ENGMECH Finals (Formulas) Flashcards
Formulas for Rectilinear Motion with Constant Acceleration
V = V0 + at
s - s0 = v0t + 1/2 at^2
(v final)^2 - (v inital)^2 = 2a (s - s0)
a ds = v dv
1 m / s = _________ km/ hr
3.6 km/hr
A constant acceleration of 9.81 m/s^2 is equivalent to _________ in ft/s^2
32.2 ft/s^2
1 mile = ________ ft
5280 ft
Formula for p (radius of curvature)
(1+(dy/dx)^2)^3/2 / abs value of (d^2y/dx^2)
The unit “MPa” is equivalent to ________
Newtons/ mm^2
The unit “Pa” is equivalent to ________.
Newtons/ m^2
1 kip = _____ lbs
1000
Formula for Normal Strain
Epsilon = change in L /L
Formulas for Deformation
Delta = Lf-Lo (Final- Initial Length)
Delta = PL/AE = (Stress x L)/ E
Formulas for Stress
Stress = P/A
In the formula given by Delta = PL/AE, what are the three restrictions on the use of this equation?
- Load must be axial
- The bar must have a constant cross section and homogenous
- The stress must not exceed the proportional limit
Formula for Bearing Stress
Sigma b = Pb / Ab = P / td
Formula for Poisson’s Ratio
v = - Epsilon (lat or trans) / Epsilon (long)
Epsilon (trans) = Change in diameter / diameter
Epsilon (long) = Deformation / Length
Formula for Hooke’s Law
Stress = E (Young’s Modulus) x Epsilon (Normal or Longitudinal Strain)
Formula for Shear Stress
Tau = V / A = P / nDt
Formula for Cosine Law
C^2 = A^2 + B^2 - 2AB cos C
Capital letters = sides
Lowercase letters = points/angles
Formula for Sine Law
A / sin a = B / sin b = C / sin c
Capital letters = sides
Lowercase letters = points/angles
Formula for Rectangular Components
F = sqrt [(Fx)^2 + (Fy)^2]
Theta = arctan (Fy/Fx)
Type of moment turning counter clockwise
Positive
Type of moment turning clockwise
Negative
Formula for Normal Acceleration
an = v^2 / p ; p = radius of curvature
Order of Derivatives for Equations
S (Position)
V (Velocity)
A (Acceleration)
Formula for average acceleration
a = change in v / change in t
Formulas for Free-Falling Bodies
V = V0 + at
y - y0 = v0t + 1/2 at^2
(v final)^2 - (v inital)^2 = 2a (y - y0)
In free-fall, if initial motion is upward, a = ____ .
- g
In free-fall, if initial motion is downward, a = ____ .
g
Formula for average velocity
v average = change in s / change in t
Formula for Thermal Strain
Epsilon t = alpha (change in t)
