materials Flashcards
What does Hooke’s Law state?
Extension is proportional to force
Hooke’s Law defines the relationship between the force applied to an elastic material and the extension produced.
Who discovered Hooke’s Law?
Robert Hooke
Robert Hooke discovered the law in the 17th century.
What is the formula for Hooke’s Law?
F = kx
Where F is the force applied, k is the force constant, and x is the extension.
What does the constant k represent in Hooke’s Law?
Force constant or stiffness
k is specific to the object being stretched and has units of Nm^-1.
How does Hooke’s Law apply to springs?
Extension or compression is proportional to the force applied
For springs, k is also referred to as the spring constant.
What types of forces does Hooke’s Law apply to?
Tensile and compressive forces
Hooke’s Law applies equally to both types of forces for most materials.
What is the limit of Hooke’s Law?
The elastic limit
Beyond this limit, materials may be permanently deformed.
What happens when the elastic limit is exceeded?
The material will be permanently stretched
After force removal, the material remains longer than its original length.
What is the point on the graph where Hooke’s Law is no longer obeyed called?
Elastic limit (point E)
The graph shows a transition from linear to nonlinear behavior.
How can you combine the force constants of springs?
In series and in parallel
The formulas are: In series: 1/k = 1/k₁ + 1/k₂; In parallel: k = k₁ + k₂.
True or False: Hooke’s Law applies to all materials without exception.
False
Hooke’s Law only applies to most materials up to a certain point.
Fill in the blank: Hooke’s Law works for _______ forces as well as _______ forces.
tensile, compressive
Both types of forces result in deformation as described by Hooke’s Law.
What is tensile deformation?
Extension of a material
This occurs when tensile forces are applied.
What is compressive deformation?
Compression of a material
This occurs when compressive forces are applied.
What type of materials may only obey Hooke’s Law for small extensions?
Rubber
Rubber exhibits non-linear behavior at larger extensions.
What does the graph of force against extension demonstrate?
A straight-line relationship up to the limit of proportionality
Beyond this point, the relationship becomes nonlinear.
What is Hooke’s law?
Hooke’s law states that the force exerted by a spring is directly proportional to the extension of the spring, provided the elastic limit is not exceeded.
Hooke’s law is often expressed as F = kx, where F is the force applied, k is the spring constant, and x is the extension.
What is meant by the elastic limit of a material?
The elastic limit is the maximum extent to which a material can be deformed elastically without permanent deformation.
Beyond this limit, the material will undergo plastic deformation.
What is the difference between elastic and plastic deformation?
Elastic deformation allows the material to return to its original shape after the forces are removed, while plastic deformation results in permanent change in shape.
Elastic deformation occurs within the elastic limit, while plastic deformation occurs beyond it.
What happens to the atoms in a material when it is under elastic deformation?
Atoms are pulled apart slightly from their equilibrium positions, but they return to their original positions once the load is removed.
What happens to the atoms in a material during plastic deformation?
Some atoms move positions relative to one another, and they do not return to their original positions when the load is removed.
What is the formula to calculate extension in a material?
Extension = new length - original length.
What does a straight line on a force-extension graph indicate?
A straight line indicates that Hooke’s law is being obeyed, and the gradient of the line represents the spring constant k.
What happens to the force-extension graph when the elastic limit is exceeded?
The graph will start to curve, indicating that the material has undergone plastic deformation.
What are tensile forces?
Tensile forces are forces that attempt to stretch or elongate a material.
What are compressive forces?
Compressive forces are forces that attempt to compress or shorten a material.
How can you investigate the effect of force on extension for a length of wire?
Set up an experiment by measuring the original length of the wire, adding weights incrementally, measuring the new length after each weight, and calculating the extension.
What safety precautions should be taken during the extension investigation?
Stand up to quickly move away if weights fall, and wear safety goggles to protect your eyes in case the object snaps.
What is the formula for calculating stress?
Stress = Force / Area
What does the gradient of the stress-strain graph represent?
The gradient represents The Young’s Modulus of a material
What is the relationship between stress and strain in the context of the Young modulus?
E = Stress / Strain
What does the area under the stress-strain graph represent?
Elastic potential energy per unit volume
How is strain defined?
Strain = Extension / Original length
What is the Young modulus for a material?
The Young modulus is a measure of the stiffness of a material
What are the units for the Young modulus?
Nm^-2 (Newtons per square meter)
True or False: The stress-strain graph is a straight line if Hooke’s law is obeyed.
True
Fill in the blank: The energy per unit volume can also be calculated as _______.
Energy per unit volume = ½ × stress × strain
What is the Young modulus (E) calculated from the gradient of the stress-strain graph?
E = Stress / Strain = gradient
Describe an experiment to find the Young modulus of a test wire.
Use a thin test wire, apply a known force, measure the extension and original length
Why is a thin test wire used in experiments to find the Young modulus?
A thin test wire is used to ensure accurate measurements and minimize errors
What is the Young modulus of the wire calculated from the given gradient?
E = 4 × 10^10 Nm^-2
What happens to a material subjected to a pair of opposite forces?
It may deform, i.e. change shape.
What are tensile forces?
Forces that stretch the material.
What are compressive forces?
Forces that squash the material.
Define tensile stress (o).
Tensile stress is defined as the force applied (F) divided by the cross-sectional area (A).
What are the units of stress?
Nm² or pascals (Pa).
Define tensile strain (s).
Tensile strain is defined as the change in length (extension) divided by the original length of the material.
What are the units of strain?
Strain has no units; it’s just a number.
True or False: The same equations apply to tensile and compressive forces.
True.
What is the Ultimate Tensile Strength (UTS)?
The maximum stress that a material can withstand before breaking.
What happens as a greater tensile force is applied to a material?
The stress on the material increases and starts to pull the atoms apart.
What is breaking stress?
The stress at which atoms separate completely and the material breaks.
What do engineers consider when designing a structure?
The UTS and breaking stress of materials.
What is elastic potential energy?
The energy stored in a stretched or compressed material.
What does the area under a force vs. extension graph represent?
The work done in deforming the material.
What happens to the work done before the elastic limit?
All the work done is stored as potential energy in the material.
Fill in the blank: The stored energy in a deformed material is called _______.
elastic potential energy.
What is the formula for Young’s Modulus?
Young modulus = tensile stress / tensile strain
E = F/A / (x/L) where F = force in N, A = cross-sectional area in m², L = unstretched length in m, and x = extension in m.
What are the units of Young’s Modulus?
N/m² or pascals
Since strain is dimensionless, the units of Young’s Modulus are the same as stress.
What does Young’s Modulus measure?
The stiffness of a material
What is the limit of proportionality?
The point up to which stress and strain are proportional to each other
Fill in the blank: The Young Modulus is a constant value when stress is divided by strain below the _____ of proportionality.
limit
What is the relationship between tensile stress and tensile strain up to the limit of proportionality?
They are proportional to each other
What is the significance of Young’s Modulus for engineers?
It ensures materials can withstand sufficient forces
What type of wire should be used in the Young’s Modulus experiment?
Thin and as long as possible wire
What is the first step in conducting the Young’s Modulus experiment?
Find the cross-sectional area of the wire using a micrometer
How do you calculate the area of a circular cross-section?
Area = πr²
True or False: The weight used to straighten the wire should be included in final calculations.
False
What should be measured to determine the unstretched length of the wire?
The distance between the fixed end of the wire and the marker
What should be done when increasing the weight in the experiment?
Increase the weight in steps and record the marker reading each time
What is the purpose of using a mass meter or digital scales in the experiment?
To accurately find the weight added at each step
What should you do to ensure accurate measurements of extension?
Use a thin marker and look from directly above the marker and ruler
What should be re-measured as the wire is unloaded?
The extension for each weight
What must be ensured when unloading the wire?
That you haven’t gone past the wire’s elastic limit
