Solids and Liquids

NHS Physics

Classifying Materials

• Humans have been analyzing and classifying materials since the stone age.

• Let’s start with Solids:• Why bother analyzing materials with any more detail

than classifying it as a solid?

Solids: Crystal Structure

• Crystals are geometric shapes found within many minerals and other solids

• Atoms in a crystal structure have an ordered pattern• Each point on the lattice represents an atom

Crystal Structure

• Iron, Copper and gold have simple crystal structures• Tin and cobalt are a little more complex

• The crystal structure of a mineral can determine properties of a material and how likely it is to bond with other materials.

Properties of Solids: Density

• Density is a measure of how much mass is packed into a certain volume of material.

• Density = Mass/Volume• Decreasing the volume of an object (leaving mass the

same) will increase its density.• Increasing the volume of an object (leaving mass the

same) will decrease its density.

Why is Density Important?

• Think of few examples (could be historical) for how density can be used in real world applications.

Practice!

• Find the density of a block 2m x 2m x 1m that has a mass of 20kg.

D = M/V

Practice

• You have a graduated cylinder with 25mL of water in it. If you drop a mineral into the graduated cylinder, the volume rises to 32mL. If the mineral weighs 0.2kg, what is the density?

D = M/V

Practice!

• If you have 2000g of cake batter squeezed into a 10cm x 10cm x 10cm cubic container for storage and delivery, what is the density of the batter?

D = M/V

Practice!

• When the same batter is baked, it rises in height by 10 cm. What is the new density?

• What would the density be if each linear dimension (length, width and height) doubled from the original batter dimensions?

D = M/V

Practice!

• A radiologist is choosing between two aprons for protecting patients from radiation. Apron X contains a lead alloy with a density of 10.4 g/cm3. Apron Y is more cost effective, but has a lead alloy with a density of 11.3 g/cm3. If the apron is 50 cm x 30 cm x 1.5 cm, and can weigh no more than 25kg, which apron should he order?

D = M/V

Properties of Solids: Specific Gravity

• Specific Gravity: The ratio of the mass of a substance to the mass of an equal amount of water.

• Also called relative density• Sometimes used in calculations for horsepower of

engines, or in calculations for hydraulic pumps

Properties of Solids: Specific Gravity

• Water has a specific gravity of 1.• Substances with a higher specific gravity than 1 will sink

in water• Substances with a lower specific gravity than 1 will float

in water• E.g. Rubbing Alcohol has a specific gravity of 0.789, so it

is 0.789 times as dense as water.

Practice

• You have a beaker of water with a mass of 50 grams. What is the specific gravity of a liquid of equal volume, but a mass of 0.25kg?

Properties of Solids: Elasticity

• Elasticity is a measure of how likely an object is to deform, and return to its original state.

• Objects deform when a “deforming force” acts on it that causes a change in shape.

Properties of Solids: Elasticity

• If an object is inelastic, it does not go back to its original shape when deformed.

• Clay, putty and even lead are considered inelastic

Hooke’s Law

• In springs, elasticity is measured by Hooke’s law• Hooke’s Law states that the amount of displacement of

a spring is directly proportional to the applied force.

• F = • k = • x =

F = -kx

Hooke’s Law

• Hooke’s law is only true until an object reaches its elastic limit, or yield.

• Elastic limit is the distance where permanent distortion occurs.

• https://www.youtube.com/watch?v=I28m4FZzqro

Hooke’s Law

• The elastic limit is used when designing consumer products.

• As long as a material doesn’t exceed this limit, it can be cycled again and again without permanently deforming.

• E.g. Remote control battery covers

Practice

• Find the spring constant for a pogo stick if a 75kg Physics student compresses the spring by 12cm when standing on it.

Felastic = -kx

Properties of Solids: Compression and Tension

• Compression: When an object is squeezed together

• Tension: When an object is stretched apart

Properties of Solids: Compression and Tension

• When a beam is under stress, there are areas of tension, and areas of compression.

• The center part of the beam is neutral and experiences much less stress than the top and bottom surface of the beam.

Properties of Solids: Compression and Tension

• Why use I-Beams in construction?

Scaling

• The ant and the elephant…• As the size of something increases, it gets

heavier much faster than it gets stronger• Multiplying the linear dimensions of an object

by a factor, will increase the volume by a cube of that factor.

Scaling

• Since strength is determined by cross sectional area, and mass is determined by volume and density, objects grow more massive at a faster rate than they grow stronger if scaled up.

Scaling

• Surface Area vs. Volume– When scaled, both surface area and volume

increase, but volume increases at a faster rate– This means that the ratio of surface area to

volume decreases.– Smaller objects have more surface area per kg

Quiz Tomorrow!

• 10-15 minutes– Density Calculations– Hooke’s Law Calculations– Compression and Tension of a beam

Liquids

• About 70% of the earth is covered with water, and it is necessary for life

• Other liquids are used as cleaners, hydraulic fluids for heavy machinery or lubricants

Liquids

• Liquids take the shape of whatever container they are placed in

• The molecules in a liquid are packed tighter together than in a gas, but not as tight as a solid so the molecules are free to slide past one another.

• We will discuss pressure, buoyancy, Archimedes’ principle and Pascal’s principle

Pressure

• Pressure on a surface is calculated using P = F/A

Pressure

• If you have equal volumes of 2 different liquids, what determines how much pressure it exerts at the bottom of the container?

Pressure

• Pressure due to liquid = weight density x depth OR

• Pressure due to liquid = mass density x gravity x depth

• Turn to p. 274 and read the text at the bottom of the page for discussion.

P = ρgh

Pressure

• For a given depth, liquid will exert the same pressure on the bottom and sides of its container.

Pressure• Total Pressure: When you consider not only

the pressure from the liquid, but also the atmospheric pressure.

• E.g.: If you fill up a fish tank, the total pressure on the glass is not only from the water, but from the atmospheric pressure pushing in the opposite direction

Pressure

• Pressure does not depend on the amount of the liquid, only the density and depth.

• E.g.: The water pressure 1 meter below the surface of a small pond, and 1 meter below a large lake is the same.

Practice!• Calculate the pressure in N/m2 of the NHS

pool at a depth of 10ft (3.048 meters).

ρ = 1,000 kg/m3

g =h =

P = ρgh

Practice!• In March of 2012, after 2 hours and 36

minutes of descent, James Cameron was the first human to reach the depths of the Mariana Trench, at a depth of 11km. The density of sea water is 1,030kg/m3.

1) Find the pressure in N/m2 at that depth. 2) Find the force on a 0.5m x 0.5m section of the research vessel.

P = ρgh

Challenger

• http://www.youtube.com/watch?v=Y2tm40uMhDI&edufilter=AL46EZ_QUrHPyIKNB5UCCA

Buoyancy Introduction

• Buoyancy is the apparent loss of weight of objects when submerged in a liquid.

• Since pressure, and therefore forces, from the water are higher at greater depth, the upward force on an object from the water is greater than the downward force from the water.

Archimedes

• Born in 287 BC• Greek physicist, mathematician,

inventor, engineer and astronomer.

• Determined exact value for pi• Discovered the relationship

between displaced fluid and buoyancy.

Archimedes Principle

• Archimedes Principle: An immersed object is buoyed up by a force equal to the weight of the fluid it displaces

Fb = ρVg

Fb = Buoyant Forceρ = Density of fluidg = acceleration due to gravity

Buoyancy

• Since the amount of displaced water determines the buoyant force, larger objects have larger buoyant forces.

• Whether an object will sink or float depends on its weight (downward force) and buoyant force (upward force).

Fb = ρVg

Buoyancy

• A floating object displaces a weight of fluid equal to it’s own weight

• A submerged object displaces a volume of fluid equal to it’s own volume.

Buoyancy

• Objects Density < Fluids Density = Object Floats

• Objects Density > Fluids Density = Object Sinks• Objects Density = Fluid’s Density: doesn’t sink

or float

Fb = ρVg

Practice!

• Calculate the Buoyant Force on a boat floating on the surface if the boat weighs 200kg.

Fb = ρVg

Practice!

• Calculate the Volume of water the boat displaces.

Fb = ρVg

Practice!

• During Physical Therapy, Mr. Stickman is lifting weights in a pool to reduce stress on his joints. If he has a disc shaped weight with a volume of 0.05m3 and a mass of 30kg, how much force does he need to apply:

1) To lift the mass above his head (out of the water)

2) To lift the mass while it is underwater

Fb = ρVg

Practice!

• Given a triple beam balance, a metal block, a cup of water and a beaker, how could you calculate the apparent weight (the weight of the block while submerged) for the block at your table?

• Hint: There are a couple of ways to do this!!!

Possible Answers

• Find the mass of water that spills out when the block is dropped in. The mass times gravity will equal Fb. Use the TBB to find the mass of the block.

• Record the volume of the liquid that spills out and use it to calculate Fb

• Put the mass in the water while on a TBB.

Fb = ρVg

Pascal’s Principle

• Pascal’s Principle states that changes in pressure at any point in an enclosed fluid at rest are transmitted undiminished to all points in the fluid and act in all directions.

Pascal’s Principle

• In Physics, you don’t get anything for free.• Transferring a force from a small area to a

large area will give you a larger output force, but smaller displacement.

Pascal’s Principle

• Pascal’s Principle is applied to hydraulic lifts in auto repair shops and car jacks

• Also applies to heavy machinery that needs to be able to lift heavy loads

Example

• If you apply a force of 1N to an area of 0.1m2, that will transmit a Pressure of 10N/m2 to the fluid.

• If the larger piston has an area of 0.5m2, then the force on this piston will be 5N

Useful Equations for Pascal’s Principle

P1 = P21

2 F1/A1 = F2/A2

V1 = V2

A1D1 = A2D2

•Because pressure is transmitted equally from side 1 to side 2

•Because the volume of fluid displaced is transmitted equally from side 1 to side 2

A = AreaD = Distance Moved

Practice!

• Side 1 of a hydraulic lift has a cylinder diameter of 2cm, Side 2 has a diameter of 8cm. If you apply a force of 5N to Side 1, what is the output force on Side 2?

F1/A1 = F2/A2

12

A1D1 = A2D2

Practice!

• How far does side 2 move if side 1 is pushed down 10cm?

Side 1 Diameter = Side 2 Diameter =

F1/A1 = F2/A2

12

A1D1 = A2D2