A-Level Physics – Materials

A rectangular block has mass $0.540\,\text{kg}$ and volume $200\,\text{cm}^3$.Calculate the density of the block, in $\text{kg m}^{-3}$, and suggest which common material it might be made from.

(a) State Hooke’s law.(b) A spring extends by $2.4\,\text{cm}$ when a force of $6.0\,\text{N}$ is applied. Calculate the spring constant $k$.

For the spring in Question 2, calculate the elastic potential energy stored when it is extended by $2.4\,\text{cm}$.

Define, giving the SI unit of each:(a) tensile stress(b) tensile strain

A wire of original length $L_0 = 2.500\,\text{m}$ and diameter $0.56\,\text{mm}$ is loaded with a force of $45.0\,\text{N}$, producing an extension of $2.18\,\text{mm}$.(a) Calculate the cross-sectional area of the wire.(b) Calculate the stress in the wire.(c) Calculate the strain in the wire.(d) Calculate the Young modulus of the wire material.

For the experiment in Question 5 the measurements have uncertainties $\Delta F = 0.5\,\text{N}$, $\Delta d = 0.01\,\text{mm}$, $\Delta L_0 = 1\,\text{mm}$ and $\Delta(\Delta L) = 0.05\,\text{mm}$.Calculate the percentage uncertainty in the Young modulus.

Describe the shape of a stress–strain graph for a ductile metal wire loaded to fracture, identifying on it: the limit of proportionality, the elastic limit, the yield point, the ultimate tensile stress and the fracture point.

For the wire in Question 5:(a) Calculate the elastic strain energy stored per unit volume when the force is $45.0\,\text{N}$.(b) Hence calculate the total elastic potential energy stored in the wire, and confirm your answer using $E_p = \tfrac{1}{2}F\Delta L$.

Two springs, of spring constants $k_1 = 150\,\text{N m}^{-1}$ and $k_2 = 300\,\text{N m}^{-1}$, are combined. Calculate the effective spring constant when they are connected:(a) in series(b) in parallel

The wire in Question 5 breaks when the load reaches $65.0\,\text{N}$. Calculate the breaking stress (ultimate tensile stress) of the wire material.

The Young modulus found in Question 5 was $2.10\times10^{11}\,\text{Pa}$. A data book gives the Young modulus of steel as approximately $2.0\times10^{11}\,\text{Pa}$.(a) Suggest, with a reason, whether the wire is likely to be made of steel.(b) Calculate the percentage difference between the experimental value and the data-book value.

Explain the difference between elastic and plastic deformation of a material, and describe how each would appear if the wire were unloaded partway through the stress–strain test.