel t one of the coordinate axes. Replace these forces with an equivalent force-couple system at A.arrow_forwardThe forces and couples shown are applied to two screws as a piece of sheet metal is fastened to a block of wood. Reduce the forces and the couples to an equivalent wrench and determine (a) the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the xz plane.arrow_forward6 in. 6 in. 160 lb-in. 18 in. B 30 lb 34 lb H 18 in. 12 in. D 6 in. 8 in. in. Determine whether the force-and-couple system shown can be reduced to a single equivalent force R. If it can, determine R and the point where the line of action of R intersects the yz-plane. If it cannot be so reduced, replace the given system with an equivalent wrench and determine its resultant, its pitch, and the point where its axis intersects the yz-plane.arrow_forward
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