1. Physics Support Materials Higher Mechanics and Properties of Matter
Solutions to Problems Density and Pressure
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1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19

2. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 1
A block of iron has a mass of kg and a volume of 5 m3 . What is its density?
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3. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 2
What is the mass of a cylinder of aluminium with a volume of 2.5 m3. (The density of aluminium is 2700 kg m-3).
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4. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 3
1 kg of nitrogen gas is used to fill a balloon. If the density of nitrogen is 1.25 kg m-3 , find the volume of the balloon.
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5. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 4
A tank measures 60 cm long and 40 cm wide. 72 kg of water are to be poured into the tank. How deep will the water be? (Density of water is 1000 kg m-3).
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6. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 5
What will be the mass of air in a classroom with the dimensions: length 15 m, breadth 10 m, and height 4 m? (The density of air is 1.3 kg m-3).
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7. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 6
In the diagram below the piston contains 0.2 kg of oxygen, which has a density of 1.43 kg m-3.
Oxygen
40 cm
a) If the plunger is at a height of 40 cm, what is the cross-sectional area of the plunger?
b) The gas is heated and the plunger rises a further 20 cm.
What is the density of the oxygen now?
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8. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 7
0.01 m3 of water is heated until it changes to steam. What will be the approximate volume of steam?
Increase in volume is approximately x 1000
Volume of steam is therefore 0.01 x = 10 m3
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9. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 11
A box weighs 120 N and has a base area of 0.2 m2. What pressure does it exert on the ground?
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10. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 12
If atmospheric pressure is Pa, what force does the air exert on a wall of area 10 m2 ?
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11. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 13
A rectangular steel block measures 10 cm x 8 cm x 6 cm. What is the greatest and the least pressure which it can exert on a surface? (Density of steel is 8000 kg m-3 ).
The greatest pressure is exerted when the block is rested on its end with area 8 x 6
The least pressure is exerted when the block is rested on its end with area 10 x 8
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12. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 14
Estimate the pressure you exert on the floor when you are standing on one foot.
Estimate your mass - say 80 kg
Estimate the area of one foot - say 25 cm x 10 cm = m2
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13. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 15
What is the pressure due to a depth of 10 m of water? (Density of water = 1000 kg m3 ).
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14. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 16
A water tank has a base of cross-sectional area 0.5 m2 and a depth of water 1.5 m. Calculate:
a) the pressure at the bottom of the tank (caused by the water and by the pressure of the air above the water)
b) the resultant force on the base.
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15. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 17
Water is supplied to flats from a tank on the roof. Find the extra water pressure available to residents on the ground floor if the taps are 30 m below the level of the taps on the top floor.
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16. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 18
A cube of side 12 cm is completely immersed in a liquid of density kg m-3 , so that the top surface is horizontal and 20 cm below the surface of the liquid. Calculate the fluid pressure:
a) at a depth of 20 cm
12 cm
20 cm
b) at a depth of 30 cm
c) Hence calculate the force exerted on:
i) the top surface of the cube
ii) the bottom surface of the cube
d) Calculate the size and direction of the vertical force due to this pressure difference
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17. Physics Support Materials Higher Mechanics and Properties of Matter
Density and Pressure 19
A cube of wood of sides 0.5 m floats in a large tank of water at a height of 0.3 m above the surface. Calculate the:
0.3 m
0.5 m
a) weight of the cube
b) vertical upthrust given to the cube by the water
c) volume of water displaced by the cube.
(density of water = 1000 kg m-3 ; density of wood = 400 kg m-3 )
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