Work, energy and power & Materials

Equation for work

W = Fx cosθ

The principle of the conservation of energy

In a closed system the total energy of the system before an event is equal to the total energy of the system after the event.

Forms of energy; transfer and conservation

Kinetic, GPE, chemical, elastic potential, electrical potential, nuclear, radiant, sound, internal/thermal

Work done (by a force)

The energy transferred when a force moves an object over a distance

Equation for K.E.

K.E. = 1/2mv²

Equation for GPE

Ep = mgh

Equation for power

P = W/t

Power

The rate of work done, measured in watts, W

A watt

A Joule per second

Equation for power using speed

P = Fv

Efficiency

The useful output (e.g. power, energy) of a system divided by the total output.

Equation for efficiency

efficiency = (useful output energy / total input energy) x 100%

Tensile deformation

The changing of an object’s shape due to tensile forces.

Compressive deformation

The changing of an object’s shape due to compressive forces.

Extension

The increase in length of an object when a tensile force is exerted on it.

Compression

The result of two coplanar forces acting into an object. Compression usually results in a reduction in the length of the object.

Hooke’s Law

The extension of an elastic object will be directly proportional to the force applied to it up to the object’s limit of proportionality.

Force constant

A quantity determined by dividing force by extension for an object obeying Hooke’s Law, measured in Nm^-1

Equation for Force applied to a spring

F = kx

Elastic potential energy

The energy stored in an object because of its deformation

Equation for elastic potential energy using force

E 1/2Fx

Equation for elastic potential energy using the force constant

E = 1/2kx²

Tensile stress

The force per unit cross-sectional area, measured in Pa

Strain

The extension per unit length, a dimensionless quantity

Ultimate tensile strength

The maximum stress that a material can withstand before it breaks

Equation for Young modulus

Young modulus = tensile stress / tensile strain, E = σ/ε

Elastic deformation

If a material deforms with elastic behaviour, it will return to its original shape when the deforming forces are removed.

Plastic deformation

If a material deforms with plastic behaviour, it will not return to its original shape when the deforming forces are removed.