Determine the stretch in each spring for equilibrium of the 2-kg block. The springs are shown in the equilibrium position.
The stretch in each spring for the equilibrium of the block.
Answer to Problem 14P
The stretch in spring AD,
The stretch in spring AC,
The stretch in spring AB,
Explanation of Solution
Given information:
- The mass of the block (m) is 2 kg.
Assumption:
Consider point E in between the points B and C.
Show the free body diagram of the springs in the equilibrium position as in Figure 1.
Determine the length of the spring AC using the formula.
Here, the length of the point AE is
Determine the length of the spring AB using the formula.
Here, the length of the point BE is
Determine the force in spring AD using the formula.
Here, the mass of the block is m and the acceleration due to gravity is g.
Determine the stretch in spring AD.
Here, the stiffness of the spring AD is
Determine the stretch in the springs AC and AB for equilibrium of the block by applying the equation of equilibrium.
Along the horizontal direction:
Here, the force acting on spring AB is
Along the vertical direction:
Determine the stretch in spring AC.
Here, the stiffness of the spring AC is
Determine the stretch in spring AB.
Here, the stiffness of the spring AB is
Conclusion:
Substitute 3 m for
Substitute 3 m for
Substitute 2 kg for m and
Substitute 19.62 N for
Thus, the stretch in spring AD is
Determine the
Substitute 4 m for
Determine the
Substitute 3m for
Substitute
Determine the
Substitute 3 m for
Determine the
Substitute 3m for
Substitute
Substitute 15.86 N for
Thus, the stretch in spring AC is
Substitute 15.86 N for
Substitute 14.01 N for
Thus, the stretch in spring AB is
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Chapter 3 Solutions
Engineering Mechanics Masteringengineering With Pearson Etext Standalone Access Card: Statics & Dynamics
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