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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
Option (a)
The stiffness of the half-spring is2ks.
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A chain of length L, and mass M is suspended vertically by one end with the bottom end just above a table. The chain is released and falls, and the links do not rebound off the table, but they spread out so that the top link falls very nearly the full distance L. Just before the instant when the entire chain has fallen onto the table, how much force does the table exert on the chain? Assume that the chain links have negligible interaction with each other as the chain drops, and make the approximation that there is very large number of links. Hint: Consider the instantaneous rate of change momentum of the chain as the last link hits the table.
Young鈥檚 modulus for aluminium is .The density of aluminium is ,and the mass of one mole is 27g. If we model the interactions of neighbouring aluminium atoms as though they were connected by spring, determine the approximate spring constant of such a spring. Repeat this analysis for lead is: Young鈥檚 modulus for Lead and the density of lead is , and the mass of one mole is 207g. Make a note of these results, which we will use for various purposes later on. Note that aluminium is a rather stiff material, whereas lead is quite soft.
Suppose that we hang a heavy ball with a mass of 10 kg (about 22 lb ) from a steel wire 3m long that is 3 mm in diameter. Steel is very stiff, and Young鈥檚 modulus for steel is unusually large, Calculate the stretch of the steel wire. This calculation shows why in many cases it is a very good approximation to pretend that the wire doesn鈥檛 stretch at all (鈥渋deal non extensible wire鈥�).
A box sits on a table. The coefficient of static friction localid="1657707248507" between table and box is , and the coefficient of kinetic friction is . (a) What is the force required to start the box moving? (b) What is the force required to keep it moving at constant speed? (c) What is the force required to maintain an acceleration of?
A block of one mole of a certain material whose atoms are in a cubic array has dimensions of 5 cm by 4 cmby0.5 cm. What is the interatomic distance?
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