EP MODIFIED MASTERING ENGINEERING WITH
EP MODIFIED MASTERING ENGINEERING WITH
14th Edition
ISBN: 9780133941357
Author: HIBBELER
Publisher: PEARSON CO
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Chapter 3.3, Problem 17P

Determine the stiffness kT of the single spring such that the force F will stretch it by the same amount s as the force F stretches the two springs. Express kT in terms of stiffness k1, and k2 of the two springs.

Chapter 3.3, Problem 17P, Determine the stiffness kT of the single spring such that the force F will stretch it by the same

Expert Solution & Answer
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To determine

The stiffness kT of the single spring.

Answer to Problem 17P

The stiffness kT of the single spring, 1kT=1k1+1k2_.

Explanation of Solution

Given information:

  • The force F will stretch it by the same amount s as the force F stretches the two springs.

Write the magnitude of force exerted on a linearly elastic spring in an unstretched position.

F=kss=FkT

Here, the stiffness of the spring is k and the stretch of the spring is s.

Write the stretch value for two springs.

s=s1+s2 (I)

Here, the stretch of the first spring is s1 and the stretch of the first spring is s2.

Write the equation for the magnitude of force exerted on a linearly elastic spring 1.

F=k1s1s1=Fk1

Here, the stiffness of the spring 1 is k1.

Write the equation for the magnitude of force exerted on a linearly elastic spring 2.

F=k2s2s2=Fk2

Here, the stiffness of the spring 2 is k2.

Conclusion:

Substitute FkT for s, Fk1 for s1, and Fk2 for s2 in Equation (I).

FkT=Fk1+Fk2F(1kT)=F(1k1+1k2)1kT=1k1+1k2

Thus, the stiffness kT of the single spring is 1kT=1k1+1k2_.

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Chapter 3 Solutions

EP MODIFIED MASTERING ENGINEERING WITH

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