Suppose that an object was formed using 7.25 x 10° Pa. When it was released from the press and brought to atmospheric pressure, 1.01 x 10° Pa, its volume changed from 6.829 x 10° m³ to 7.12 x 10* m, what is the bulk modulus of the object?

An aluminium (=2.7g/cm3) wire is suspended from the ceiling and hangs vertically. How long must the wire be before the stress at its upper end reaches the proportionality limit, which is 8.0107N/m2 ?

Review the relationship between stress and strain. Can you find any similarities between the two quantities?

Two thin rods, one made of steel and the other of aluminium, are joined end to end. Each rod is 2.0m long and has cross-sectional area 9.1mm2 . If a 10,000N tensile force is applied at each end of the combination, find: (a) stress in each rod; (b) strain in each rod; and, (c) elongation of each rod.

Can Young’s modulus have a negative value? What about the bulk modulus?

By how much does a 65.0kg mountain climber stretch her 0.800cm diameter nylon rope when she hangs 35.0m below a rock outcropping? (For nylon, Y=1.35109Pa. )

A brass wire and a steel wire, both of the same length, are extended by 1.0 mm under the same force. Is the cross-sectional radius of the brass wire more, less, or equal to the cross-sectional radius of the steel wire? Explain. Youngs moduli for brass and steel are 1.0 1010 N/m2 and 2.0 1011 N/m2, respectively.

A 90-kg mountain climber bangs from a nylon rope and stretches it by 25.0 cm. If the rope was originally 30.0 m bog and its diameter is 1.0 cm, is Young’s modulus for the nylon?

The lintel of prestressed reinforced concrete in Figure P12.27 is 1.50 m long. The concrete encloses one steel reinforcing rod with cross-sectional area 1.50 cm2. The rod joins two strong end plates. The cross-sectional area of the concrete perpendicular to the rod is 50.0 cm2. Youngs modulus for the concrete is 30.0 109 N/m2. After the concrete cures and the original tension T1 in the rod is released, the concrete is to be under compressive stress 8.00 106 N/m2. (a) By what distance will the rod compress the concrete when the original tension in the rod is released? (b) What is the new tension T2 in the rod? (c) The rod will then be how much longer than its unstressed length? (d) When the concrete was poured, the rod should have been stretched by what extension distance from its unstressed length? (e) Find the required original tension T1 in the rod. Figure P12.27

A copper rod with length 1.4 m and cross-sectional area 2.0 cm2 is fastened to a steel rod of length L and cross-sectional area 1.0 cm2. The compound structure is pulled on each side by two forces of equal magnitude 6.00 104 N (Fig. P14.57). Find the length L of the steel rod if the elongations (L) of the two rods are equal. Use the values Ysteel = 2.0 1011 Pa and YCu = 1.1 1011 Pa. FIGURE P14.57