ENGMECH Finals (Formulas)

Question 1

Formulas for Rectilinear Motion with Constant Acceleration

Answer 1

V = V0 + at
s - s0 = v0t + 1/2 at^2
(v final)^2 - (v inital)^2 = 2a (s - s0)
a ds = v dv

Question 2

1 m / s = _________ km/ hr

Answer 2

3.6 km/hr

Question 3

A constant acceleration of 9.81 m/s^2 is equivalent to _________ in ft/s^2

Answer 3

32.2 ft/s^2

Question 4

1 mile = ________ ft

Answer 4

5280 ft

Question 5

Formula for p (radius of curvature)

Answer 5

(1+(dy/dx)^2)^3/2 / abs value of (d^2y/dx^2)

Question 6

The unit “MPa” is equivalent to ________

Answer 6

Newtons/ mm^2

Question 7

The unit “Pa” is equivalent to ________.

Answer 7

Newtons/ m^2

Question 8

1 kip = _____ lbs

Answer 8

1000

Question 9

Formula for Normal Strain

Answer 9

Epsilon = change in L /L

Question 10

Formulas for Deformation

Answer 10

Delta = Lf-Lo (Final- Initial Length)
Delta = PL/AE = (Stress x L)/ E

Question 11

Formulas for Stress

Answer 11

Stress = P/A

Question 12

In the formula given by Delta = PL/AE, what are the three restrictions on the use of this equation?

Answer 12

1. Load must be axial
2. The bar must have a constant cross section and homogenous
3. The stress must not exceed the proportional limit

Question 13

Formula for Bearing Stress

Answer 13

Sigma b = Pb / Ab = P / td

Question 14

Formula for Poisson’s Ratio

Answer 14

v = - Epsilon (lat or trans) / Epsilon (long)
Epsilon (trans) = Change in diameter / diameter
Epsilon (long) = Deformation / Length

Question 15

Formula for Hooke’s Law

Answer 15

Stress = E (Young’s Modulus) x Epsilon (Normal or Longitudinal Strain)

Question 16

Formula for Shear Stress

Answer 16

Tau = V / A = P / nDt

Question 17

Formula for Cosine Law

Answer 17

C^2 = A^2 + B^2 - 2AB cos C

Capital letters = sides
Lowercase letters = points/angles

Question 18

Formula for Sine Law

Answer 18

A / sin a = B / sin b = C / sin c

Capital letters = sides
Lowercase letters = points/angles

Question 19

Formula for Rectangular Components

Answer 19

F = sqrt [(Fx)^2 + (Fy)^2]
Theta = arctan (Fy/Fx)

Question 20

Type of moment turning counter clockwise

Answer 20

Positive

Question 21

Type of moment turning clockwise

Answer 21

Negative

Question 22

Formula for Normal Acceleration

Answer 22

an = v^2 / p ; p = radius of curvature

Question 23

Order of Derivatives for Equations

Answer 23

S (Position)
V (Velocity)
A (Acceleration)

Question 24

Formula for average acceleration

Answer 24

a = change in v / change in t

Question 25

Formulas for Free-Falling Bodies

Answer 25

V = V0 + at
y - y0 = v0t + 1/2 at^2
(v final)^2 - (v inital)^2 = 2a (y - y0)

Question 26

In free-fall, if initial motion is upward, a = ____ .

Answer 26

• g

Question 27

In free-fall, if initial motion is downward, a = ____ .

Answer 27

g

Question 28

Formula for average velocity

Answer 28

v average = change in s / change in t

Question 29

Formula for Thermal Strain

Answer 29

Epsilon t = alpha (change in t)