Bulk properties of solids：練習問題

A uniform cube has a mass of \(0.64\text{ kg}\) and side lengths of \(4.0\text{ cm}\). What is the density of the material from which the cube is made?

A wire made of a material with Young modulus \(E\), length \(L\), and cross-sectional area \(A\) is stretched by a force \(F\) within its limit of proportionality. Which expression represents the elastic strain energy stored in the wire?

A metal wire of length \(L\) and cross-sectional area \(A\) is stretched by a force \(F\). The Young modulus of the material is \(E\). If the wire is replaced by another wire of the same material but with twice the length and half the diameter, what is the new spring constant of the wire compared to the original spring constant \(k\)?

A metal wire has a length of \(2.5\text{ m}\) and a cross-sectional area of \(0.40\text{ mm}^2\). When a tensile force of \(80\text{ N}\) is applied, the wire extends by \(1.2\text{ mm}\). What is the tensile stress in the wire?

A spring with a stiffness of \(150\text{ N m}^{-1}\) is compressed by \(4.0\text{ cm}\). Calculate the elastic strain energy stored in the spring, assuming it obeys Hooke's law.

A copper wire and a steel wire of the same initial length and cross-sectional area are subjected to the same tensile force. The Young modulus of steel is twice that of copper. Determine the ratio of the extension of the copper wire to the extension of the steel wire.

A composite rod consists of a brass section and a steel section joined end-to-end. Both sections have a diameter of \(1.2\text{ mm}\). The brass section is \(0.80\text{ m}\) long and the steel section is \(1.20\text{ m}\) long. Calculate the total extension when a load of \(50\text{ N}\) is applied.
(Young modulus: \(E_{\text{brass}} = 1.0 \times 10^{11}\text{ Pa}\), \(E_{\text{steel}} = 2.0 \times 10^{11}\text{ Pa}\))

A metal wire of original length \(1.5\text{ m}\) and cross-sectional area \(2.0 \times 10^{-7}\text{ m}^2\) is suspended vertically from a fixed support. When a load of \(40\text{ N}\) is attached to the lower end, the wire extends by \(1.2\text{ mm}\). Assume the elastic limit is not exceeded.

(a) Calculate the tensile stress in the wire.
(b) Calculate the tensile strain in the wire.
(c) Determine the Young modulus of the metal.