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LECTURE 3 BUOYANCY (’ PRINCIPLE) Lecture Instructor: Kazumi Tolich Lecture 3 2

¨ Reading chapter 11-7 ¤ Archimedes’ principle and buoyancy Buoyancy and Archimedes’ principle 3

¨ The exerted by a on a body wholly or partially submerged in it is called the buoyant force.

¨ Archimedes’ principle: A body wholly or partially submerged in a fluid is buoyed up by a force equal to the of the displaced fluid.

Fb = wfluid = ρfluidgV V is the volume of the object in the fluid. Demo: 1 4

¨ Archimedes’ principle ¤ The buoyant force is equal to the weight of the displaced. Lifting a rock under water 5

¨ Why is it easier to a rock under water?

¨ The buoyant force is acting upward.

¨ Since the of water is much greater than that of air, the buoyant force is much greater under the water compared to in the air.

Fb air = ρair gV

Fb water = ρwater gV The crown and the nugget 6

Archimedes (287-212 BC) had been given the task of determining whether a crown made for King Hieron II was pure gold. In the above diagram, crown and nugget balance in air, but not in water because the crown has a lower density. Clicker question: 1 & 2

7 Demo: 2

8

¨ Helium in helium

¨ Helium balloon in nitrogen ¤ Demonstration of buoyancy and Archimedes’ principle Floatation 9

¨ When an object floats, the buoyant force equals its weight.

¨ An object floats when it displaces an amount of fluid whose weight is equal to the weight of the object.

¨ An object that is denser than fluid can float if it displaces enough fluid because of its shape.

Fb = wfluid Demo: 3

10

¨ Battleship

¨ Board and Clicker question: 3 & 4 11 Example: 1 12

¨ What is the minimum area of the top surface of a slab of ice with thickness, h = 0.30 m, floating on fresh water that will hold up an automobile of mass mc = 1100 kg sitting on top? The density of water and ice 3 3 are ρw = 0.998 × 10 kg/m 3 3 and ρi = 0.917 × 10 kg/m , respectively. Example: 2

13

¨ A block of an unknown material weighs

Wa = 5.00 N in air and Ww = 4.55 N when submerged in water. What is the density of the material? Example: 3 14

¨ You decide to enroll in a fitness program. To determine your initial fitness, your percentage of body fat is measured. Assume the average density of fat is 3 3 ρf = 0.90 × 10 kg/m , and lean tissue is 3 3 ρl = 1.10 × 10 kg/m . Your in water is 5.0% of your weight in air. What fraction, f, of your body mass is fat?