VECTOR MECHANICS FOR ENGINEERS W/CON >B
VECTOR MECHANICS FOR ENGINEERS W/CON >B
12th Edition
ISBN: 9781260804638
Author: BEER
Publisher: MCG
bartleby

Videos

Textbook Question
Book Icon
Chapter 3.3, Problem 3.79P

Solve part a of Prob. 3.78, assuming that two 15-N vertical forces have been added, one acting upward at A and the other downward at C.

Chapter 3.3, Problem 3.79P, Solve part a of Prob. 3.78, assuming that two 15-N vertical forces have been added, one acting

(a)

Expert Solution
Check Mark
To determine

The net couple acting on the rectangular co-ordinates.

Answer to Problem 3.79P

The net couple acting on the rectangular co-ordinates is 8.78Nm.

Explanation of Solution

Write the equation of the couple acting at the reactangular side B and C (Refer fig P3.78).

M1=Fd

Here, moment of couple at the point B and C is M1, the force acting couple at the point B and C is F, and the perpendicular distance from the point B and C to the line of action of force is d.

Substitute 25N for F and 0.75m for d.

M1=(25N)(0.75m)=18.75Nm

Write the equation of the couple acting at the reactangular side D and E (Refer fig P3.78).

M2=Fd

Here, moment of couple at the point D and E is M2, the force acting couple at the point D and E is F, and the perpendicular distance from the point D and E to the line of action of force is d.

Substitute 20N for F and 0.4m for d.

M2=(20N)(0.4m)=8.0Nm

Write the equation of the couple vector acting at the reactangular co-ordinates at point B and C (Refer fig P3.78).

M1=(M1sinθ)i^+(M1cosθ)j^

Here, the projection angle is θ represented in x and y axis.

Substitute 18.75Nm for M1 and 40° for θ.

M1=[(18.75Nm)sin40°]i^+[(18.75Nm)cos40°]j^=(12.0523Nm)i^+(14.3633Nm)j^ (I)

Write the equation of the couple vector acting at the reactangular co-ordinates at point D and E (Refer fig P3.78).

M2=(M2cosθ)j^

Substitute 8.0Nm for M2 and 0° for θ.

M2=[(8.0Nm)cos0°]j^=(8.0Nm)j^ (II)

Sketch the moment of additional couple is added to the moment about A of the force applied at C is shown in the Figure 1.

VECTOR MECHANICS FOR ENGINEERS W/CON >B, Chapter 3.3, Problem 3.79P

Write the equation of the additional couple vector acting at the point A of the force applied at C.

M3=Fy×(dxdz)

Here, the additional couple vector formed by the force at the point A and C is M3, force at the point A and C is Fy, perpendicular distance at the point A to the line of action of force is dx, and perpendicular distance at the point C to the line of action of force is dz.

The negative sign of the force shows that the force acting downward direction.

Substitute 15N for Fy, 0.4m for dx, and 0.75m for dz.

M3=(15N)j^×[(0.4m)i^(0.75m)k^]=(11.25Nm)i^(6Nm)k^ (III)

Conclusion:

Write the equation for the net couple acting on the rectangular co-ordinates.

M=M1+M2+M3

Adding the equations (I), (II), and (III) to obtained the net couple.

M=(12.0523Nm)i^+(14.3633Nm)j^(8.0Nm)j^(11.25Nm)i^(6Nm)k^=(0.80Nm)i^+(6.36Nm)j^(6Nm)k^

Write the equation for the magnitude of net couple.

|M|=(0.80Nm)2+(6.36Nm)2+(6Nm)2M=8.780Nm8.78Nm

Therefore, the net couple acting on the rectangular co-ordinates is 8.78Nm.

(b)

Expert Solution
Check Mark
To determine

The direction of the two forces acting on the point B and C that can be used to form couple.

Answer to Problem 3.79P

The direction of the two forces acting on the point B and C is

θx=84.8°, θy=43.6°, θz=133.1°.

Explanation of Solution

Write the equation for direction of the moment of couple formed by the forces at point B and C along x axis.

cosθx=MxM

Here, the angle formed by the moment of couple due to the force located at the point B and C along x axis is θx and moment of couple formed along x axis is Mx.

Rewrite the equation for θx.

θx=cos1(MxM) (IV)

Write the equation for direction of the moment of couple formed by the forces at point B and C along y axis.

cosθy=MyM

Here, the angle formed by the moment of couple due to the force located at the point B and C along y axis is θy and moment of couple formed along y axis is My.

Rewrite the equation for θy.

θy=cos1(MyM) (V)

Write the equation for direction of the moment of couple formed by the forces at point B and C along z axis.

cosθz=MzM

Here, the angle formed by the moment of couple due to the force located at the point B and C along z axis is θz and moment of couple formed along z axis is Mz.

Rewrite the equation for θz.

θz=cos1(MzM) (VI)

Conclusion:

Substitute 0.80Nm for Mx and 8.78Nm for M in equation (IV).

θx=cos1(0.80Nm8.78Nm)=84.8°

Substitute 6.36Nm for My and 8.78Nm for M in equation (V).

θy=cos1(6.36Nm8.78Nm)=43.6°

Substitute 6Nm for Mz and 8.78Nm for M in equation (VI).

θz=cos1(6Nm8.78Nm)=133.1°

Therefore, the direction of the two forces acting on the point B and C is

θx=84.8°, θy=43.6°, θz=133.1°.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
2 A metal block of mass m = 10 kg is sliding along a frictionless surface with an initial speed Vo, as indicated below. The block then slides above an electromagnetic brake that applies a force FEB to the block, opposing its motion. The magnitude of the electromagnetic force varies quadratically with the distance moved along the brake (x): 10 FEB = kx², with k = 5 N m² V₁ = 8 m/s m = 10 kg FEB Frictionless surface Electromagnetic brake ⇒x Determine how far the block slides along the electromagnetic brake before stopping, in m.
Q1: Determine the length, angle of contact, and width of a 9.75 mm thick leather belt required to transmit 15 kW from a motor running at 900 r.p.m. The diameter of the driving pulley of the motor is 300 mm. The driven pulley runs at 300 r.p.m. and the distance between the centers of two pulleys is 3 meters. The density of the leather is 1000 kg/m³. The maximum allowable stress in the leather is 2.5 MPa. The coefficient of friction between the leather and pulley is 0.3. Assume open belt drive.
5. A 15 kW and 1200 r.p.m. motor drives a compressor at 300 r.p.m. through a pair of spur gears having 20° stub teeth. The centre to centre distance between the shafts is 400 mm. The motor pinion is made of forged steel having an allowable static stress as 210 MPa, while the gear is made of cast steel having allowable static stress as 140 MPa. Assuming that the drive operates 8 to 10 hours per day under light shock conditions, find from the standpoint of strength, 1. Module; 2. Face width and 3. Number of teeth and pitch circle diameter of each gear. Check the gears thus designed from the consideration of wear. The surface endurance limit may be taken as 700 MPa. [Ans. m = 6 mm; b= 60 mm; Tp=24; T=96; Dp = 144mm; DG = 576 mm]

Chapter 3 Solutions

VECTOR MECHANICS FOR ENGINEERS W/CON >B

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. 3.19PCh. 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. 3.40PCh. 3.2 - Ropes AB and BC are two of the ropes used to...Ch. 3.2 - Prob. 3.42PCh. 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. 3.62PCh. 3.2 - Prob. 3.63PCh. 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. 3.74PCh. 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. 3.82PCh. 3.3 - Prob. 3.83PCh. 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. 3.92PCh. 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. 3.95PCh. 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. 3.98PCh. 3.3 - Prob. 3.99PCh. 3.3 - Prob. 3.100PCh. 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. 3.111PCh. 3.4 - Prob. 3.112PCh. 3.4 - The roof of a building frame is subjected to the...Ch. 3.4 - Prob. 3.114PCh. 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. 3.117PCh. 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. 3.123PCh. 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. 3.129PCh. 3.4 - Prob. 3.130PCh. 3.4 - A concrete foundation mat of 5-m radius supports...Ch. 3.4 - Prob. 3.132PCh. 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. 3.135PCh. 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 - Prob. 3.140PCh. 3.4 - Prob. 3.141PCh. 3.4 - Prob. 3.142PCh. 3.4 - Replace the wrench shown with an equivalent system...Ch. 3.4 - Prob. 3.144PCh. 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 - The force and couple shown are to be replaced by...Ch. 3 - Prob. 3.156RPCh. 3 - Prob. 3.157RPCh. 3 - While using a pencil sharpener, a student applies...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
How to balance a see saw using moments example problem; Author: Engineer4Free;https://www.youtube.com/watch?v=d7tX37j-iHU;License: Standard Youtube License