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Chapter 4: Q29P (page 166)
Five identical springs, each with stiffness , are attached in parallel (that is, side by side) to hold up a heavy weight. If these springs were replaced by an equivalent single spring, what should be the stiffness of this single spring?
The value of stiffness of one of the individual springs is
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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 titanium wire with diameter() is initially long. When a mass is hung from it, the wire stretches an amount , and when a mass is hung from it, the wire stretches an amount . A mole of titanium has a mass of , and its density is . Find the approximate value of the effective spring stiffness of the interatomic force, and explain your analysis .
Two blocks of mass m1 and m3 , connected by a rod of mass m2 , are sitting on a low friction surface, and you push to the left on the right block (mass m1 ) with a constant force of magnitude F(Figure 4.57).
(a) What is the acceleration of the blocks?
(b) What is the vector force exerted by the rod on the block of mass m3 ? ( is approximately equal to the compression force in the rod near its left end.)What is the vector forceexerted by the rod on the block of massm1? is approximately equal to the compression force in the rod near its right end.)
(c) Suppose that instead of pushing on the right block (mass m1 ), you pull to the left on the left block (mass m3) with a constant force of magnitude F . Draw a diagram illustrating this situation. Now what is the vector force exerted by the rod on the block of mass m3?
Question:A certain metal with atomic mass 2 脳 10鈭�25 kg has an interatomic bond with length 2.1 脳 10鈭�10 m and stiffness 40 N/m. What is the speed of sound in a rod made of this metal?
It was found that a mass hanging from a particular spring had an oscillation period of . (a) When two masses are hung from this spring, what would you predict for the period in seconds? Explain briefly.
Figure 4.58
(b) When one mass is supported by two of these vertical, parallel springs (Figure 4.58), what would you predict for the period in seconds? Explain briefly. (c) Suppose that you cut one spring into two equal lengths, and you hang one mass from this half spring. What would you predict for the period in seconds? Explain briefly. (d) Suppose that you take a single (full-length) spring and a single mass to the Moon and watch the system oscillate vertically there. Will the period you observe on the Moon be longer, shorter, or the same as the period you measured on Earth? (The gravitational field strength on the Moon is about one-sixth that on the Earth.) Explain briefly.
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