1.5 Solids under Stress Flashcards
Define the spring constant.
● The force per unit extension required to stretch a spring.
● Denoted by k.
● Inherent property of the spring.
State Hooke’s law
Extension (denoted by ∆L or 𝑥) is directly proportional to force applied (F), given that the environmental conditions are kept constant.
F= k∆L, where k is the spring constant in Nm-1
What is meant by tensile stress?
The force applied per unit cross-sectional area Stress, σ = F/A
Stress units: Nm-2
Force units: N
Cross-sectional area units: m2
What is tensile strain?
A measure of how a material stretches. It is equal to the extension (ΔL) divided by the original length (L). Since strain is a ratio, it has no units.
Strain, ε = ΔL / L
What is the difference between elastic and plastic deformation?
Elastic deformation: when the force is removed the object will return to its original shape.
Plastic deformation: after the load is removed the object will not return to its original shape. It has been stretched beyond its elastic limit.
What is breaking stress?
The minimum stress needed to break a material.
What is meant when a material is described as brittle?
It does not extend much when a force is applied (tensile strain stays low). The material tends to break rather than stretch under a large force.
What is the elastic limit?
The point after which plastic deformation occurs. It is also sometimes referred to as the ‘limit of proportionality’.
What does the area underneath a force-extension graph represent?
The energy stored in the material.
Give the equation that calculates elastic strain energy in terms of the spring constant and extension.
E = 1⁄2 k ΔL^2
What is Young’s modulus?
Young’s modulus = tensile stress / tensile strain
How do you find the Young’s modulus from a stress-strain graph?
Using the gradient of the line.
How can a force-extension graph show Hooke’s Law is being obeyed?
When it is a straight line through the origin – force and extension are directly proportional.
What is the limit of proportionality and what does it look like on a force-extension graph?
The point after which Hooke’s law is no longer obeyed. It is shown by the line beginning to curve on a force-extension graph.
What is meant by elastic strain?
Strain that disappears when a stress is removed – the material returns to its original shape.
What is meant by plastic (or inelastic) strain?
Strain that decreases only slightly when stress is removed. The material does not return to its original shape.
How is the work done to stretch or compress a material stored?
It is stored as elastic strain energy.
Why are the loading and unloading lines parallel on a force-extension graph for a plastically deformed material?
The stiffness constant (k) has not changed - the forces between the atoms are the same when loading and
unloading.
Why isn’t all work done stored as elastic strain energy when an object undergoes plastic deformation?
Work is done to move atoms apart, so energy is not stored as elastic strain energy.
How is the dissipation of energy in plastic deformation used to design safer vehicles?
●Crumple zones deform plastically in a crash using the car’s kinetic energy, so less energy is transferred to the passengers.
● Seat belts stretch to convert the passenger’s kinetic energy into elastic strain energy.
Outline the energy changes that occur when a spring fixed at the top is pulled down and released.
The work done in pulling the spring down (stretching it) is stored as elastic strain energy. When the spring is released, this is converted to kinetic energy, which is then converted to gravitational potential energy as the spring rises.
Do stress-strain graphs show the behaviour of a material or a specific object?
Material.
