VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
12th Edition
ISBN: 9781260916942
Author: BEER
Publisher: MCG
bartleby

Videos

Textbook Question
Book Icon
Chapter 10.1, Problem 10.6P

A spring of constant 15 kN/m connects points C and F of the linkage shown. Neglecting the weight of the spring and linkage, determine the force in the spring and the vertical motion of point G when a vertical downward 120-N force is applied (a) at point E, (b) at points E and F.

Chapter 10.1, Problem 10.6P, A spring of constant 15 kN/m connects points C and F of the linkage shown. Neglecting the weight of

Fig. P10.5 and P10.6

(a)

Expert Solution
Check Mark
To determine

Find the force in the spring and the vertical motion of point G when a vertical load of 120N force is applied at point E.

Answer to Problem 10.6P

The force in the spring is 120N(C)_.

The vertical motion of point G is 16mm()_.

Explanation of Solution

Given information:

The spring constant is k=15kN/m.

Calculation:

Show the free-body diagram of the spring assembly as in Figure 1.

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA), Chapter 10.1, Problem 10.6P

Write the relation of the deflections at point G, H, F, E, D with C as follows;

yG=4yC;δyG=4δyC

yH=4yC;δyH=4δyCyF=3yC;δyF=3δyCyD=2yC;δyD=2δyCyE=2yC;δyE=2δyC

The deflection Δ of the spring is;

Δ=yFyC=3yCyC=2yC

Assume the spring force Q is in tension.

Find the force in the spring Q using the relation.

Q=+kΔ

Here, the spring constant is k.

Substitute 15kN/m for k and 2yC for Δ.

Q=15(2yC)=30yC (1)

Use the virtual work principle:

δU=0CδyC+QδyCQδyFFδyFHδyHEδyE=0

Here, E=120N;F=0;H=0;C=0

Substitute 0 for C, 3δyC for δyF, 0 for F, 0 for H, 4δyC for δyH, 120 N for E, and 2δyC for δyE.

(0)δyC+QδyCQ(3δyC)(0)(3δyC)(0)(4δyC)120(2δyC)=00+Q3Q00240=02Q=240Q=120N

Q=120N(C)

The spring force Q is in compression. The assumption is incorrect.

Therefore, the force in the spring is 120N(C)_.

Substitute –120 N for Q in Equation (1).

120=30yCyC=4mm

Find the vertical motion (yG) of point G using the relation.

yG=4yC

Substitute –4 mm for yC.

yG=4(4)=16mm=16mm()

Therefore, the vertical motion of point G is 16mm()_.

(b)

Expert Solution
Check Mark
To determine

Find the force in the spring and the vertical motion of point G when a vertical load of 120-N force is applied at point E and F.

Answer to Problem 10.6P

The force in the spring is 300N(C)_.

The vertical motion of point G is 40mm()_.

Explanation of Solution

Given information:

The spring constant is k=15kN/m.

Calculation:

Use the virtual work principle:

δU=0CδyC+QδyCQδyFFδyFHδyHEδyE=0

Here, E=120N;F=120N;H=0;C=0

Substitute 0 for C, 3δyC for δyF, 120 N for F, 0 for H, 4δyC for δyH, 120 N for E, and 2δyC for δyE.

(0)δyC+QδyCQ(3δyC)(120)(3δyC)(0)(4δyC)(120)(2δyC)=00+Q3Q3600240=02Q=600Q=300N

Q=300N(C)

The spring force Q is in compression. The assumption is incorrect.

Therefore, the force in the spring is 300N(C)_.

Substitute –300 N for Q in Equation (1).

300=30yCyC=10mm

Find the vertical motion (yG) of point G using the relation.

yG=4yC

Substitute –10 mm for yC.

yG=4(10)=40mm=40mm()

Therefore, the vertical motion of point G is 40mm()_.

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
Find the reaction at A and B The other response I got was not too accurate,I need expert solved answer, don't use Artificial intelligence or screen shot it solving
No chatgpt pls
Solve for the reaction of all the forces Don't use artificial intelligence or screen shot it, only expert should solve

Chapter 10 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

Ch. 10.1 - Solve Prob. 10.10, assuming that the force P...Ch. 10.1 - Prob. 10.12PCh. 10.1 - Prob. 10.13PCh. 10.1 - Prob. 10.14PCh. 10.1 - Prob. 10.15PCh. 10.1 - 10.15 and 10.16 Derive an expression for the...Ch. 10.1 - Prob. 10.17PCh. 10.1 - Prob. 10.18PCh. 10.1 - Prob. 10.19PCh. 10.1 - Prob. 10.20PCh. 10.1 - Prob. 10.21PCh. 10.1 - A couple M with a magnitude of 100 Nm isapplied as...Ch. 10.1 - Rod AB is attached to a block at A that can...Ch. 10.1 - Solve Prob. 10.23, assuming that the 800-N force...Ch. 10.1 - In Prob. 10.9, knowing that a = 42 in., b = 28...Ch. 10.1 - Determine the value of corresponding to...Ch. 10.1 - Prob. 10.27PCh. 10.1 - Determine the value of corresponding to...Ch. 10.1 - Prob. 10.29PCh. 10.1 - Two rods AC and CE are connected by a pin at Cand...Ch. 10.1 - Solve Prob. 10.30 assuming that force P is movedto...Ch. 10.1 - Prob. 10.32PCh. 10.1 - Prob. 10.33PCh. 10.1 - Prob. 10.34PCh. 10.1 - Prob. 10.35PCh. 10.1 - Prob. 10.36PCh. 10.1 - Prob. 10.37PCh. 10.1 - Prob. 10.38PCh. 10.1 - Prob. 10.39PCh. 10.1 - Prob. 10.40PCh. 10.1 - Prob. 10.41PCh. 10.1 - The position of boom ABC is controlled by...Ch. 10.1 - Prob. 10.43PCh. 10.1 - Prob. 10.44PCh. 10.1 - Prob. 10.45PCh. 10.1 - Prob. 10.46PCh. 10.1 - Denoting the coefficient of static friction...Ch. 10.1 - Prob. 10.48PCh. 10.1 - Prob. 10.49PCh. 10.1 - Prob. 10.50PCh. 10.1 - Prob. 10.51PCh. 10.1 - Prob. 10.52PCh. 10.1 - Prob. 10.53PCh. 10.1 - Prob. 10.54PCh. 10.1 - Prob. 10.55PCh. 10.1 - Prob. 10.56PCh. 10.1 - Prob. 10.57PCh. 10.1 - Determine the horizontal movement of joint C if...Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.29....Ch. 10.2 - Prob. 10.60PCh. 10.2 - Prob. 10.61PCh. 10.2 - Prob. 10.62PCh. 10.2 - Prob. 10.63PCh. 10.2 - Prob. 10.64PCh. 10.2 - Prob. 10.65PCh. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.38....Ch. 10.2 - Prob. 10.67PCh. 10.2 - Prob. 10.68PCh. 10.2 - Prob. 10.69PCh. 10.2 - Prob. 10.70PCh. 10.2 - Prob. 10.71PCh. 10.2 - Prob. 10.72PCh. 10.2 - Prob. 10.73PCh. 10.2 - Prob. 10.74PCh. 10.2 - A load W of magnitude 144 lb is applied to...Ch. 10.2 - Solve Prob. 10.75, assuming that the spring...Ch. 10.2 - Bar ABC is attached to collars A and B that...Ch. 10.2 - Solve Prob. 10.77, assuming that the spring...Ch. 10.2 - Prob. 10.79PCh. 10.2 - Prob. 10.80PCh. 10.2 - Prob. 10.81PCh. 10.2 - A spring AB of constant k is attached to two...Ch. 10.2 - Prob. 10.83PCh. 10.2 - Prob. 10.84PCh. 10.2 - Prob. 10.85PCh. 10.2 - Prob. 10.86PCh. 10.2 - Prob. 10.87PCh. 10.2 - Prob. 10.88PCh. 10.2 - Prob. 10.89PCh. 10.2 - Prob. 10.90PCh. 10.2 - Prob. 10.91PCh. 10.2 - Prob. 10.92PCh. 10.2 - Prob. 10.93PCh. 10.2 - Prob. 10.94PCh. 10.2 - Prob. 10.95PCh. 10.2 - Prob. 10.96PCh. 10.2 - Bars AB and BC, each with a length l and of...Ch. 10.2 - Solve Prob. 10.97 knowing that l = 30 in. and k =...Ch. 10.2 - Bars AB and CD, each of length l and of negligible...Ch. 10.2 - Solve Prob. 10.99, assuming that the vertical...Ch. 10 - Determine the vertical force P that must be...Ch. 10 - Determine the couple M that must be applied...Ch. 10 - Prob. 10.103RPCh. 10 - Prob. 10.104RPCh. 10 - Prob. 10.105RPCh. 10 - Prob. 10.106RPCh. 10 - Prob. 10.107RPCh. 10 - Prob. 10.108RPCh. 10 - Prob. 10.109RPCh. 10 - Prob. 10.110RPCh. 10 - Prob. 10.111RPCh. 10 - Prob. 10.112RP
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
Mechanical SPRING DESIGN Strategy and Restrictions in Under 15 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=dsWQrzfQt3s;License: Standard Youtube License