Page 117 - Physics

Sinking and fl oating

Solution where, ρ, g, and V are the density of
Let the volume of a man V= 1 water, acceleration due to gravity, and
Volume of the submerged body of a volume of water and V and ρ are
b
b
man V= 2 the volume and density of the body,
respectively.
Density of a man = ρ
person Since 98% of the body is immersed,
Density of water = ρ
water 0.98V b
The man’s density can be obtained by ρ = V ×ρ water
b
solving the equation, b
V ρ = 0.98×1 000 kg/m 3
1 = water
V ρ ! 980 kg/m 3
2 man
V Therefore, the density of the body is
ρ = 2 ×ρ
3
man V water 980 kg/m .
1
ρ = 0.92V 1 ×ρ
man V water Law of fl oatation in everyday life
1
Some objects and vessels fl oat or can be
ρ = 0.92×1 000 kg/m 3 made to fl oat. Balloons, canoes, ships,
man
boats and submarines obey the law of
ρ man = 920kg/m 3 fl otation in their operations. These bodies

Therefore, the man’s density is less are designed in such a way that the
than the density of the fl uid, hence, he average density of the body is less than
will fl oat in water. the density of the fl uid in which they fl oat.
Therefore, an object made of a material of
Example 5.7 high density, such as a metal, must have
a lot of space fi lled with material of very
Calculate the density of a wood, if a low density like air. Remember that an
fl oating body is 98% submerged in object will fl oat if its average density is
water. Take the density of water to be less than the density of the fl uid in which
1 000 kg/m . it is immersed. The operation principles
3
Solution of various fl oating objects are discussed
Given, in the forthcoming sections.
ρ
Density of water, = 1 000 kg/m 3
Balloons
From Archimedes’ principle, Suppose we have a 5.5 g balloon made of
buoyant force = weight of the body rubber, which has a density of 1.52 g/cm .
3
3
F = ρ ×V × g The volume of the balloon is 3.62 cm .
b b b
Since the density of rubber is much greater
F =V ρ g than the density of air (0.001293 g/cm ) a
3
b b b
defl ated balloon would not fl oat in air. Now
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Physics Form 1 Final.indd 111 16/10/2024 20:56