Answer: I tried...
When a person is completely submerged in water, they experience a buoyant force equal to the weight of the water displaced by their body. This buoyant force partially counteracts the gravitational force acting on the person, which is why they weigh less when submerged.
Here's how you can calculate the reading on the scale:
Calculate the weight of the person in air using the formula:
Weight = mass × gravitational acceleration
Weight = 89.2 kg × 9.81 m/s² (standard value for gravitational acceleration)
Weight = 876.252 N
Now, calculate the volume of water displaced by the person using the formula:
Volume = mass / density
Volume = 89.2 kg / 1025 kg/m³
Volume ≈ 0.087 m³
Calculate the buoyant force acting on the person, which is equal to the weight of the water displaced:
Buoyant Force = Volume of water displaced × density of water × gravitational acceleration
Buoyant Force = 0.087 m³ × 1000 kg/m³ × 9.81 m/s² (density of water and gravitational acceleration)
Buoyant Force ≈ 853.617 N
Finally, calculate the reading on the scale, which is the weight of the person in air minus the buoyant force:
Reading on the Scale = Weight in air - Buoyant Force
Reading on the Scale = 876.252 N - 853.617 N
Reading on the Scale ≈ 22.635 N
So, the scale will read approximately 22.635 Newtons when the person is completely submerged in water.