2.2 Statics Flashcards
Formula for Turning Moment
Moment (Nm) = Force (N) x Perpendicular Distance (m)
M = F x s
Formula for torque loading with extension
M1 = M2 x L1 / L2
* M1 = Torque setting
* M2 = Actual torque applied
* L1 = Length of wrench
* L2 = total extended length of wrench
Formula for Anti Clockwise Moment
M1 = F1 x S1
M1 = Total Anti-Clockwise movement
F1 = Force to the left of fulcrum
S1 = Lefthand distance from the fulcrum
Formula for Clockwise Moment
M2 = F2 x S2
M2 = Total Clockwise movement
F2 = Force to the Right of fulcrum
S2 = Right hand distance from the fulcrum
What is a Couple
A couple is a pair of forces that are equal in magnitude and opposite in direction applied at points separated by distances perpendicular to the forces. The combined moment of the forces produces a torque on the object they act on.
Couple Formula
Torque (T) = Force (N) x Distance (s) T = F x s
Torque (T) = Force (N) x Radius (r) x 2 T = Fr^2
Note that the factor of 2 in the second equation above is due to this being for a force couple.
For one force at a distance from the centre of rotation, this becomes a moment equation.
Calculation for Resultant forces
Resultant of two or more vectors that act in the same direction along the same line, add their values together. 300Nm + 300Nm = 600Nm
Resultant of two or more vectors that act in the Opposite direction along the same line, Take away the values from each other 300Nm - 300Nm = 0Nm
Triangle Method (Pythagoras’ Theorem)
a^2 + b^2 = c^2
What is a scaler Quantity
Scalar quantities have a magnitude but no direction. Some scalar quantities may have a direction, or undergo a change in direction, but they can be expressed by a numerical value regardless. Examples include length, distance and speed.
Distance, Volume, Area, Mass, Density, Length & Speed
Explain Vector Quantity
Vectors are usually represented in diagrams by arrows that point in the direction of an action. An arrow’s length represents the magnitude of the vector quantity.
Displacement, Force, Acceleration, Weight, Momentum, Moment & Velocity
Formula for Stress
Stress = Force (N) / Area (m^2)
Formula for Strain
Strain (-) = Change in Length (m) / Original Length (m)
Strain = /\L / Lo
Formula for Axial Stress
Axial Stress = Force / Cross sectional area.
S=F/A
Define Hook’s Law
Hooke’s law states that the extension of an elastic object is directly proportional to the force applied to it. F = k x e
Force (N) = k (Spring Constant N/m) x e (Extension (m)
Formula for Young’s Modulas
Youngs Modulas (E) = Stress/Strain
Formula for Pressure
Pressure (N/m2 or Pa) = Force (N) / Area (m^2)
or P=F/A
what are the 3 units of pressure
Bar, Millibar (mb) & Hectopascals (hPa)
Formula for Area
Area= Pi x r^2
What is the average Atmospheric Pressure
14.7 lb/in^2 Pounds per square inch (psi)
760 mmHg Millimetres of mercury
29.92 inHg Inches of mercury
1.01 bar Bar
101 325 Pa Pascal
1013.25 hPa Hectopascals
1013.25 mb Millibars
Formula for Absolute Pressure
Pabs = Pg+Patm
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Archimedes’ Principle states
That a body in a fluid will be subject to an upward force equal to the weight of fluid it displaces. This force is called the buoyant force.
What does the Bouyant Force equal
Weight of Fluid Displaced
Formula for Displacement Ratio
Ratio =P1/P2
P1 = Density of the Body (kg/m^3)
P2 = Density of Liquid (kg/m^3)
An object in uniform motion always has a ?
Constant speed
Formulas for Motion SUVAT
S = (u + v)t / 2 Distance (m)
S = ut +1/2at^2 Distance (m)
S = vt Distance (m)
h = ut +1/2gt^2 Distance (m)
v = u + at Final Velocity (m/s)
v2 = u2 + 2as Final Velocity (m/s)
a = v2 - u2 / 2s Acceleration (m/s2)
Formula for Centripetal Force
Fc = m x v^2/r
Explain Centripetal acceleration
Centripetal acceleration is the acceleration experienced while in uniform circular motion. It always points toward the centre of rotation.
Formula for Centripetal acceleration
Ac = v^2 / r
Ac = Centripetal Acceleration (m/s2)
In Resonance - 1 Hertz (Hz) equals
1 Cycle per second (cps)
Name the 4 types of Vibration
- Free Vibration
- Forced Vibration
- Harmonics
- Resonance
Velocity Ratio Formula
Velocity Ratio (VR) = Distance in / Distance out
Mechanical Advantage Formula
MA = R/E
- Resistance (N)
- Effort (N)
Actual Mechanical Advantage Formula
AMA = F,out/F,in
- Output Force (N)
- Input Force (N)
Ideal Mechanaical Advantage Formula
IMA = s,in / s,out
- Input Distance (m)
- Output Distance (m)
Name the 3 types of Levers
1st, 2nd & 3rd Class
First Class lever formula
E x L = R x I
E = Effort (N)
L = Length of Arm 9m)
R = Resistance (N)
l = Length of Resistance (m)
Formula for Opposing Moment & Inclined planes
F1 x s1 = F2 x s2
Formula re-arranged F1 = F2 x s2 / s1
The mechanical advantage of a single fixed pulley is
1, input force = weight of load
Pulley system with a Mechanical advantage of 2
Input force is halved. Load is 100N, Input force is 50N
Formula for Gears
MA = Driven Gear/Drive Gear
Formula for Efficiency
Efficiency (%) = MA / VR x 100
MA = Mechanical adv
VR = Velocity Ratio
or
Efficiency(%) = W,out(J) / W,in(J) x 100
1J = 1Nm
Newtons 2nd Law
F = M x A
Force = Mass x Acceleration
What does 1Kg measure in amu
1 kg = 6.02 × 10^26 amu.
Formula for mass
M = W/g
- M = Mass (Kg)
- W = Weight (N)
- g = Gravity (m/s2)
Formula for Weight
W = M x g
- W = Weight (N)
- M = Mass (Kg)
- g = Gravity (m/s^2)
Unit of Work
W = Joules
1 J = 1Nm
Formula of Work
W = F x s
Work(J)=Force(N) x Distance(m)
Formula for Power
P = W / T
- P = Power (Watts)
- W = Work (Joules)
- T = Time (secs)
Formula for Potential Energy
PE = M x g x h
- PE = gravitational potential energy (J)
- M = mass (Kg)
- g = gravitational acceleration (m/s^2)
- h = height (m)
Formula for Kinectic Energy
KE = 1/2mv^2
- KE = Kinectic Energy (J)
- M = mass (Kg)
- V = Velocity (m/s)
Formula for Efficiency
n = Eout/Ein x 100
- n = Efficiency (%)
- Eout = Usefull Energy output (J)
Ein = Total Energy input (J)
Formula for Momentum
p = m x v
- p = momentum (kg m/s)
- m = Mass (kg)
- v = Velocity (m/s)
Formula for Conservation of Momentum
M1u1 + m2u2 = m1v1 + m2v2
- m = Mass of body (Kg)
- u = Velocity of body before event (m/s)
- v = Velocity of body after event (m/s)
Formula for Impulse
J = F x t therefore F = J/t or t = j/F
- J = impulse (Ns)
- F = force (N)
- t = time (s)
The rigidity of a spinning rotor in a Gyro is affected by following factors:
. Rotor Mass
. Effective radius at which the mass acts
. Speed of rotation
. Bearing friction
Formula for Friction
F = uN or F = uW
- F = Friction (N)
- u = Coefficient of friction (starting, sliding or rolling) no units
- N = Normal Force (N)
- W = Weight (N)
Formula for Density
p = m/V
p = density (Kg/m^3)
m = mass (Kg)
V = Volume (m^3)
Formula for SG
SG = p1 / p2 or SG = W1 / W2
p1 = density of a liquid/solid or gas
p2 = density of water/density of air
W1 = weight of a volume of a liquid/solid or gas
W2 = weight of water or air of equal volume
Formula for Fluid Pressure
P = F/A
m = p x V p=density
Formula can be rewritten as:-
P = p x V x g / A g=gravitational acceleration
Explain Pascals Law
Pascal’s law explains that when pressure is applied to a contained liquid, the liquid exerts an equal pressure at right angles to the container that encloses it.
F = A x P
F = Force producted of a hydraulic piston (N)
A = Area of piston (m^2)
P = Fluid pressure (Kg/m^3)
Name the 3 types of pressure
- Static - exists in addition to any dynamic factors that may also be present at the same time
- Dynamic - s the pressure that emerges from velocity of the fluid in motion.
- Total - is the sum of dynamic and static pressure.
Define Bernoullis Theorem
Energy is neither added to nor taken away from a fluid in motion, the potential energy, and hence pressure decreases when the kinetic energy or velocity increases.
Formula for Pressure Energy
Ep = m x P/p
- Ep = pressure energy
- m = mass
- P = Pressure
- p = density
