Concept explainers
Determine the unstretched length of DB to hold the 40-kg crate in the position shown. Take k = 180 N/m.
The unstretched length of spring DB.
Answer to Problem 19P
The unstretched length
Explanation of Solution
Given information:
The stiffness of the spring is
The mass of a crate is 40 kg.
Assumption:
Consider the point E in between the points B and C.
Show the free body diagram of the spring as in Figure 1.
Determine the length of the member CD using the formula.
Here, the length of the point DE is
Determine the length of the spring BD using the formula.
Here, the length of the point BE is
Determine the weight of the crate.
Here, the mass of a crate is m and the acceleration due to gravity is g.
Determine the tension force of the member BD and CD by applying the equation of equilibrium.
Along the horizontal direction:
Here, the tension force of the member CD is
Along the vertical direction:
Determine the unstretched length of the spring BD.
Here, the tension force of the spring member BD is
Conclusion:
Substitute 2 m for
Substitute 2 m for
Determine the
Substitute 3 m for
Determine the
Substitute 2m for
Substitute
Substitute 40 kg for m and
Determine the
Substitute 2 m for
Determine the
Substitute 2 m for
Substitute
Substitute 332.96 N for
Substitute 282.96 N for
Thus, the unstretched length of spring DB is
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Chapter 3 Solutions
Engineering Mechanics: Statics & Dynamics, Student Value Edition (14th Edition)
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L