The density of fresh water is \(1000 kg/m^3\) (1 \(m^3\) of fresh water has a mass of 1000 \(kg\))
The density of saltwater is \(1025 kg/m^3\) (1 \(m^3\) of saltwater has a mass of 1025 \(kg\))
An object placed in water will float if,
density of object < density of water
buoyant force > weight
Example:
A brick of an unknown substance has a mass of 15 kg and a volume of 0.055 \(m^3\). What is the density of this brick? Will it sink or float in fresh water?
A brick of an unknown substance has a mass of 71 kg and a volume of 0.070 \(m^3\). What is the density of this brick? Will it sink or float in fresh water?
After solving on your own, check the
A beachball is filled with freshwater and put in the water at a beach of saltwater. The beachball with the fresh water has a mass of \(520~kg\) and a volume of \(0.52~m^3\). With this water-filled beachball sink or float?
After solving on your own, check the
Why do Hydrogen and Helium balloons float in the air?
After solving on your own, check the
Why is the density of the atmosphere greatest near the surface and smaller as you go up in altitude?
After solving on your own, check the
## Question 1.5.1
1. A brick of an unknown substance has a mass of 71 kg and a volume of 0.070 $$m^3$$. What is the density of this brick? Will it sink or float in fresh water?
* $$Density = \frac{mass}{Volume} = \frac{71~kg}{0.070~m^3}=1014.3~kg/m^3$$
* $$Weight = mass\cdot 9.8 = 71~kg\cdot 9.8 = 695.8~N$$
* $$Buoyant~Force = 9.8\cdot 1000\cdot 0.070~m^3 = 686~N$$
Since the Weight is more than the Buoyant Force, this brick will sink in fresh water.
## Question 1.5.2
2. A beachball is filled with freshwater and put in the water at a beach of saltwater. The beachball with the fresh water has a mass of $$520~kg$$ and a volume of $$0.52~m^3$$. With this water-filled beachball sink or float?
* $$Density = \frac{mass}{Volume} = \frac{520~kg}{0.52~m^3}=1000~kg/m^3$$ (this is the density of fresh water)
* $$Weight = mass\cdot 9.8 = 520~kg\cdot 9.8 = 5096~N$$
* $$Buoyant~Force = 9.8\cdot 1025\cdot 0.52~m^3 = 5223.4~N$$ (Note that we use 1025 since the beachball will be put in saltwater)
Since the Buoyant Force is more than the Weight, a beachball filled with fresh water will float when put in saltwater.
## Question 1.5.3
3. Why do Hydrogen and Helium balloons float in the air?
The mass of hydrogen and helium atoms are much smaller than the average mass of molecules in the air. So the density of hydrogen and helium is small (small mass = low density) while the density of air is larger (larger mass = high density).
The low density of the hydrogen and helium will cause the buoyant force of the balloon to be more than its weight.
## Question 1.5.4
4. Why is the density of the atmosphere greatest near the surface and smaller as you go up in altitude?
Gravity pulls the atmosphere down toward the surface, so the atmosphere accumulates toward the surface, creating a larger amount of mass in a small volume. Mathematically, a large mass divided by a small volume will give a high density.
The lighter gases, such as Hydrogen and Helium, will stay higher in the atmosphere and are more spread out.