archimede's principle. buoyancy

BUOYANCY

BUOYANCY

Video 1

Buoyancy…

1. In physics, buoyancy is the upward force, caused by fluid pressure, that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body. This force enables the object to float.

2. When an object is fully immersed in a fluid the amount of water it displaces is equal to its own volume. There are two forces acting upon it:

An upward force – the buoyant force

A downward force – the gravity force

Buoyancy…

Archimedes’ Principle

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

Material Density (kg/m3)Air (1 atm, 20 degrees C 1.20

Aluminum 2,700Benzene 900

Blood 1,600Brass 8,600

Concrete 2,000Copper 8,900Ethanol 810Glycerin 1,260

Gold 19,300Ice 920

Iron 7,800Lead 11,300

Mercury 13,600Neutron star 1018

Platinum 21,400Seawater (Saltwater) 1,030

Silver 10,500Steel 7,800

Water (Freshwater) 1,000White dwarf star 1010

Density of Common Substances

The Formulas:The buoyant force upward on a submerged object (magnitude Fb) due to the fluid in which the object is submerged is equal to the weight of the fluid displaced by the submerged object:

Fb = mfluid g;mfluid = ρ V;Fb = ρ V g Eqn. 1

where ρ is the density of the fluid, V is the volume of the object (assuming it is completely submerged), g is acceleration due to gravity. This model for buoyant forces is called Archimedes' Principle.

Fb = ρ V g

In solving for ρ,

Fb

ρ = Eqn. 2 V g

Sample Problem 1:

A basketball floats in a bathtub of water. The ball has a mass of 0.5 kg and a diameter of 22 cm.

(a) What is the buoyant force? (b) What is the volume of water displaced by the ball? (c) What is the average density of the basketball?

a) To find the buoyant force: ∑F = ma Fb - mg = 0 Fb = (0.5 kg) (9.8 m/s2) = 4.9 N

b) By Archimedes' principle, the buoyant force is equal to the weight of fluid displaced.

Fb = ρ Vdisp g Vdisp= Fb / ρ g = 4.9 / (1000*9.8) = 5 x 10-4 m3

c) To find the density of the ball, we need to determine its volume. The volume of a sphere is:

V = (4/3)πr3

with r = 0.11 m, we get: Vbasketball = 5.58 x 10-3 m3

The density is mass divided by volume: ρ = m/V

= 0.5 / 5.58 x 10-3

ρ = 90 kg/m3

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Video 4Video 3

Why do you think an object weighs less in water than in

air?

An object underwater weighs less than if it is in air. This is because when a submerged object is weighed, the weight minus the buoyant force is actually being measured. In this case, the apparent mass, mapparent, will be less than the actual mass, mactual. The difference between the apparent mass and the actual mass will be due to the buoyant force on the object. That is:

Fb = mactua lg – mapparent g = (mactual - mapparent)g

Eqn. 3

Assuming that the submerged object is a rectangular solid of height h, width w and length l: mactual - mapparent

ρ = hwl

Eqn. 5

The figure at the right was weighed and gave a mass of 250 kg. When it was put in a container filled with water, the resulting mass became 220 kg. What is the buoyant force acting on the box? What is its density?

Sample Problem 2:

Given:Mactual = 250 kgmapparent= 220 kgV = 4 cm x 3 cm x 6 cm = 72 cm3

Find: Fb = (mactual - mapparent)g = 30 kg (9.8) = 294 N mactual - mapparent

ρ = V = 30 kg/0.72 m3

= 41.67kg/m3

Sample Problem 3:

A buoyant force of 34 N acts on a 75 kg block of wood with a volume of 13 m3. What is its density?

What is buoyancy? How do you explain the factors involved in it?

In what particular situations in our life do we consider buoyancy an advantage? a disadvantage?

Coin Boat ChallengeThe Problem: Design a boat out of aluminum foil that will hold the most number of coins and still stay afloat.Materials: 30cm x 30cm aluminum foil a number of 25-centavo coins a basin of water

Rules:1. Construct your boat using only one (1) piece of the

aluminum foil provided.2. Coins are the only item you may add to your boat.3. Slowly add coins to your boat. Once water enters the boat, or

if any part of the boat touches the bottom of the basin, your turn is over.

4. The last coin added will not count in the total amount held.5. Predict how many coins your boat will hold: ____________

After the activity:

1. Our boat held _________coins.2. If each coin had the mass of 2.5 grams, our boat

held _________ grams total.3. How did you design your boat?4. How did you place the coins into your boat? Did

you have a strategy?

Reflection:

Write about the strategies you used to solve this problem? What worked? What didn’t? What would you change if you did this again?

Solve the following problems.

1. A block of wood of mass 3.5 kg floats in water. Calculate the buoyant force on the block. 

2.A floating object displaces 0.6 m3 of water. Calculate the buoyant force on the object and the weight of the object.

ASSIGNMENT:

StudyBernoulli’s Principle.