In a measurement of a man’s density he is found to have a mass of 75.0 kg in air and an apparent mass of 2.25 kg when completely submerged in water with his lungs empty. he has a lung capacity of two and half liters. (a) what mass of water does he displace? (b) determine his volume. (c) calculate his density. (d) if his lungs are half filled with air, will he float or sink? (show calculation. yes/no without calculations give you zero points.) (e) if his lungs are completely filled with air, will he float or sink?

a) = 72.75 kg , b)  V = 0.07275 m³ , c)   ρ₂ = 1030.9 km / m³ , d)  ρ₂= 996 kg / m³   float

Explanation:

This is an exercise that we must solve using the Archimedes principle, where the thrust is

         B = ρ g V

a) Let's use Newton's second law

         F = B - W

         F = ρ g V - mg

The force is the apparent weight (m₂ = 2.25 kg) is directed downwards so it is negative

         F = m₂ g

        -m₂ g = ρ g V - m g

        -m₂ g = g - mg

          = -m₂ + m

          = -2.25 + 75.0

          = 72.75 kg

b) let's use the definition of density

         ρ = m / V

         V = m /ρ

         V = 72.75 / 1000

         V = 0.07275 m³

c) the density of man is

          ρ₂ = m / V

          ρ₂ = 75.0 / 0.07275

          ρ₂ = 1030.9 km / m³

d) the volume of man increases because the lungs are full of air, as they are half full, with a capacity of 2.5 liters and two lungs the volume is

         V’= ½ 2.5 2

         V’= 2.5 liters

         V’= 2.5 10⁻³ m³

The total volume of man is

         Vt = 0.07275 + 0.0025

         Vt = 0.07525

Let's calculate the density

         ρ₂ = 75.0 / 0.07525

         ρ₂= 996 kg / m³

As this is less than the density of water (1000 kg / m3) man must float

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the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.