VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
11th Edition
ISBN: 9781259633133
Author: BEER
Publisher: MCG
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 4.1, Problem 4.24P

(a)

To determine

The reaction at A and B of the plate shown in P4.24(a).

(a)

Expert Solution
Check Mark

Answer to Problem 4.24P

The reaction at A is 20.0lb and reaction at B is 50.0lb and is directed along 36.9° above negative x axis in the upward direction.

Explanation of Solution

Take vectors along positive x and y axis are positive.

Let A is the reaction at the point A , B is the reaction at the point B and Bx and By are the component of the reaction B.

The free body diagram is sketched below as figure 1.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 4.1, Problem 4.24P , additional homework tip  1

Here, Bx and By are the magnitude of x and y component of reaction B at the point A and B is the magnitude of reaction B.

Write the expression for the moment at B.

MB=F×D (I)

Here, MB is the net moment at B, F is the force, and D is the perpendicular distance between the B and the point where force is experienced.

Above equation implies that net moment at any point is the sum of product of each force acting on the system and perpendicular distance of the force and the point.

The moment at B is due to the reaction A and forces 50lb and 40lb.

Thus, the complete expression of MB is

MB=A(20in.)+(50lb)(16in.)(40lb)(10in.) (II)

Here, MB is the sum of all anticlockwise moment of force at A.

At equilibrium, the sum of the moment acting at A will be zero

MB=A(20in.)+(50lb)(16in.)(40lb)(10in.)=0 (III)

Write the expression for the net force along the x direction.

Fx=Bx+40lb (IV)

Here, Fx is the sum of all force along the x direction.

At equilibrium, the net force along the x direction will be zero.

Fx=Bx+40lb=0 (V)

Write the expression for the net force along the y direction.

Fy=By+A50lb=0 (VI)

Here, Fy is the sum of all force along the y direction.

At equilibrium, the net force along the y direction will be zero.

Fy=By+A50lb=0 (VII)

Let α be the angle that B makes with x axis.

Write the expression for the magnitude of net reaction at B.

B=Bx2+By2 (VIII)

Here, B is the magnitude of net reaction at point B.

Therefore, write the expression for the tanα.

tanα=ByBx (IX)

Calculation:

Rearrange equation (III) to get B.

A(20in.)+(50lb)(16in.)(40lb)(10in.)=0A=+20lb

From figure 1, the reaction A acts in the upward direction.

Rearrange equation (V) to get Bx .

Bx=40lb

The x component of reaction acts in the x direction.

Rearrange equation (VII) to get By.

By=50lbA

Substitute 20.0lb for A in above equation to get By.

By=50lb20.0lb=30.0lb

Substitute 40lb for Bx and 30.0lb for By in the equation (VIII) to get B.

B=(40lb)2+(30lb)2=50.0lb

Substitute 40lb for Bx and 30.0lb for By in the equation (IX) to get α.

tanα=30.0lb40.0lbα=36.9°

Therefore, the reaction at A is 20.0lb and reaction at B is 50.0lb and is directed along 36.9° above negative x axis in the upward direction.

(b)

To determine

The reaction at A and B of the plate shown in P4.23(b).

(b)

Expert Solution
Check Mark

Answer to Problem 4.24P

The reaction at A is 23.1lb and is directed 60.0° above positive x axis and reaction at B is 59.6lb and is directed 30.2° above negative x axis.

Explanation of Solution

Take vectors along positive x and y axis are positive.

Let A is the reaction at the point A , B is the reaction at the point B and Bx and By are the component of the reaction B.

The free body diagram is sketched below as figure 1.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 4.1, Problem 4.24P , additional homework tip  2

Here, Bx and By are the magnitude of x and y component of reaction B at the point A and B is the magnitude of reaction B.

Write the expression for the moment at B.

MB=F×D (I)

Here, MB is the net moment at B, F is the force, and D is the perpendicular distance between the B and the point where force is experienced.

Above equation implies that net moment at any point is the sum of product of each force acting on the system and perpendicular distance of the force and the point.

The moment at B is due to the y component of reaction A and forces 50lb and 40lb.

Thus, the complete expression of MB is

MB=(Acos30°)(20in.)+(50lb)(16in.)(40lb)(10in.) (II)

Here, MB is the sum of all anticlockwise moment of force at A.

At equilibrium, the sum of the moment acting at A will be zero

MB=(Acos30°)(20in.)+(50lb)(16in.)(40lb)(10in.)=0 (III)

Write the expression for the net force along the x direction.

Fx=Asin30°+Bx+40lb (IV)

Here, Fx is the sum of all force along the x direction.

At equilibrium, the net force along the x direction will be zero.

Fx=Asin30°+Bx+40lb=0 (V)

Write the expression for the net force along the y direction.

Fy=By+Acos30°50lb (VI)

Here, Fy is the sum of all force along the y direction.

At equilibrium, the net force along the y direction will be zero.

Fy=By+Acos30°50lb=0 (VII)

Let α be the angle that B makes with x axis.

Write the expression for the magnitude of net reaction at B.

B=Bx2+By2 (VIII)

Here, B is the magnitude of net reaction at point B.

Therefore, write the expression for the tanα.

tanα=ByBx (IX)

Calculation:

Rearrange equation (III) to get B.

(Acos30°)(20in.)+(50lb)(16in.)(40lb)(10in.)=0A=23.1lb

From figure 1, the reaction A is directed at 60° above positive x axis

Rearrange equation (V) to get Bx .

Bx=40lbAsin30°

Substitute 23.09lb for A in above equation to get Bx.

Bx=40lb(23.09lb)sin30°=51.55lb

The x component of reaction B acts in the x direction.

Rearrange equation (VII) to get By.

By=50lbAcos30°

Substitute 23.09lb for A in above equation to get By.

By=50lb(23.09lb)cos30°=30lb

Substitute 51.55lb for Bx and 30lb for By in the equation (VIII) to get B.

B=(51.55lb)2+(30lb)2=59.64lb

Substitute 51.55lb for Bx and 30lb for By in the equation (IX) to get α.

tanα=30lb51.55lbα=30.2°

Therefore, the reaction at A is 23.1lb and is directed 60.0° above positive x axis and reaction at B is 59.6lb and is directed 30.2° above negative x axis.

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
الثانية Babakt Momentum equation for Boundary Layer S SS -Txfriction dray Momentum equation for Boundary Layer What laws are important for resolving issues 2 How to draw. 3 What's Point about this.
R αι g The system given on the left, consists of three pulleys and the depicted vertical ropes. Given: ri J₁, m1 R = 2r; απ r2, J2, m₂ m1; m2; M3 J1 J2 J3 J3, m3 a) Determine the radii 2 and 3.
B: Solid rotating shaft used in the boat with high speed shown in Figure. The amount of power transmitted at the greatest torque is 224 kW with 130 r.p.m. Used DE-Goodman theory to determine the shaft diameter. Take the shaft material is annealed AISI 1030, the endurance limit of 18.86 kpsi and a factor of safety 1. Which criterion is more conservative? Note: all dimensions in mm. 1 AA Motor 300 Thrust Bearing Sprocket 100 9750 เอ

Chapter 4 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

Ch. 4.1 - Prob. 4.7PCh. 4.1 - Prob. 4.8PCh. 4.1 - Three loads are applied as shown to a light beam...Ch. 4.1 - Prob. 4.10PCh. 4.1 - Prob. 4.11PCh. 4.1 - For the beam of Sample Prob. 4.2, determine the...Ch. 4.1 - The maximum allowable value of each of the...Ch. 4.1 - For the beam and loading shown, determine the...Ch. 4.1 - 4.15 Two links AB and DE are connected by a bell...Ch. 4.1 - Prob. 4.16PCh. 4.1 - 4.17 The required tension in cable AB is 200 lb....Ch. 4.1 - Prob. 4.18PCh. 4.1 - The bracket BCD is hinged at C and attached to a...Ch. 4.1 - The ladder AB, of length L and weight W, can be...Ch. 4.1 - 4.21 The 40-ft boom AB weighs 2 kips; the distance...Ch. 4.1 - A lever AB is hinged at C and attached to a...Ch. 4.1 - 4.23 and 4.24 For each of the plates and loadings...Ch. 4.1 - Prob. 4.24PCh. 4.1 - A rod AB, hinged at A and attached at B to cable...Ch. 4.1 - Prob. 4.26PCh. 4.1 - Prob. 4.27PCh. 4.1 - Determine the reactions at A and C when (a) = 0,...Ch. 4.1 - Prob. 4.29PCh. 4.1 - Prob. 4.30PCh. 4.1 - Neglecting friction, determine the tension in...Ch. 4.1 - Fig. P4.31 and P4.32 4.32 Neglecting friction,...Ch. 4.1 - PROBLEM 4.33 A force P of magnitude 90 lb is...Ch. 4.1 - PROBLEM 4.34 Solve Problem 4,33 for a = 6 in,...Ch. 4.1 - Prob. 4.35PCh. 4.1 - PROBLEM 4.36 A light bar AD is suspended from a...Ch. 4.1 - Prob. 4.37PCh. 4.1 - Prob. 4.38PCh. 4.1 - Prob. 4.39PCh. 4.1 - Prob. 4.40PCh. 4.1 - Prob. 4.41PCh. 4.1 - Prob. 4.42PCh. 4.1 - The rig shown consists of a 1200-lb horizontal...Ch. 4.1 - Fig. P4.43 4.44 For the rig and crate of Prob....Ch. 4.1 - Prob. 4.45PCh. 4.1 - Knowing that the tension in wire BD is 1300 N,...Ch. 4.1 - Prob. 4.47PCh. 4.1 - Beam AD carries the two 40-lb loads shown. The...Ch. 4.1 - Fig. P4.48 and P4.49 4.49 For the beam and loading...Ch. 4.1 - Prob. 4.50PCh. 4.1 - A uniform rod AB with a length of l and weight of...Ch. 4.1 - Rod AD is acted upon by a vertical force P at end...Ch. 4.1 - A slender rod AB with a weigh of W is attached to...Ch. 4.1 - 4.54 and 4.55 A vertical load P is applied at end...Ch. 4.1 - 4.54 and 4.55 A vertical load P is applied at end...Ch. 4.1 - A collar B with a weight of W can move freely...Ch. 4.1 - A 400-lb weight is attached at A to the lever...Ch. 4.1 - Prob. 4.58PCh. 4.1 - Prob. 4.59PCh. 4.1 - Prob. 4.60PCh. 4.2 - A 500-lb cylindrical tank, 8 ft in diameter, is to...Ch. 4.2 - 4.62 Determine the reactions at A and B when a =...Ch. 4.2 - Prob. 4.63PCh. 4.2 - Prob. 4.64PCh. 4.2 - Determine the reactions at B and C when a = 30 mm.Ch. 4.2 - Prob. 4.66PCh. 4.2 - Determine the reactions at B and D when b = 60 mm....Ch. 4.2 - For the frame and loading shown, determine the...Ch. 4.2 - A 50-kg crate is attached to the trolley-beam...Ch. 4.2 - One end of rod AB rests in the corner A and the...Ch. 4.2 - For the boom and loading shown, determine (a) the...Ch. 4.2 - Prob. 4.72PCh. 4.2 - Prob. 4.73PCh. 4.2 - Prob. 4.74PCh. 4.2 - Rod AB is supported by a pin and bracket at A and...Ch. 4.2 - Solve Prob. 4.75, assuming that the 170-N force...Ch. 4.2 - Prob. 4.77PCh. 4.2 - Using the method of Sec. 4.2B, solve Prob. 4.22....Ch. 4.2 - Knowing that = 30, determine the reaction (a) at...Ch. 4.2 - Knowing that = 60, determine the reaction (a) at...Ch. 4.2 - Determine the reactions at A and B when = 50....Ch. 4.2 - Determine the reactions at A and B when = 80.Ch. 4.2 - Rod AB is bent into the shape of an arc of circle...Ch. 4.2 - A slender rod of length L is attached to collars...Ch. 4.2 - An 8-kg slender rod of length L is attached to...Ch. 4.2 - Prob. 4.86PCh. 4.2 - A slender rod BC with a length of L and weight W...Ch. 4.2 - A thin ring with a mass of 2 kg and radius r = 140...Ch. 4.2 - A slender rod with a length of L and weight W is...Ch. 4.2 - Fig. P4.89 4.90 Knowing that for the rod of Prob....Ch. 4.3 - Two tape spools are attached to an axle supported...Ch. 4.3 - Prob. 4.6FBPCh. 4.3 - A 20-kg cover for a roof opening is hinged at...Ch. 4.3 - Prob. 4.91PCh. 4.3 - Prob. 4.92PCh. 4.3 - A small winch is used to raise a 120-lb load. Find...Ch. 4.3 - Prob. 4.94PCh. 4.3 - A 250 400-mm plate of mass 12 kg and a...Ch. 4.3 - Prob. 4.96PCh. 4.3 - Prob. 4.97PCh. 4.3 - Prob. 4.98PCh. 4.3 - Prob. 4.99PCh. 4.3 - Prob. 4.100PCh. 4.3 - PROBLEM 4.101 Two steel pipes AB and BC, each...Ch. 4.3 - PROBLEM 4.102 For the pipe assembly of Problem...Ch. 4.3 - PROBLEM 4.103 The 24-lb square plate shown is...Ch. 4.3 - PROBLEM 4.104 The table shown weighs 30 lb and has...Ch. 4.3 - PROBLEM 4.105 A 10-ft boom is acted upon by the...Ch. 4.3 - PROBLEM 4.106 The 6-m pole ABC is acted upon by a...Ch. 4.3 - PROBLEM 4.107 Solve Problem 4.106 for a = 1.5 m....Ch. 4.3 - Prob. 4.108PCh. 4.3 - Prob. 4.109PCh. 4.3 - Prob. 4.110PCh. 4.3 - PROBLEM 4.111 A 48-in. boom is held by a...Ch. 4.3 - PROBLEM 4.112 Solve Problem 4.111, assuming that...Ch. 4.3 - PROBLEM 4.114 The bent rod ABEF is supported by...Ch. 4.3 - The bent rod ABEF is supported by bearings at C...Ch. 4.3 - The horizontal platform ABCD weighs 60 lb and...Ch. 4.3 - Prob. 4.116PCh. 4.3 - Prob. 4.117PCh. 4.3 - Solve Prob. 4.117, assuming that cable DCE is...Ch. 4.3 - PROBLEM 4.119 Solve Prob. 4.113, assuming that the...Ch. 4.3 - PROBLEM 4.120 Solve Prob. 4.115, assuming that the...Ch. 4.3 - PROBLEM 4.121 The assembly shown is used to...Ch. 4.3 - Prob. 4.122PCh. 4.3 - Prob. 4.123PCh. 4.3 - Prob. 4.124PCh. 4.3 - Prob. 4.125PCh. 4.3 - Prob. 4.126PCh. 4.3 - Prob. 4.127PCh. 4.3 - Prob. 4.128PCh. 4.3 - Frame ABCD is supported by a ball-and-socket joint...Ch. 4.3 - Prob. 4.130PCh. 4.3 - The assembly shown consists of an 80-mm rod AF...Ch. 4.3 - Prob. 4.132PCh. 4.3 - The frame ACD is supported by ball-and-socket...Ch. 4.3 - Prob. 4.134PCh. 4.3 - Prob. 4.135PCh. 4.3 - Prob. 4.136PCh. 4.3 - Prob. 4.137PCh. 4.3 - Prob. 4.138PCh. 4.3 - Prob. 4.139PCh. 4.3 - Prob. 4.140PCh. 4.3 - Prob. 4.141PCh. 4 - Prob. 4.142RPCh. 4 - 4. 143 The lever BCD is hinged at C and attached...Ch. 4 - Prob. 4.144RPCh. 4 - Neglecting friction and the radius of the pulley,...Ch. 4 - Prob. 4.146RPCh. 4 - PROBLEM 4.147 A slender rod AB, of weight W, is...Ch. 4 - PROBLEM 4.148 Determine the reactions at A and B...Ch. 4 - Prob. 4.149RPCh. 4 - PROBLEM 4.150 A 200-mm lever and a 240-mm-diameter...Ch. 4 - Prob. 4.151RPCh. 4 - Prob. 4.152RPCh. 4 - A force P is applied to a bent rod ABC, which may...
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
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
EVERYTHING on Axial Loading Normal Stress in 10 MINUTES - Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=jQ-fNqZWrNg;License: Standard YouTube License, CC-BY