DEPARTMENT OF PHYSICS UNIVERSITY OF CAPE TOWN PHY1031F 2019 Weekly Problem Set 4 (submit before 10h00 on Friday 22 March 2019) 1. Use your mass to estimate: a) the buoyant force which the sea exerts on you (density 985 kg m−3) when you are 80 % under water. b) the buoyant force which the air exerts on you when you are not in the sea. 2. A 30 kg child floats in a dam on top of a block of polystyrene (styrofoam). What is the minimum volume of polystyrene needed to keep the child afloat? (polystyrene = 32 kg m−3). 3. The U-tube shown contains two liquids in static equilibrium: water in the right arm and oil of unknown density x in the left. l = 135 mm and d = 12.3 mm. What is the density of the oil? 4. You are given a crown and told that it is made of gold. You find that a spring balance gives a measurement of 98.0 N when the crown is suspended in air, and 92.9 N when the crown is suspended in water. Is the crown made of gold? (Hint: work with symbols for as long as you can in answering this question.) 5. At one point in a pipeline, the water’s speed is 3.00 m s−1 and the gauge pressure is 4.00 × 104 Pa. Find the gauge pressure at a second point in the line 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first. 1