Question

1. a) A buoy containing scientific equipment is tethered below the surface of a river by a rope attached to the river bed. The buoy has a mass of 250 kg and is spherical with a total volume of 0.50 m3. Given that g ≈ 10 ms-2 and the density of the river water is 1000 kg m-3, show that the tension in the rope is approximately 2.5 kN.

   [10 marks]

2. b) The rope used to tether the buoy described in part (a) is made of nylon and has an effective diameter of 6.0 mm. Given that the Young’s modulus of nylon is 2.2 GPa and that the un-stretched length of the rope is 2 m show that:

   i) The stress in the nylon is approximately 9×107 Pa.
   ii) The extension of the rope under these conditions is approximately 8 cm.

   [6 marks]

3. c) Suppose the buoy previously described were tethered using a stainless steel cable with Young’s modulus 1.8×1011 Pa. Show that the minimum cable diameter required if the cable is not to exceed a strain of 0.2% under these conditions is approximately 3 mm.

   [4 marks]

4. d) A wire is under tension. All things being equal, explain whether doubling the length or halving the diameter of the wire would have the biggest effect on the elastic energy density stored in the wire.

   [5 marks]

Answer 1