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PHY1031F Weekly Problem Sheet 4

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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
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