AQA A-Level Physics: Materials and Mechanics Concepts

Hooke's law

Extension (∆L) is directly proportional to force applied (F), given that the environmental conditions are kept constant. F= k∆L k is the stiffness constant in Nm^-1

Density equation

Density = Mass / Volume. Density units: kgm^-3. Mass: kg. Volume: m^3

Tensile stress

The force applied per unit cross sectional area. Stress = force / CSA. Stress units: Nm-2. Force units: N. Cross sectional area units: m2

Tensile strain

A measure of how the material stretches: the extension (ΔL) divided by the original length (L), strain has no units. Strain = ΔL / L

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.

Breaking stress

The minimum stress needed to break a material.

Brittle material

It doesn't deform plastically but breaks when the stress reaches a certain value.

Elastic limit

The force above which the material will be plastically deformed (permanently stretched).

Force-extension graph area

The work done to deform the material. Work done= ½ x F x ΔL

Elastic strain energy equation

E = ½ kΔL2

Young's modulus

Young's modulus (E) = tensile stress/ tensile strain. E = FL / ΔLA (by substituting stress and strain equations). It describes the stiffness of a material.

Finding Young's modulus

The gradient of the line from a stress-strain graph.

Graph representing plastic deformation

A graph that shows a wire which has plastically deformed.

Loading line

The line representing the loading phase in a force-extension graph.

Force/N

The force applied measured in Newtons.

Unloading time

The time taken for the unloading phase in a force-extension graph.

Extension/m

The amount of extension measured in meters.

Limit of proportionality

The point after which Hooke's law is no longer obeyed, shown by the line beginning to curve on a force-extension graph.

Elastic strain energy

The work done to stretch or compress a material stored as energy.

Stiffness constant (k)

A measure of the stiffness of a material, which remains unchanged during loading and unloading for plastically deformed materials.

Plastic deformation

A permanent change in shape that occurs when a material is stretched beyond its elastic limit.

Energy dissipation in plastic deformation

The process where energy is not stored as elastic strain energy but is dissipated as heat.

Crumple zones

Areas in vehicles designed to deform plastically in a crash, using kinetic energy to reduce the force transferred to passengers.

Seat belts

Safety devices that stretch to convert a passenger's kinetic energy into elastic strain energy during a crash.

Energy changes in a spring

When a spring is pulled down and released, work done in pulling it down is stored as elastic strain energy, converted to kinetic energy, and then to gravitational potential energy as it rises.

Stress-strain graphs

Graphs that show the behavior of a material rather than a specific object.

Ultimate tensile stress

The highest point on a stress-strain graph, representing the maximum stress a material can withstand.

Ductile material

A material that can undergo a large amount of plastic deformation before fracturing.

Scalar quantity

A quantity that has only magnitude.

Vector quantity

A quantity that has magnitude as well as direction.

Acceleration

Vector.

Mass

Scalar.

Difference between mass and weight

Mass is scalar and is not dependent on the gravity acting upon it. Weight is a vector and depends on the gravitational field strength. W = mg

Equilibrium and anti clockwise moments

Equal to the sum of the clockwise moments (principle of moments).

Equilibrium of an object

Not accelerating, so is either: ●Stationary, or ●Moving at a constant velocity.

Forces in equilibrium

●Adding the horizontal and vertical components of the forces acting on it, showing they equal zero. ●Or if there are 3 forces acting on the object you can draw a scale diagram, if the scale diagram forms a closed triangle, then the object is in equilibrium.

Moment

A turning force: force multiplied by the perpendicular distance from the point to the line of action of the force.

Couple

A pair of equal and opposite coplanar forces.

Centre of mass

The point through which all the mass of an object acts, for a uniform object the centre of mass is the centre of the object.

Centre of mass of a uniform object

At the centre of the solid.

Change in displacement per unit of time

Velocity, instantaneous velocity can be found by measuring the gradient of a tangent to a displacement-time graph.

Area under a velocity-time graph

The displacement travelled.

Area under an acceleration-time graph

The velocity.

Air resistance and speed

Increases (proportional to the square of the speed).

Horizontal velocity of a projected ball

The horizontal velocity remains the same as there is no acceleration in that direction.

SUVAT equations and falling objects

Mass is not included in the SUVAT equations, showing that the mass of an object does not affect its speed or acceleration.

Vertical acceleration

The vertical acceleration is equal to gravitational field strength (g).

Terminal velocity

When the forces acting on the falling object become balanced, the acceleration becomes zero and the object is moving at maximum velocity.

Friction

A resistance to motion between an object and a surface or an object moving through a fluid. Friction is a force that acts in the opposite direction to the movement.

Newton's third law

States that every action force has an equal and opposite reaction force.

Newton's second law

F = ma, where mass (m) is constant, F is the force applied and a is the acceleration.

Newton's first law

An object stays moving at a constant velocity until a force acts upon it.

Elastic collision

In an elastic collision the kinetic energy before is equal to the kinetic energy afterwards.

Inelastic collision

In an inelastic collision the kinetic energy at the end is not equal to the kinetic energy at the start.

Momentum equation

momentum = mass × velocity.

Linear momentum conservation

False, linear momentum is always conserved.

Rate of change of momentum

Force.

Impulse

The change in momentum. F∆t = ∆mv.

Area under force-time graph

Impulse, the change in momentum.

Work done equation

Fscos(𝜽) = The work done / the energy transferred.

Rate of work done

The power.

Efficiency

Efficiency = The useful output power / input power.

Principle of conservation of energy

Energy cannot be created or destroyed, only transferred into other forms of energy. Therefore the total energy in a closed system will always remain the same.

Resultant force on a boat

Forces are perpendicular so use Pythagoras's theorem. Resultant force2 = 192 + 452. Resultant force = 48.84669897 N, Resultant force = 49N (2sf). Direction, tanθ = 45/19, θ = tan-1(45/19) θ = 67° above the horizontal.

Vertical and horizontal components of velocity

x = 10 cos 30°, y = 10 sin 30° = 8.7 m/s, = 5 m/s.

Lift

An upward force which acts on objects travelling in a fluid, it is caused by the object creating a change in direction of fluid flow and acts perpendicular to the direction of fluid flow.