International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN: 9781305501607
Author: Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
bartleby

Videos

Textbook Question
Book Icon
Chapter 10, Problem 10.19P

Determine the force F and the angle a required to hold the linkage in the position θ 1 = 60 ° , θ = 15 ° . Each bar of the linkage is homogeneous and of weight W.

Chapter 10, Problem 10.19P, Determine the force F and the angle a required to hold the linkage in the position 1=60,=15. Each

Expert Solution & Answer
Check Mark
To determine

Force F and angle α required to hold the linkage.

Answer to Problem 10.19P

The force F is equal to 0.753W and angle α is 24.89° with horizontal.

Explanation of Solution

  θ1=60°θ2=15°

Virtual work δU done by force F is defined as:

  δU=F.δr=Fcosαδr

In above equation:

  F - Force

  δr - Virtual force

  α - Angle between F and δr

Virtual displacement δrB of point B is defined as:

  δrB=rABδθ

In above equation:

  δθ - Virtual rotation

  rAB - Magnitude of vector drawn from A to B:

Calculation:

International Edition---engineering Mechanics: Statics, 4th Edition, Chapter 10, Problem 10.19P

The length y1 :

  y1=L2sinθ1

The virtual displacement δy1 :

  δy1=L2cosθ1δθ1

The length y2 :

  y2=Lsinθ1+L2sinθ2

The virtual displacement δy2

  δy2=Lcosθ1δθ1+L2cosθ2δθ2

The length yC :

  yC=Lsinθ1+Lsinθ2

The virtual displacement δyC :

  δyC=Lcosθ1δθ1+Lcosθ2δθ2

The length xC :

  xC=Lcosθ1+Lcosθ2

The virtual displacement δxC :

  δxC=Lsinθ1δθ1Lsinθ2δθ2

Virtual work δU done by acting forces:

  δU=Wδy1+Wδy2+FxδxCFyδyC=WL2cosθ1δθ1+W(Lcosθ1δθ1+L2cosθ2δθ2)+Fx(Lsinθ1δθ1Lsinθ2δθ2)Fy(Lcosθ1δθ1+Lcosθ2δθ2)=(32Wcosθ1Fxsinθ1Fycosθ1)Lδθ1+(12Wcosθ2Fxsinθ2Fycosθ2)Lδθ2

We know that:

  δU=0

Therefore:

  32Wcosθ1Fxsinθ1Fycosθ1=0

Substitute:

  32Wcos60°Fxsin60°Fycos60°=00.866Fx+0.5Fy=0.75W(1)

  12Wcos15°Fxsin15°Fycos15°=00.2588Fx+0.9659Fy=0.4829W(2)

Solve above equations:

  Fx=0.683WFy=0.317W

The magnitude and angle α of force F:

  F=Fx2+Fy2=0.753Wα=tan1( 0.317 0.683)=24.89°

Conclusion:

The force F is equal to 0.753W and angle α is 24.89° with horizontal.

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
Determine the n- and t-components of the force F which is exerted by the rod AB on the crank OA. Evaluate your general expression for F = 118 N and (a) e = 30°, B = 25° and (b) e = 21°, B = 29° Answers: (a) Fn= i N, F: = i N (b) Fn = i N. F:= N
Determine the n- and t-components of the force F which is exerted by the rod AB on the crank OA. Evaluate your general expression for F = 90 N and (a) 0 = 29°, 3= 25° and (b) = 14°, 3 = 37° Answers: (a) Fn = (b) Fn = i i B BI A N, Ft= N, Ft= i N N
Determine the n- and t-components of the force F which is exerted by the rod AB on the crank OA. Evaluate your general expression for F = 106 N and (a) e = 16°, B = 14° and (b) e = 23°, B = 30° B Answers: N, F =| N (a) Fn = N (b) Fo N, F =

Chapter 10 Solutions

International Edition---engineering Mechanics: Statics, 4th Edition

Ch. 10 - Determine the ratio P/Q of the forces that are...Ch. 10 - Find the vertical force P that will hold the...Ch. 10 - The linkage of the braking system consists of the...Ch. 10 - The automatic drilling robot must sustain a thrust...Ch. 10 - Determine the couple C for which the mechanism...Ch. 10 - The scissors jack is used to elevate the weight W....Ch. 10 - Prob. 10.17PCh. 10 - Calculate the torque C0 that must be applied to...Ch. 10 - Determine the force F and the angle a required to...Ch. 10 - Locate the instant center of rotation of bar AB...Ch. 10 - Prob. 10.21PCh. 10 - Determine the force P that will keep the mechanism...Ch. 10 - Prob. 10.23PCh. 10 - Prob. 10.24PCh. 10 - Prob. 10.25PCh. 10 - Determine the ratio P/Q for which the linkage will...Ch. 10 - Prob. 10.27PCh. 10 - Prob. 10.28PCh. 10 - If the input force to the compound lever is P = 30...Ch. 10 - Determine the roller reaction at F due to the...Ch. 10 - Prob. 10.31PCh. 10 - Prob. 10.32PCh. 10 - Prob. 10.33PCh. 10 - Prob. 10.34PCh. 10 - Prob. 10.35PCh. 10 - For the pliers shown, determine the relationship...Ch. 10 - When activated by the force P, the gripper cm a...Ch. 10 - Prob. 10.38PCh. 10 - The hinge is of the type used on some automobiles,...Ch. 10 - The spring attached to the sliding collar is...Ch. 10 - The weight W is suspended from end B of the...Ch. 10 - The uniform bar of weight W and length L = 1.8R...Ch. 10 - A slender homogeneous bar is bent into a right...Ch. 10 - The body shown is a composite of a hemisphere and...Ch. 10 - Prob. 10.45PCh. 10 - The uniform bar AB of weight W and length L is...Ch. 10 - Uniform rods of weights W1 and W2 are welded to...Ch. 10 - Prob. 10.48PCh. 10 - The semi-cylinder of radius r is placed on a...Ch. 10 - Prob. 10.50PCh. 10 - The spring attached to the homogenous bar of...Ch. 10 - The spring is connected to a rope that passes over...Ch. 10 - Find the equilibrium positions of the 30-lb...Ch. 10 - The mechanism of negligible weight supports the...Ch. 10 - Solve Prob. 10.54 assuming that A and B are...Ch. 10 - The stiffness of the ideal spring that is...Ch. 10 - Find the stable equilibrium position of the system...Ch. 10 - The uniform bar AB of weight W = kL is in...Ch. 10 - The weight of the uniform bar AB is W. The...Ch. 10 - The weightless bars AB and CE, together with the...Ch. 10 - Prob. 10.61PCh. 10 - The bar ABC is supported by three identical, ideal...
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