Archimede's Principle


 

Definition

Example 1

Example 2

Example 3

Problems with Answers

 

Archimede's principle states that a body immersed in a fluid is buoyed up with a force equal to the weight of the displaced fluid.

 

Example 1:

A 10-mL body, "weighting" 50 grams, will displace 10 mL of H2O. This amount of water has a mass of 10 grams because the density of H2O is 1-g/mL. Therefore, the 50-g body will weigh 10-grams less, or 40 grams when immersed in the liquid.

 

Mass of body

50-g

50-g

Volume of body

10-mL

.

Volume of fluid displaced

10-mL

.

Mass of fluid displaced (H2O has a density of 1-g/mL)

10-g

- 10-g

Mass of body while in water (subtract)

.

40-g

 

Example 2:

A 5 mL body with a mass in air of 40-g is immersed in CCl4 (carbon tetrachloride) whose density is 1.59 g/mL.  What is the apparent mass of the body while submerged in the CCl4?

Solution:

A submerged 5-mL body will displace 5-mL of liquid.  Since the density of CCl4 is 1.59-g/mL, the 5-mL of  CCl4 will weigh 7.95-g.  Therefore the mass of the submerged body will weigh 40-g minus 7.95-g or 32.05-g.

 

Mass of body

40-g

40-g

Volume of body

5-mL

.

Volume of fluid displaced

5-mL

.

Mass of fluid displaced 
(CCl4 has a density of 1.59-g/mL)

7.95-g

- 7.95-g

Mass of body while in water (subtract)

.

32.05-g

 

Example 3:

You are deep-sea fishing off of Catalina Island.  You catch a yellowfin tuna and accurately estimate that the tuna has a volume of 20-L (20,000-mL), and a mass in sea water of 30-kg. If the density of sea water is 1.1 g/mL, what will be the mass of the tuna when lifted from the water.

 

Mass of body in water

30,000-g

30,000-g

Volume of body

20,000-mL

.

Volume of fluid displaced

20,000-mL

.

Mass of fluid displaced 
(Salt water has a density of 1.1-g/mL)

22,000-g

+22,000-g

Mass of body while in air (add)

.

52,000-g

Practice Problems:

  1. A 50-mL, 75-g object is immersed in water.  What is its apparent mass in water? (Density of water is 1 g/mL) Answer
  2. A 10-mL, 50-g object is immersed in CCl4.  What is its apparent mass while in CCl4?  (Density of CCl4 = 1.59 g/mL) Answer
  3. An object is immersed in water.  Its apparent mass in water is 15 g.  Its apparent mass in air is 35 g.  What is the volume of the object? Answer
  4. A 100-mL object has a mass in air of 50 g.  The object is put into a jar from which all the air is pumped out (vacuum).  How much does the object weigh in the vacuum? (Density of air = 0.00118-g/mL). Answer