Problem 2. A steel plate that is 20 mm wide is loaded with a tensile stress of 5 MPa as shown. The fracture toughness of the steel is KI = 99 MPa √mm. The plate contains a crack that is 16 mm long due to a punched hole that is 5 mm in diameter. According to linear elastic fracture mechanics (LEFM), what is the safety factor to fracture? 20 mm 16 mm WH25 Winter 2005

Problem 2. A steel plate that is 20 mm wide is loaded with a tensile stress of 5 MPa as shown. The fracture toughness of the steel is KI = 99 MPa √mm. The plate contains a crack that is 16 mm long due to a punched hole that is 5 mm in diameter. According to linear elastic fracture mechanics (LEFM), what is the safety factor to fracture? 20 mm 16 mm WH25 Winter 2005

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Static Equilibrium And Elasticity

Section: Chapter Questions

Problem 12.28P: Assume Youngs modulus for bone is 1.50 1010 N/m2. The bone breaks if stress greater than 1.50 108...

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Assume Youngs modulus for bone is 1.50 1010 N/m2. The bone breaks if stress greater than 1.50 108 N/m2 is imposed on it. (a) What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.50 cm? (b) If this much force is applied compressively, by how much does the 25.0-cm-long bone shorten?
Review. On a day that the temperature is 20.0C, a concrete walk is poured in such a way that the ends of the walk are unable to move. Take Youngs modulus for concrete to be 7.00 109 N/m2 and the compressive strength to be 2.00 109 N/m2. (a) What is the stress in the cement on a hot day of 50.0C? (b) Does the concrete fracture?
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 nanotube with a Youngs modulus of 1.000 1012 Pa is subjected to a stress of 3.14 1011 Pa by being pulled at its ends. Assuming the tube had an initial length of 8.12 106 m, what is the new length of the nanotube?
Use the graph in Figure P14.46 to list the three materials from greatest Youngs modulus to smallest. Explain your reasoning. FIGURE P14.46
A 100-N weight is attached to a free end of a metallic wire that hangs from the ceiling. When a second 100-N weight is added to the wire, it stretches 3.0 mm. The diameter and the length of the wire are 1.0 mm and2.0 m, respectively. What is Young’s modulus of the metal used to manufacture the wire?
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
Consider the sketch of a portion of a roller-coaster track seen in Figure P14.5. Identify places on the track that could be considered possible locations of static equilibrium for a rollercoaster car were the car to be placed at any spot on the track.Which places are candidate locations for stable, unstable, andneutral static equilibrium? FIGURE P14.5
Consider a nanotube with a Youngs modulus of 2.130 1012 N/m2 that experiences a tensile stress of 5.3 1010 N/m2. Steel has a Youngs modulus of about 2.000 1011 Pa. How much stress would cause a piece of steel to experience the same strain as the nanotube?
What Is Static Equilibrium? Problems 13 are grouped. 1. C A ball is attached to a strong, lightweight rod (Fig. P14.1). The rod is supported by a horizontal pin near the top. The ball is at rest. Is the ball in static equilibrium? If not, why not? If so, which type of equilibrium is itstable, unstable, or neutral? Hint: What would happen if you displaced the ball slightly? FIGURE P14.1
Review. A wire of length L, Youngs modulus Y, and cross-sectional area A is stretched elastically by an amount L. By Hookes law, the restoring force is kL. (a) Show that k = YA/L. (b) Show that the work done in stretching the wire by an amount L is W=12YA(L)2/L.
(a) Estimate the force with which a karate master strikes a board, assuming the hands speed at the moment of impact is 10.0 m/s and decreases to 1.00 m/s during a 0.002 00-s time interval of contact between the hand and the board. The mass of his hand and arm is 1.00 kg. (b) Estimate the shear stress, assuming this force is exerted on a 1.00-cm-thick pine board that is 10.0 cm wide, (c) If the maximum shear stress a pine board can support before breaking is 3.60 106 N/m2, will the board break?