Physics 2: Physical Science & Technology (PHYC10004)
Week 8
Discussion Questions
1
True or false?
• if the hydrostatic (gauge) pressure at a depth h in the ocean is 2.5 atmospheres, then at a depth of 2h the hydrostatic (gauge) pressure will be 5.0 atmospheres.
• if an object is floating, the buoyant force on it is equal to its weight.
• water flows through a pipe having a varying width. More water flows per second through the wide section than through the narrow section because there is more room for it to flow.
2
A jet of air (e.g. from a leaf blower) is directed between two balloons hanging a little way apart. Will the balloons move further apart, closer together, or be unaffected?
Problem-solving Questions (take g = 9.8 N/m, 1 atmosphere = 101 kPa) 3
Oxygen with a mass of 200 kg is stored in a spherical container at atmospheric pressure and at room temperature. At room temperature, oxygen has a density of 1.43 kg m–3.
• Calculate the volume occupied by this amount of oxygen.
The oxygen is now compressed into the container, which has a radius of 0.521 m.
• Calculate the density of the compressed gas.
4
The density of material at the centre of a neutron star is approximately 1.0 × 1018 kgm-3. Calculate the mass of a cube of side 2.0 μm at the centre of a neutron star.
5
One of the dangers of cyclones is the rapid drop in air pressure associated with them. Assume that the air pressure inside of a house is 1 atmosphere when a cyclone hits and that the cyclone rapidly decreases the external air pressure to 0.9 atmosphere. Calculate the net force (magnitude and direction) exerted on a 2.0 m2 square window.
6
The Tonga Trench in the Pacific Ocean is 10 km deep. Calculate the absolute pressure at the bottom of the trench in pascal.
(DATA: seawater density = 1025 kg m–3, assume constant)
7
The earth’s atmosphere has a pressure versus altitude relation approximated by P = P0exp(-αh), where α = 0.116 km–1. As QF30 was flying from the UK to Australia at 10,000 m, the internal cabin pressure was equivalent to the atmosphere at 2500 m. Calculate the force exerted by air pressure on a square metre of cabin wall area. Take P0 = 101 kPa.
8
A 120 cm3 block of aluminium (p = 2700 kg m–3) is hung fully immersed on the end of a piece of string in a bucket of water (p = 1000 kg m–3). Take g = 9.8 N kg–1.
• calculate the tension in the string
• the apparatus is now placed in a lift accelerating downwards at 1.8 m s–2; does this effect the buoyancy force? If so, how? Either way, calculate the tension in the string now
• the apparatus is now taken on an amusement park ride. In part of the ride the passengers are in a ‘free fall’ situation; calculate the tension in the string now
9
How much work is done by pressure in forcing 1.4 m3 of water through a pipe with an internal diameter of 13 mm if the pressure difference at the two ends is 1.0 atmosphere?
10 (mini-challenge question)
A dam wall of width w is holding backwater of density 1000 kg.m–3 with a depth h.
Calculate the total force exerted by the water on the dam wall. Take g = 9.8 m s–2, h = 30 m, and w = 100 m. You can assume that the density of water is equal to 1000 kg m–3.
(Hint: an integral may be required).
Past examination Questions
11
A solid spherical object floats in water with half of its volume submerged.
(i) Given that the density of water is Pw = 1000kg. m-3, what is the density of the object?
(ii) If the object is placed in paraffin oil of density Pparafin = 800 kg. m-3, what fraction of the sphere’s volume will be submerged?
12
A venturi tube is shown in the diagram, with the flow direction marked by horizontal arrows. The cross-sectional areas of the fluid stream at points A, B and C are a m2, a/2 m2 and a m2 respectively. The density of the incompressible fluid flowing in the tube past points A, B and C is P kg.m-3.
a) If the speed of the fluid at point A is v ms-1, what is the speed of the fluid at:
i) Point B?
ii) Point C?
[Express your answers in terms of v.]
b) Find an expression for the pressure difference between points A & B in terms of ρ & v.
c) If the incompressible fluid in the curved section of tubing (indicated by the shading) has a density of σ kg m-3, find an expression for v in terms of σ, P and g (the gravitational acceleration constant in ms-2) and h (difference in the fluid levels in metres)