physics 2.2 mechanics

Mechanics is the physical science concerned with the state of

rest or motion of bodies under the action of forces

The subject of mechanics is conveniently divided into two major areas

statics and dynamics

statics is concerned about the

equilibrium of bodies under the action of forces

dynamics in concerned about the

motion of bodies

dynamics can be sub divided into

the motion of rigid bodies and the motion of fluids

the effects of a force and be represented by

a vector quantity

what law must vectors obey

the parallelogram law of combination

why is the parallelogram law of combination

two vectors V1 and V2 can be replaced by their equivalent vector VT

vectors may be added head to tail using the

triangle law

does the order of vectors added affect their sim

no

the - sign in vectors mean

reverse the direction so we can still add

vector V1 and V2 is known as the

components of vector VT

any number of forces may be added vectorially in any order providing the

head to tail rule is observed

what would be the result if vectors was added in the reverse order

same result

If a force, or system of forces, is acting on a body and is balanced by some other force, or system of forces then the body is said to be in

equilibrium

a system of forces is that force which, when added to a system, produces equilibrium is known as

equilibrant

the resultant force is a single force which replaces

the exsisting system of forces and and produce the same effect

to produce equilibrium the magnitude of the equilibrant must

be equal and opposite to the resultant force

a convenient system of labelling the forces for ease of reference using lower case letters when there are three or more forces to be considered is called

bows notation

do arrowheads need to be used when using bows notation

no

a mathematical method of calculating forces is called

resolution of forces

a single force can be split into two equivalent forces

F cos θ and F sin θ

using trigonometry F cos θ is what component in a vector

horizontal

using trigonometry F sin θ is what component in a vector

vertical

F cos θ and F sin θ act at right angles and said to be

orthogonal to each other

coplanar forces act

on the same plane

equilibrium on a smooth plane ignores

friction

a body is kept in equilibrium on a plane by what three forces

Weight acting vertically down

reaction R of the plane to the weight of the body

force P that stops the body from sliding

on a smooth plane forces P and R are dependant on what three things

angle of inclination of the plane

magnitude of W

inclination of force P to the plane

forces P and R in terms of W and be expressed as

trigonometric values

a moment is turning force that produces

a turning effect

the magnitude of a moment depends on the

size of the force and the perpendicular distance from the pivot or axis

the moment of a force is defined as

the product of the magnitude of force F and its perpendicular distance (s) from the pivot or axis to the line of action of the force.

moment can be written mathematically as

M= FXS (force x distance)

the SI unit for moment is

Nm

the english/american unit for moment

foot pounds force (ft/lbf)

CWM and ACWM are considered to be what polarity

CWM positive

ACWM negative

If the line of action of the force passes through the turning point it has

no turning effect and so no moment.

the fulcrum is defined as

the point or axis about which rotation takes place

the moment arm is defined as

the perpendicular distance from the line of action of the force to the fulcrum

the resulting moment is defined as

the resulting moment is the difference in magnitude between the total CWM and ACWM

if the body is in static equillibrium the resultant will be

zero

when a body is in equilibrium can there be any resultant forces acting on it

no however a body is not necessarily in equilibrium even when there is no resultant forces

The resultant force on the body is zero but two forces would cause the body to

rotate

the principle of moments states

when a body is in static equilibrium under the action of a number of forces CWM=ACWM

for static equilibrium the algebraic sum of the moments must be

zero

a further necessary condition for static equilibrium is that:

The upward forces = The downward forces.

If a solid, such as a metal bar, is subjected to an external force (or load), a resisting force is set up within the bar and the material is said to be in a state of

stress

three baisc types of stress

tensile compressive and shear

tensile stress is

forces pulling the martial apart

compressive stress is produced by

forces crushing the material

shear stress is defined as

resulting forces cutting through the material

to calculate stress is per unit area is

stress equals force/area

the basic SI unit of stress is

N/m²

components that carry tensile loads are known as

tiesco

components that carry compressive loads are known as

struts

a material that is altered in shape due to action of a force acting on it is said to be

strained

direct strain may be defined as

a ratio of change

direct strain is calculated by

deformation/original length

the units for strain is

meters

hooke’s law law states that

within the elastic limit of a material the change in shape is directly proportional to the applied force producing it

in hooks law stiffness (k) is calculated by

force/deflection

the SI unit for stiffness is

N/m or NM^-1

while the material remains elastic stress and strain are

directly proportional

since stress and strain is directly proportional in the elastic range modules of elasticity can be calculated as

stress/strain

what are the preferred units of modulus of elasticity

GN/m² or GPa

the modulus of rigidity is calulated as

shear stress/shear strain

bulk modulus is calulated by

bulk stress/bulk strain

the negative sign is the bulk modulus is introduced since

the change in volume is a negative since its a decrease

layman’s terms the elasticity rigidity and bulk modulus is

• Modulus of Elasticity (E): Changes length (stretching a rubber band).

• Modulus of Rigidity (G): Changes shape (twisting a metal rod).

• Bulk Modulus (K): Changes volume (squeezing a sponge from all sides)

linear equations rely on the assumption that

acceleration is constant

the symbol for distance in a velocity time graph is

S= distance(m)

the symbol for initial velosity is

u=initial velocity (m/s)

the symbol for final velocity

v =final velocity (m/s)

the symbol for acceleration is

a =acceleration (m/s2)

the symbol for time is

t =time (s)

distance travelled is

velocity m/s multiplied by the time s

acceleration is calculated by

What does the area under a velocity-time graph represent?

Displacement (s) or the total distance travelled

What does the gradient (slope) of a velocity-time graph represent?

Acceleration (a)

In the equation s = u.t+ (v-u/2) .t what do the two individual parts represent geometrically?

u.t is the area of the rectangle (bottom) and v-u/2 the area of the triangle (top)

What is the standard simplified SUVAT equation derived from splitting the graph into a rectangle and a triangle?

s=ut + ½ at²

What formula do you get when you calculate the area under the graph as a single trapezium (average velocity x time)?

S = (u+v/2) t

What is the fundamental definition formula for acceleration derived from a graph's gradient?

a= v-u/t

newtons second law is

force = mass x acceleration

momentum may be defined as

the mass of a body multiplied by its velocity

what is newtons third law

(every action that has a equal and opposite reaction) the inertia force is such as to be equal and opposite to the accelerating force that produced it,

thrust = m( Vje-Va) what are the components

m ̇ = mass flow rate of the air (kg/s)

Va = true velocity of the aircraft, i.e. true airspeed or TAS, which you will meet later (m/s)

Vje = velocity of slipstream or effective velocity of the gas stream (m/s).

mass flow rate x velocity gives the units of

force

transformation equations are

linear motion transformed to represent angular motion

angular velocity refers to a body moving in a circular path and is defined as

angular distance moved / time taken or rad/s

angular distance is measured in

rad

to convert from rpm to rad/s we multiply by

2 pie/60

2 pie/60 equals

0.1

angular acceleeration is defined as

the rate of change of angular velocity with respect to time, i.e.

Change angular velocity/time taken

rad / s Time taken s

Why can't we apply Newton's laws directly to a whole rotating wheel?

Mass is spread out. Different parts of the wheel sit at different distances from the centre.

How do we simplify a complex rotating object for calculation?

We look at a single, tiny element of mass (\(\delta m\)) at a fixed radius (r)

What formula links linear velocity (v) to angular velocity (w) at any point

v = w x r

• What is the standard linear equation for Newton's second law?

force = mass x acceleration

what happens when you apply a force at a radius from a pivot

it creates a torque T= F X R