Floating and Sinking

EHS Physics Mr. Heiman Floating and Sinking
Name:_______________
Use Archimedes’ principle and your knowledge of physics to solve the following problems.
Useful information:
Net force: ΣF = ma
Volume of a block: V = lwh
ρaluminum = 2.7 g/cm3
ρglycerol = 1.26 g/cm3
ρwater = 1.0 g/cm3
Density: ρ = m/V
Weight: Fg = mg
Volume of a sphere: V = (4/3)πr3
ρbutane = 0.599 g/cm3
ρethanol = 0.76 g/cm3
3
ρair = 1.20 kg/m
ρHe = 0.18 kg/m3
1 m3 = 1000 L = 1,000,000 cm3
PART I
1. If a block of aluminum measures 4.0 cm x 5.0 cm x 2.0 cm is completely submerged in
a fluid, what volume of fluid does it displace?
2. What is the mass of the displaced fluid if it is:
water?
butane?
glycerol?
3. How large of a buoyant force acts on the block in each fluid?
water?
butane?
glycerol?
4. In which fluid does the aluminum block float?
water?
butane?
glycerol?
5. If you suspend the completely submerged 108 g aluminum block from a string what will
be the tension in the string in each fluid? (Hint: The net force on the block is zero.)
water?
butane?
glycerol?
6. What would happen to the aluminum block if you dropped it into a large container of
liquid mercury? Explain your answer.
EHS Physics Mr. Heiman PART II
7. A block of plastic has dimensions 4.0 cm x 5.0 cm x 2.5 cm. Its mass is 35.0 g. What is
the density of the block of plastic?
8. If the block of plastic is completely submerged in ethanol, how large of a buoyant force
will act on it?
9. If you let go of the plastic block when it is completely submerged, what will be its initial
acceleration?
10. Once the block is floating on the surface, how large of a buoyant force acts on the block
as it floats on the surface?
11. What volume of ethanol is being displaced by the plastic block as it floats?
12. What percentage of the plastic block is above the surface of the water?
13. How much mass could you add to the block before it’s top surface was level with the
ethanol?
EHS Physics Mr. Heiman PART III
14. Imagine a person with a mass of 85 kg. If their density is 940 kg/m3, what is their
volume in cubic meters?
15. What is the weight of the air that is displaced by the person?
16. Do people experience an upward buoyant force? If so, why don’t we notice it much?
17. What is the volume of a spherical balloon with a radius of 2.0 meters?
18. Determine both the mass and the weight of the helium in the balloon.
19. Determine both the mass and the weight of the air that would be displaced by the
balloon.
20. If the balloon was tethered to the ground by a string, what would be the tension in the
string? You can ignore the weight of the balloon material (draw a free body diagram!)
BONUS: What radius would the helium balloon have to lift the person off the ground?