Materials: Hooke's Law, Young Modulus and Strain Energy：練習問題

A spherical object is held completely submerged at the bottom of a deep tank of water. It is then released and begins to rise. While the object is fully submerged and moving upwards, how does the upthrust acting on it change?

A wire made of a specific metal has an original length \(L\) and a cross-sectional area \(A\). When a force \(F\) is applied, the wire extends by an amount \(\Delta x\). A second wire of the same metal has a length \(2L\) and a diameter twice that of the first wire. What is the extension of the second wire when the same force \(F\) is applied?

A mass is suspended from a system of two identical springs, each with a stiffness \(k\). In Arrangement 1, the springs are in parallel. In Arrangement 2, the springs are in series. What is the ratio of the total stiffness of Arrangement 1 to Arrangement 2?

A composite block is made by mixing two metals. Metal X has a density of \(8000\text{ kg m}^{-3}\) and Metal Y has a density of \(4000\text{ kg m}^{-3}\). If the block contains equal volumes of Metal X and Metal Y, what is the average density of the composite block?

A force-extension graph for a nylon cord shows a linear region from the origin to a force of \(20\text{ N}\) at an extension of \(0.05\text{ m}\). Following this, the graph becomes a horizontal line until the extension reaches \(0.15\text{ m}\). Calculate the total work done in stretching the cord to \(0.15\text{ m}\).

What is meant by laminar flow and how does it differ from turbulent flow in a fluid?

Two identical springs, each with a stiffness of \(250\text{ N m}^{-1}\), are connected in parallel. Determine the total extension of the system when a force of \(15\text{ N}\) is applied.

A force-extension graph for a rubber sample shows a hysteresis loop. If the area under the loading curve is \(1.20\text{ J}\) and the area of the enclosed loop is \(0.45\text{ J}\), calculate the percentage efficiency of the rubber in returning energy.

Define the term upthrust and explain its origin in terms of the pressure exerted by a fluid on an immersed object. Calculate the upthrust acting on a completely submerged cube of side length \(0.10\text{ m}\) in water (density \(1000\text{ kg m}^{-3}\)).

Explain the physical significance of the following features on a stress-strain graph for a ductile material:
(i) Yield point.
(ii) Elastic limit.
(iii) Breaking stress.
Why is the Young modulus only calculated from the initial linear portion of the graph?