1. Fluids The theory behind building a boat …

2. Fluid Topics:
We will cover the following topics related to fluids over the next few days. These topics will help you build your boat:
Pressure
Density
Buoyancy (Archimedes Principle)
To complete the unit, we will also look at:
Factors that affect pressure
Fluid dynamics

3. Pressure
You need to think about pressure when designing the bottom of your boat.
Pressure is defined as the amount of force that acts over a given area.
pressure = P (units: N/m2 or Pa)
F = force (units: N)
A = area (units: m2)
1 N/m2 = 1 Pascal

4. Pressure: Ex1
A 20 kg crate, at rest on the floor, has a length of 1.2 m, a width of .8 meters, and a height of .4 meters. Calculate the pressure that the crate exerts on the floor. (Answer: Pa)

5. Activity:
Gertrude is a large girl and she has an equally large shoe collection! If Gertrude weighs 250 pounds, calculate the pressure she exerts on the floor in each of these situations:
a) wearing her black sneakers
b) wearing her red heels
c) practicing her ballet spin on one foot

6. Activity: How??
Pretend you are Gertrude. Trace the outline of a large tennis shoe on a piece of graph paper. Count the squares covered to approximate the area of the shoe. Use Gertrude’s weight to calculate the pressure acting on the area covered by the shoe.
Repeat with a high-heeled shoe.
Repeat while standing on your tip-toes.
(For equal comparisons, we’ll assume she is standing on one foot in each case.)

7. Force vs Area Gallinule bird
Summary: If you spread your weight out over a larger area, you will exert less pressure on the bottom of the boat.
Remember this fact when getting into your boat!
Gallinule bird

8. Bottom of Boat
How does this relate to your boat? The bottom of your boat must be structurally strong! Most students enter their boat on the ball of one foot. Many will step right through the bottom of their boat!!
The bottom of your boat must be able to support your weight over a very small area.
Secondly, you can prevent this from happening by NOT stepping into your boat on your tip-toes!
Analogy on the next slide …

9. OMG!!!
Suppose you are playing ice hockey on a frozen lake. Suddenly, the ice begins to crack!! What should you do?
a) run to shore as fast as you can
b) stand still and call for help
c) stand on one foot to minimize the pressure on the ice
d) slither like a snake to shore

10. Bottom of Boat Construction tips for bottom of boat:
layer the cardboard (glue multiple pieces together)
create some sort of support structure
Search for this video on YouTube: Pi-Rate Ship Building Profile by austinwagenhals
Note: the support structures must be made out of cardboard of similar thickness!!
Double or triple bottom as they are doing for this support

11. Activity: Mini-Boats
You’re not ready to make a big boat until you can make a little boat!
Is the design stable??

12. Density In chemistry, you probably learned that:
It still does! But in physics, we used different variables and must use SI units. Therefore, the equation looks a little different:
density =  (units: kg/m3)
m = mass (units: kg)
V = volume (units: m3)

13. Demo …
An object submerged in a fluid weighs ______ than it does in air
Weight in air =
Weight in fluid =
Buoyant force =

14. A New Force …
An object submerged in a fluid weighs less than it does in a vacuum!!
Archimedes (250 BC) reasoned that an upward force must be acting on the object. He named this upward force the buoyant force.
287 – 212 B.C.

15. Archimedes’ Discovery
Legend …
King’s crown

16. Archimedes’ Principle
Archimedes’ Principle: The buoyant force is equal to the weight of the fluid displaced by the object.
Buoyancy (whether something floats or not) is based on Archimedes’ Principle.

17. Understanding Arch. Prin.
If you want more lift (buoyant force), you must displace more water!

18. Buoyant Force Equation
DERIVATION:
Archimedes’ Principle: The buoyant force is equal to the weight of the fluid displaced by the object.

19. Buoyant Force Equation
DERIVATION:
Archimedes’ Principle: The buoyant force is equal to the weight of the fluid displaced by the object.
Fb = weight of displaced fluid
Fb = mfg
Fb = pfVfg
Vf = Vo
Fb = pfVog

20. Floating/Sinking
To predict whether an object will sink or float, compare Fw and Fb.
Fw > Fb: object will sink
Fb > Fw: object will float
An object “floats” in equilibrium.
When in equilibrium: Fw = Fb (i.e. HOW will it float??)
Fw > Fb
Fw = Fb
Fw = Fb

21. Sink or float??

22. The Dead Sea The Dead Sea is 8.6 times saltier than the ocean.
As a result, objects are very buoyant in the Dead Sea

23. Will it float?
Class Discussion: Discuss possible dimensions of simple, rectangular boat …
Notes: Physics Floats My Boat worksheet
a) Predict whether the boat will float or sink in water
b) If it floats, how much of the raft is beneath the surface of the water.

24. Ex 3: Floating in air
A spherically shaped balloon has a radius of 7 m and is filled with helium. The balloon (not including the mass of the helium) has a mass of 550 kg. What is the maximum cargo weight the balloon can lift? (The density of He = kg/m3 and density of air = 1.29 kg/m3)

25. Product Testing:
Next …