4- Materials

Density equation

ρ = m/V

How does the density determine whether an object floats

An object will float in a fluid it is less dense than

Normal pressure equation

p = F/A

Pressure in a fluid equation

p = hρg

Explain why upthrust occurs

The upward force on the bottom of an object submerged in a fluid is greater than the downward force on the top of an object submerged in a fluid, so the resultant force is upwards

Explain why the upwards force below an object submerged in a fluid is greater than the downwards force above that object

There is a greater weight of fluid at the bottom, so the pressure in all directions is increased, including upwards

Archimedes principle

When a body is completely or partially immersed in a fluid, it experiences an upthrust equal to the weight of the fluid it has displaced

Viscous drag

Friction between the surface of an object and a fluid as one of them is in motion

What does Stoke’s law tell you

The force due to viscous drag

Stoke’s Law equation

F = 6πηrv

What does the η symbol mean

Viscosity of the fluid

η units

Nsm^-2

How does increasing temperature affect the viscosity of a liquid

Decreases

How does increasing temperature affect the viscosity of a gas

Increases

Laminar flow

All the parts of a fluid are flowing in the same direction such that the layers do not mix

When does laminar flow occur

When a fluid is flowing slowly or an object is moving slowly through a fluid

Turbulent flow

The layers of a fluid are moving in different directions such that the layers mix

When does turbulent flow occur

A fluid is flowing quickly or an object is moving quickly through a fluid

What does Stoke’s Law apply to

Small, spherical objects moving slowly with laminar flow

Experiment to measure the viscosity of a liquid

1- Drop a ball bearing of known radius and density ρ down a column of liquid of known density σ.

2- There is a series of 3 rubber bands near the bottom of the column at a measured distance apart. When the ball bearing reaches the first at terminal velocity, start a stop watch to calculate the time between the 1st and 2nd and 2nd and 3rd.

3- Repeat with different sized balls.

4- Calculate separate velocity with d/t and find the average for each measurement. Then, calculate viscosity with η = (2r²g(ρ-σ))/9v

Explain how the viscosity equation in the ball bearing experiment can be derived

At terminal velocity F_grav = F_upthrust + F_drag

How should the ball bearing be retrieved from the bottom of the column of liquid

A magnet

Explain why the ball bearing should not fall too close to the wall in the viscosity experiment

The flow will no longer be laminar, so Stoke’s law no longer applies

Explain how submarines float and sink

Large tanks are filled with water to increase weight so it exceeds upthrust to sink. The tanks are filled with compressed air to reduce weight to rise

Yield point

Where the material starts to stretch without any extra load

Order of stress-strain points

-Limit of proportionality

-Elastic limit

-Yield point

Stiff

Difficult to stretch or compress

Strong

Have a large breaking stress

What does it mean if a line stops on a stress-strain graph

The material has broken

Difference between what affects a force-extension graph from a stress-strain graph

Dimensions of the material affect force-extension

Unloading line

The line on a force-extension graph as the force is removed

Explain the unloading line of a force-extension graph

Parallel to the loading line as it has the same k and the forces between the atoms are the same

Explain when the unloading line would not meet the origin of the force-extension graph

If the material has been stretched beyond the elastic limit, it has now been permanently stretched

How are stress and strain related

Directly proportional up to the limit of proportionality

Young modulus

A measure of the stiffness of a material

Young Modulus symbol

E

Young modulus units

Pascals

Young Modulus equation

E = σ/ε

Young modulus experiment

1- Attach a wire with a marker on (fixed with a clamp at one end) to a pulley clamped on a bench

2- Calculate the cross-sectional area of the wire with a micrometer

3- Add a weight to the wire to straighten it

4- Measure the unstretched length from the marker to the fixed end of the wire

5- Increase the weight and record the extension

6- Repeat

Best wire for the Young Modulus experiment

Thin and long

Explain why a thinner, longer wire is better for the Young Modulus experiment

It extends more for the same force, reducing percentage uncertainty

How to find the Young Modulus from a stress-strain graph

The gradient

How to find the strain energy from a stress-strain graph

Area below the graph

Strain energy

Energy stored per unit volume

Hooke’s law

ΔF = kΔx

Spring constant symbol

k

What does the spring constant tell you

The stiffness of the spring

Extension symbol

Δx

What force acts on the support of a wire with a weight on

The third law pair of the force on the wire

Why don’t other materials fully with Hooke’s law

k has a different value depending on whether the forces are tensile or compressive

What is special about a spring

It changes length when a pair of opposite forces are applied

What materials does Hooke’s law apply to

Most of them, up to a point

Tensile forces

Forces stretching the spring

What force do tensile forces create

Tension

Compressive forces

Forces squashing the spring

What force do compressive forces create

Compression

Limit of proportionality

The point at which materials stop obeying Hooke’s law

Elastic limit

The point at which the material becomes permanently stretched

What occurs first- the limit of proportionality, or the elastic limit

Limit of proportionality

Which type of deformation occurs before the elastic limit

Elastic deformation

Which type of deformation occurs after the elastic limit

Plastic deformation

Explain elastic deformation

Atoms move relative to their equilibrium positions, without changing position in the material such that once the load is removed, atoms return to their equilibrium positions

Explain plastic deformation

Atoms move relative to one another such that when the load is removed, they don’t return to their equilibrium positions

Experiment to investigate extension

1- Attach a clamp to a spring, ruler and a clamp stand.

2- Measure the natural length of the spring, then attach a weight and record the extension

3- Plot a graph of force against extension

4- The gradient of the graph is k

Risks and preventions of the Hooke’s Law experiment

-Wear goggles in case the object snaps

-Make sure you are standing up so you can get out of the way if the weights fall

Deform

Change shape

Stress

The force applied over a cross-sectional area

Stress symbol

σ

Stress equation

σ = F/A

Stress units

Pascals

Strain

The extension over the original length

Strain symbol

ε

Strain equation

ε = Δx/x

Which sign are tensile forces

Positive

What sign are compressive forces

Negative

Explain how a large tensile force can rip a material apart

The larger the force, the larger the stress, which starts to pull the atoms apart from one another. Eventually the effect of stress is so great that atoms separate completely and the material breaks

Breaking stress

The stress at which a material breaks

Ultimate tensile stress

The maximum tensile stress a material can withstand

What conditions affect the ultimate tensile stress and breaking stress of a material

Temperature

Explain how energy is transferred when stretching a material

Work is done to stretch the material, which is stored in the elastic strain energy

How to find the elastic strain energy from a force-extension graph

The area below the graph

Elastic strain energy equation

ΔE_el = 1/2FΔx