PHYS*1080 Sample Quiz 8

  1. A vertical hollow steel tube is 2.5m long. Its internal diameter is 5cm and its external diameter is 6cm. Calculate the increase in length of the tube when a load of 1.5×104kg is suspended from the lower end. For steel Young's modulus is 21×1010N m−2 and the shear modulus is 8.3×1010N m2. (3 marks)

     
  2. In mammals, brain volume is proportional to the surface area of the mammal. A small mammal of 1.0\; \text{kg} body mass has a brain mass of 10 \; \text g. What will be the brain mass of a large mammal of mass 1000\; \text{kg} ? (4 marks)
    Solution Mark
    V(\text{large})/V(\text{small})= 1000 = L^3 (1.0)
    \therefore \; L = 10 (1.0)
    A(\text{large})/A(\text{small})= L^2 = \text{Brain}(\text{large})/\text{Brain}(\text{small}) (1.0)
    \therefore \; \text{Brain}(\text{large})= 10\; \text g \times 10^2 = 10^3 \; \text g = 1 \; \text{kg} (1.0)

     
  3. A biophysicist wants to determine the surface tension of ethyl alcohol. Its density is 790\; \text{kg m}^{-3}, and its contact angle with glass is the same as that for pure water. Inside a glass capillary tube, water "climbs" 2.7 times higher than ethyl alcohol. What is the surface tension of ethyl alcohol? (3 marks)
    Solution Marks
    2.7 = \frac{h_w}{h_a} = \frac{\frac{2 \gamma_w \cos \theta_w}{\rho_wgr}}{\frac{2 \gamma_a \cos \theta_a}{\rho _a gr}} = \frac{\gamma _w\rho_a}{\gamma _a \rho _w} (1.5)
    \gamma _a = \frac{h_a}{h_w}\frac{\gamma_w\rho_a}{\rho_w}= \frac{1}{2.7} \frac{(7.28 \times 10^{-2})(790)}{1000} (1.0)
    = 2.1 \times 10^{-2}\; \text{N/m} \; [\text{J/m}^2] (0.5) answer