## Question 1 > When a mass of 40 kg is hung from a spring, the spring stretches by 6 mm. Assuming that Hooke's Law holds good, by how much more would the spring stretch if an additional mass of 100 kg were hung from it? What is the spring constant? > [!HELP]- Solution > $ > m=40kg \qquad x=6\times 10^{-3} \qquad x=\frac{F}{k} > $ > $ > k=\frac{mg}{x}=\boxed{65.3\ kN\ m^{-1}} > $ > $ > x_{add}=\frac{(m+100)g}{k} - x=\boxed{0.015\ m} > $ ## Question 2 > A certain type of spring has a spring constant of $55\ kN\ m^{-1}$. Two such springs are connected end to end, one above the other, with the top of the upper spring being attached to the ceiling and with a mass of 10 kg being supported from the bottom of the lower spring. What is the total extension of the pair of springs due to the mass being supported? > [!HELP]- Solution > $ > k=55\ kN\ m^{-1} \qquad m=10kg \qquad k_{eff}=\frac{k_{1}\times k_{2}}{k_{1}+k_{2}} > $ > $ > x=\frac{mg}{k^2 \div 2k}=3.56 \times 10^{-3}\ m = \boxed{3.56\ mm} > $ ## Question 3 > A wire has a strain of $5 \times 10^{-4}$ and an extension of 0.8 mm. Find the original length of the wire. > [!HELP]- Solution > $ > \epsilon=5\times 10^{-4} \qquad \Delta x=8 \times 10^{-4} \qquad \epsilon=\frac{\Delta x}{L} > $ > $ > L=\frac{\Delta x}{\epsilon}=\boxed{1.6\ m} > $ ## Question 4 > Calculate the stress in a wire of circular cross section, 4 mm in diameter, when it supports a load of 1.25 kN. > [!HELP]- Solution > $ > F=1.25\ kN \qquad d=4\times 10^{-3} \qquad A=\pi\left(\frac{d}{2}\right)^2=12.56\times 10^{-6}\ m^2 > $ > $ > \sigma=\frac{F}{A}=\boxed{99.5\times 10^6\ Pa} > $ ## Question 5 > Calculate the width of the sides of the cross section of a square concrete column if it is to support a compressive load of 225 kN and the stress is not to exceed 10 MPa.