Loading PDF...
Chapter Analysis
Intermediate13 pages • EnglishQuick Summary
The chapter 'Mechanical Properties of Solids' discusses essential concepts such as elasticity, stress, strain, Hooke's law, and different types of elastic moduli including Young’s modulus, shear modulus, and bulk modulus. It also covers the applications of elastic behavior in engineering and real world scenarios, providing detailed explanations of concepts like Poisson's ratio, elastic potential energy, and the stress-strain curve. The chapter emphasizes how materials respond to different forces, and the importance of understanding these properties for structural and material design.
Key Topics
- •Elasticity and Elastic Deformation
- •Stress and Strain
- •Hooke’s Law
- •Elastic Moduli: Young’s, Shear, and Bulk Modulus
- •Poisson’s Ratio
- •Stress-Strain Curves
- •Applications in Engineering and Design
Learning Objectives
- ✓Understand and define stress and strain
- ✓Explain Hooke’s Law and its practical implications
- ✓Differentiate between types of elastic moduli and calculate them
- ✓Analyze deformation in materials through stress-strain curves
- ✓Apply concepts of elasticity to real-world engineering problems
- ✓Assess material properties for structural and design purposes
Questions in Chapter
A steel wire of length 4.7 m and cross-sectional area 3.0 × 10^-5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10^-5 m2 under a given load. What is the ratio of the Young’s modulus of steel to that of copper?
Page 178
Figure 8.9 shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
Page 178
The stress-strain graphs for materials A and B are shown in Fig. 8.10. (a) Which of the materials has the greater Young’s modulus? (b) Which of the two is the stronger material?
Page 178
Read the following two statements below carefully and state, with reasons, if it is true or false. (a) The Young’s modulus of rubber is greater than that of steel; (b) The stretching of a coil is determined by its shear modulus.
Page 178
Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in Fig. 8.11. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.
Page 178
The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?
Page 179
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.
Page 179
A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain?
Page 179
A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m–2, what is the maximum load the cable can support?
Page 179
A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratios of their diameters if each is to have the same tension.
Page 179
A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path.
Page 179
Additional Practice Questions
Consider a metal rod subjected to tensile stress until it yields. Describe the changes in its stress-strain characteristics and explain the concept of elastic limit and plastic deformation.
mediumAnswer: When a metal rod is subjected to tensile stress, initially it exhibits elastic behavior where stress is proportional to strain (Hooke's Law). The elastic limit is reached when further stress leads to permanent deformation. Beyond the elastic limit, the rod enters the plastic deformation phase, where it cannot return to its original shape even after the stress is removed.
Explain how the principles of elastic potential energy apply to a catapult mechanism when launching a projectile.
easyAnswer: A catapult stores potential energy in the elastic components when it is pulled back. This energy is directly proportional to the displacement squared and the spring constant. Upon release, this stored elastic potential energy is converted into kinetic energy, propelling the projectile forward.
In a bridge construction scenario, how would you determine the appropriate material by evaluating Young's modulus and tensile strength?
hardAnswer: Selecting materials for bridge construction involves choosing those with high Young's modulus for rigidity and sufficient tensile strength for support. Calculations of load and strain factors using these moduli help ensure the material can handle expected loads without significant deformation.
Derive the formula for calculating the strain energy stored in a spring under compression, and apply it to find the energy in a spring compressed by 0.05 m having a spring constant of 300 N/m.
mediumAnswer: Strain energy (U) in a spring is given by U = 1/2 k x^2, where k is the spring constant and x is the compression. For a spring with k = 300 N/m compressed by x = 0.05 m, U = 1/2 × 300 × (0.05)^2 = 0.375 Joules.
Describe the real-world applications of bulk modulus, and provide an example of how this property is critical in industrial applications.
mediumAnswer: Bulk modulus is crucial in determining how incompressible a material is under uniform pressure. It is essential in applications like designing underwater equipment in submersible vehicles, where materials must withstand deep-sea pressures without significant volume changes.