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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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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.
A 3 kgblock measures5 cm by 10 cm by 20cm. When it slides on a 10cm by 20 cmface, it moves with constant speed when pulled horizontally by a force whose magnitude 3N is. How big a horizontal force must be applied to pull it with constant speed of it slides on a 5 cm by 20 cm face?
In outer space, a rod is pushed to the right by a constant force F (Figure 4.54). Describe the pattern of interatomic distances along the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly in terms of fundamental principles.
Figure 4.54
Hint: Consider the motion of an individual atom inside the rod, and various locations along the rod.
(b) After the rod in part (a) reaches a speed v, the object that had been exerting the force on the rod is removed. Describe the subsequent motion of the rod and the pattern of interatomic distances inside the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly.
A certain spring has stiffness. The spring is then cut into two equal lengths. What is the stiffness of one of these half-length springs?
Uranium-238 ( ) has three more neutrons than uranium-235 ( ). Compared to the speed of sound in a bar of , is the speed of sound in a bar of higher, lower, or the same? Explain your choice, including justification for assumptions you make.
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