Concept explainers
If the spring DB has an unstretched length of 2 m. determine the stiffness of the spring to hold the 40-kg crate In the position shown.
The stiffness of the spring.
Answer to Problem 18P
The stiffness of the spring k is
Explanation of Solution
Given information:
The unstretched length of the spring DB is 2 m.
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, length of the point DE is
Determine the length of the spring AB using the formula.
Here, 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 stiffness 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
Substitute282.96 N for
Thus, the stiffness of the spring is
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