Question

Calculate the buoyant force due to the surrounding air on a man weighing 700 n . assume his average density is the same as that of water. suppose that the density of air is 1.20 kg/m3. express your answer to two significant figures and include the appropriate units.

Answer 1

The buoyant force is represented by the weight of the air which is displaced by the body.
The weight of the displaced air can be calculated using the following rule:
weight of displaced air  = (density)(volume)(gravitational force)
where "volume" is the volume of the body (the man in our case) and density is the density of air (= 1000 kg/m^3)

So, we need to calculate the volume of the man:
weight = gravitational force x volume
700 n = 9.8 x volume
Therefore, volume of man = 71.428 m^3

Substituting with this volume along with the gravitational force and density in the above equation, we can calculate the buoyant force as follows:
buoyant force = weight of air displaced = (1000)(71.428)(9.8) 
                                                              = 669.9944 x 10^3 n

Answer 2

Buoyant force due to the surrounding air on a man is 0.84 Newton

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Further explanation

The basic formula of pressure that needs to be recalled is:

Pressure = Force / Cross-sectional Area

or symbolized:

$\large {\boxed {P = F \div A} }$

P = Pressure (Pa)

F = Force (N)

A = Cross-sectional Area (m²)

Let us now tackle the problem !

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Given:

Density of Air = ρ_air = 1.20 kg/m³

Weight of the man = w = 700 N

Density of the man = ρ = 1000 kg/m³

Asked:

Buoyant Force = F = ?

Solution:

We will use Archimedes' principle to solve the problem as follows:

$F = \rho_{air} g V$

$F = \rho_{air} g \frac{m}{\rho}$

$F = \rho_{air} g \frac{w}{g\rho}$

$F = \rho_{air} \frac{w}{\rho}$

$F = 1.20 \times \frac{700}{1000}$

$F = 0.84 \texttt{ Newton}$

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Learn more

• Minimum Coefficient of Static Friction : https://brainly.com/question/5884009
• The Pressure In A Sealed Plastic Container : https://brainly.com/question/10209135
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454

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Answer details

Grade: High School

Subject: Physics

Chapter: Pressure

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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant , Liquid , Pressure