Phy 102: Fundamentals of Physics II

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Phy 102: Fundamentals of Physics II. Chapter 13: Liquids Lecture Notes. Archimedes (287-212 BC). Possibly the greatest mathematician in history Studied circles and geometric shapes Invented an early form of calculus Discovered the Principle of Buoyancy (now called Archimedes’ Principle)

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### Phy 102: Fundamentals of Physics II

Chapter 13: Liquids

Lecture Notes

Archimedes (287-212 BC)
• Possibly the greatest mathematician in history
• Studied circles and geometric shapes
• Invented an early form of calculus
• Discovered the Principle of Buoyancy (now called Archimedes’ Principle)
• Discovered the Principle of Leverage (Torque) and built several machines based on it.
• Famous quote:

“Give me a point of support

and I will move the Earth”

Liquids
• Substance with a definite volume but indefinite shape
• Take the shape of their container but always retain their volume
• Liquids are fluids (they flow)
• Liquids are difficult to compress
Pressure
• Force per unit area
• To calculate pressure:

Pressure = force/area

• Units are
• SI: N/m2 (pascals or P)
• Other: lb/in2(psi), lb/ft2, dynes/cm2, kilopascals
Pressure in a Liquid
• When submerged in a liquid, an object experiences liquid pressure due to the weight of the fluid directly above it
• Liquid Pressure (P) is equal to weight density (r) times depth (H) or

Liquid Pressure = weight density x depth

or

P = r x H

• The deeper into the liquid you are, the greater the pressure (& force) the liquid exerts on you!

H

Buoyant force

Buoyant force

Buoyant force

weight

weight

weight

Buoyancy & Archimedes’ Principle
• An object submerged in a liquid experiences a buoyant force
• The buoyant force acting on an object is equal to the weight of the fluid it displaces
• The denser the liquid the greater buoyant force it will exert on an object (for the same volume displaced)
• Floatation occurs when an object displaces the weight of fluid equal to its own weight

Float

Rise

Sink

Floatation
• In accordance with Archimedes’ Principle:
• when the buoyant force is less than the weight of liquid displaced, object will sink
• when the buoyant force is greater than the weight of liquid displaced, object will rise
• when the buoyant force is the same as the weight of liquid displaced, object will suspend
• Weight of a liquid/object is proportional to its weight density & volume: Weight = weight density x volume
• Consequences:
• It will float on the surface if its density is less than the density of the fluid
• It will sink to the bottom if its density is more than the density of the fluid
• It will neither float nor sink if its density is the same as the density of the fluid
Pascal’s Principle
• A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid
• The basis for hydraulic machines
Surface Tension
• The tendency of the surface of a liquid to contract in area and behave like a stretched elastic membrane
• Surface tension is caused by molecular attractions beneath the surface of the liquid
• Surface tension causes the area of the liquid to be forced into the shape with least surface area:
• Raindrops are spherical
• The surface of a pond is flat (when there is no wind or flow to disturb it)
• The surface of a slightly overfilled glass of beer is slightly circular (near edge) and flat in the center
Capillarity
• Adhesion: the attraction of unlike substances

Example: glass and water

• Cohesion: the attraction of like substances due to molecular “stickiness”

The cause of surface tension!