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Chapter 4: 6CP (page 144)

A spring has stiffness ks. You cut the spring in half. What is the stiffness of the half-spring?

(a) 2ks,

(b) ks,

(c) ks/2

Short Answer

Expert verified

Option (a)

The stiffness of the half-spring is2ks.

Step by step solution

01

Given data

A spring of stiffness ks is cut in half.

02

Stiffness of spring

The spring constants of springs (k1and k2) of the same material but of different lengths l1andl2are related as,

k1l1=k2l2 (I)

03

Determining the change in spring constant

Given information:

k1=ks

Since the length is halved, that can be expressed as,

I2=I122I2=I1

Substitute the values in the above equation, and we get,

ks×2I2=k2I2k2=ks

The new spring constant is 2ks.

Thus, option (a) is correct.

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Most popular questions from this chapter

A particular spring-mass oscillator oscillates with period T. Write out the general equation for the period of such an oscillator to use as a guide when answering the following questions. (a) If you double the mass but keep the stiffness the same, by what numerical factor does the period change? (That is, if the original period was T and the new period is bT. what is b?) (b) If, instead, you double the spring stiffness but keep the mass the same, what is the factor b? (c) If, instead, you double the mass and also double the spring stiffness, what is the factor b? (d) If, instead, you double the amplitude (keeping the original mass and spring stiffness), what is the factor b?

Two rods are both made of pure titanium. The diameter of rod A is twice the diameter of rod B, but the lengths of the rods are equal. You tap on one end of each rod with a hammer and measure how long it takes the disturbance to travel to the other end of the rod. In which rod did it take longer? (a) Rod A. (b) Rod B. (c) The times were equal

A certain spring has stiffness140N/m. The spring is then cut into two equal lengths. What is the stiffness of one of these half-length springs?

If a chain of 50identical short springs linked end to end has a stiffness of 270N/m, what is the stiffness of one short spring?

A hanging iron wire with diameter 0.08cm is initially 2.5m long. When a 52 kg is hung from it, the wire stretches an amount 1.27cm. A mole of iron has a mass of 56g, and its density is7.87g/cm3 . (a) What is the length of an interatomic bond in iron (diameter of one atom)? (b) Find the approximate value of the effective spring stiffness of one interatomic bond in iron.
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