A tunnel of length L =150 m, height H = 7.2 m, and width 5.8 m (with a flat roof) is to be constructed at distance d = 60 m beneath the ground. The tunnel roof is to be supported entirely by square steel columns, each with a cross-sectional area of 960 cm2.The mass of 1.0 cm3 of the ground material is 2.8 g. (a) What is the total weight of the ground material the columns must support? (b) How many columns are needed to keep the compressive stress on each column at one-half its ultimate strength?

Q: Assume the breaking stress of a bone is 1.30 x 107 N/m2, the magnitude of the maximum force a…

A: Given Breaking stress of a bone =1.30x107Nm2 Average diameter of bone =d= 3cm Area of bone=πd24…

Q: A metal wire of diameter D stretches by 0.100 mm when supporting a weight W. If the same-length wire…

A: Given: Initial diameter of metal wire, D1=D Weight supported to metal wire initially, W1=W The…

Q: A steel cube of side length L = 0.5 m is subjected to a shearing force of 5000N along the top…

A:

Q: A large uniform cylindrical steel rod of density ρ = 7.8 g/cm3 is 2.0 m long and has a diameter of…

A:

Q: By applying 2.00 x 106 N/m2 shear stress to a steel bar 2 m in length, calculated the shear bending…

A: Shear Bending Stress(S) for steel is given as,    S=(8.3×108 N/m2)=Shear StressShear strain

Q: The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends,…

A: Solution: The load L the beam can support = 5930 pounds the safe load of beam varies directly as the…

Q: A bar with a uniform cross-sectional area of 300 mm² is subjected to axial loads, as shown in the…

A: Correct option (b) 140 Mpa

Q: A high-carbon steel wire, circular in cross-section, has a diameter of 14 mm. What is the force (in…

A:

Q: A steel cable 3.00 cm2 in cross-sectional area has amass of 2.40 kg per meter of length. if 500 m of…

A: Given:- Cross-sectional area = A = 3 cm2 = 3 x 10-4 m2 Mass per unit length = 2.4 kg/m Length of the…

Q: A 1000-kg object hangs from the lower end of a steel rod 5.0 m long that is suspended vertically.…

A:

Q: 2. A 50.0 kg uniform square sign, of edge length L=2.00m, is hung from a horizontal rod of length of…

A:

Q: A nylon string on a tennis racket is under a tension of 275 N. If the string's radius is 5.00 x 10-4…

A: The equation for the change in length can be obtained from equation for the Young’s Modulus as

Q: A child slides across a floor in a pair of rubber-soled shoes. The friction force acting on each…

A: Shear modulus is the ratio of shear stress to the shear strain. Using the equation for shear…

Q: A circular shaft has a diameter d [m] that varies with axial position x [m] according to d =…

A:

Q: A copper wire is 1.0 m long and its diameter is 1.0 mm. If the wire hangs vertically, how much…

A:

Q: beam with a solid homogeneous rectangular section is simply supported at A and B. concentrated load…

A: Given B = 35 mm  D = 125 mm  Moment of inertia of rectangle = bd3/12   Hence required solution is…

Q: A body of mass 500 kg is suspended at the free end of an iron wire of length 3 m and cross-sectional…

A:

Q: A tunnel of length L = 130 m, height H = 9.4 m, and width 5.6 m (with a flat roof) is to be…

A: L = 130 m, height H = 9.4 m, and width 5.6 m (with a flat roof) is to be constructed at distance d =…

Q: a diver stands (80kg) at the end of a diving board, causing the board to dip 10cm. The board has a…

A:

Q: A child slides across a floor in a pair of rubber-soled shoes. The friction force acting on each…

A: Given information: Here, f is the friction force, A is the area of the sole of the shoe, l is the…

Q: A cylindrical aluminum rod, with an initial length of 0.8000 m and radius 1000.0 mm, is clamped in…

A: The density is constant in the given case thus expression will be,

Q: The upper surface of a cube of gelatin, 5.0 cm on a side, is displaced by 0.64 cm by a tangential…

A:

Q: 'One end of a steel rod of radius R = 10mm and length L = 90 cm is held in a vise. A force of…

A:

Q: A steel WIre of diameter I mm can support a tension of0.2 kN. À cable to support a tension of 20 kN…

A: Given : Diameter of first steel wire, d1 = 1 mm Tension the first wire can support, T1 = 0.2kN…

Q: Consider two steel rods, A and B. B has three times the area and twice the length of A, so Young's…

A: We know that Young's modulus is property of matter and not depend on size . Here, both rods are made…

Q: A steel cable 3.00 cm2 in cross-sectional area has a mass of 2.40 kg per meter of length. If 500 m…

A: The expression for the ratio of the change in length to that of the original,

Q: One end of a steel rod of radius R = 10mm and length L = 80 cm is held in a vise. A force of…

A: We need to calculate the elongation of the rod when the given force is applied.

Q: "One end of a steel rod of radius R = 10mm and length L = 100 cm is held in a vise. A force of…

A:

Q: A tunnel of length L = 180 m, height H = 9.4 m, and width 6.1 m (with a flat roof) is to be…

A:

Q: A 50-N force is applied to a metal rod with a length of 10 m and a cross-sectional area of 1.0 x…

A:

Q: 3.7 There is an imprecise relationship between the flexural strength and volumetric strain of a…

A:

Q: A 0.50 m long guitar string, of cross- sectional area 1.0 x10-6 m2, has a Young’s modulus of 2.0x…

A: Given : L = 0.50 m A = 1 × 10-6 m2 Y = 2 × 109 Pa F = 20.0 N

Q: A steel cable 3.00 cm2 in the cross-sectional area has a mass of 2.40 kg per meter of length. If 500…

A:

Q: steel wire of length 1.93 m with a circular cross-section must stretch no more than 0.240 cm when a…

A: Dear student The Young modulus is defined as: Y = Stress/ Strain Here stress = Force / Area Strain =…

Q: A steel cable of diameter 2 cm is acted upon by 50000 N of tension. If Young’s modulus is 20 x 1010…

A:

Q: A 480 mm long thighbone (femur), which is the largest and longest bone in the human body, has a…

A: Given that  young modulus = 15x 108 N/m2 length of femur = 480 mm =0.480 m cross sectional area =…

Q: QUESTION What happens to the tension in the cable if the man in Figure (a) moves farther away from…

A: Let suppose the man is standing at a distance 'l' from the left, Since the beam is not moving,…

Q: The pole in the figure is a a 90° bend in a power line and is therefore subjected to more shear…

A: Tension in wires at top , T = 3.5 x 104 N Angle made by wire with the vertical , θ = 80° Height of…

Q: The face of an aluminum plate, which is fixed in place, measures 90 cm by 90 cm. The thickness of…

A:

Q: The femur bone in a human leg has a minimum effective cross section of 3.15 cm2. How much…

A: The pressure presently working on an object can be defined as the physical force that is being…

Q: Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin…

A: Consider the mass of the Gold as 1.915g.Find the volume of the gold formed into a thin leaf.

Q: A lift of mass 2000 kg is supported by thick steel ropes. If maximum upward acceleration of the lift…

A:

Q: An object with a mass equal to 300 kg is hung on a wire of length 5.00 m and cross-sectional area of…

A:

Q: A vertical steel girder with a crosssectional area of 0.15 m2 has a 1550 kg sign hanging from its…

A:

Q: One end of a steel rod of radius R = 10mm and length L = 90 cm is held in a vise. A force of…

A:

Q: Two strips of metal are riveted together at their ends by four rivets, each of diameter 8.0 mm. What…

A: Diameter of each rivet,

Q: A cylindrical steel rod is originally 250 cm long and has a diameter of 0.263 cm. A force F is…

A: find the external force for steel rod in magnitude value .

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).