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Chapter 4: Q26P (page 166)

A certain spring has stiffness 190N/m. The spring is then cut into two equal lengths. What is the stiffness of one of these half-length springs?

Short Answer

Expert verified

The value of stiffness is 380N/m.

Step by step solution

01

Identification of given data

The given data is listed below as,

The value of the spring stiffness is, ki=190N/m.

02

Significance of the spring stiffness

The stiffness is described as the ratio of the applied load to the deflection of the spring. It is expressed as follows,

k=Fx

Here, F is the spring force and x is the deflection.

03

Calculation for the stiffness

As, the spring is cut into two equal parts so, the stiffness becomes double so, the equation of the final stiffness of the spring is expressed as:

kf=2kj

Here, kjis the initial stiffness.

Substitute the values in the above equation.

Kf=2Ki=2×190N/m=380N/m

Thus, the value of stiffness is 380N/m.

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Most popular questions from this chapter

An object of mass m is attached by two stretched springs (stiffnessKs and relaxed lengthL0 ) to rigid walls, as shown in figure 4.60. The springs are initially stretched by an amount (L-L0). When the object is displaced to the right and released, it oscillates horizontally. Starting from the momentum principle, find a function of the displacement xof the object and the timet describes the oscillatory motion.

(a) What is the period of the motion?

(b) If L0 were shorter (so the springs are initially stretched more), would the period be larger, smaller, or the same?

One mole of Nickel (6.02×1023atoms)has a mass of , and its density is 8.9g/cm3. You have a bar of nickel 2.5 m long, with a cross-section of 2mm on a side. You hang the rod vertically and attach a 40 kg mass to the bottom, and you observe that the bar becomes 1.2 mm longer. Next, you remove the 40 kg mass, place the rod horizontally, and strike one end with a hammer. How much time will elapse before a microphone at the other end of the bar will detect a disturbance?

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