EGR 245 - Midterm 1 Equation Sheet (Ch. 12 - 14)
Dynamics This Semester
P-2D
Kinematics
Kinetics (F = ma, W/E, I/M)
ERO-2D
Kinematics
Kinetics (F = ma, W/E, I/M)
Vibrations
BONUS: Introduce P/ERO in 3D
Statics:
Object: P or ERO (E = ∞)
Equilibrium: ΣF = 0 (a = 0), ΣM = 0 (α = 0)
(CT) -> n,t
(RT)
Dynamics:
Object: P or ERO (E = ∞)
Equilibrium: ΣF ≠ 0 (a ≠ 0), ΣM ≠ 0 (α ≠ 0)
(CT) -> r,θ
(RT)
Solving problems in Dynamics is not as linear as Statics
Solving problem in Dynamics is more like putting the pieces of a puzzle together
1. 1D or 2D or 3D (no 3D in this class)
2. Motion of P -> RT or CT
3. Is the motion a function of time (t) or position (s)?
4. What do I need to find?
5. What am I given?
Dependent Motion
(CT) -> x,y
Relative Motion
Ch. 12 - Kinematics of P-2D
Goal -> we want to describe the motion of the P-2D -> (s, v, a)
Rectilinear Translation (RT) -> 1D
Motion of P: 1D (RT), 2D (CT)
Tools:
1. Stopwatch/Camera -> measure time and increments of time
2. Cartesian Coordinate System
a. x,y,z (RT, CT)
b. n,t,b (CT)
c. r, θ,(z, α) (CT)
3. Dependent Motion
4. Relative Motion -> vB/A = vB - vA
θ
t
y
s
a
n
x
O
r
v
Curvilinear Translation (CT) -> 2D
Radius of Curvature Equation:
If v(s) or a(s) ->
=
If acceleration = constant -> KEoM
A
B
Ch. 13 - Kinetics P-2D(2) -> F = ma ≠ 0
FBDStatics
F2
r
θ
r
FBDDynamics
F3
=
F1
arc length, s
F = ma
(RT, CT -> x,y)
θ
x,y
[1] ΣFx:
=
[2] ΣFy:
=
π = 3.141592653589793
A = πr2
s = θr
ma
C = (2π)r
(CT -> n,t)
θ (rad, °)
If you end up with too many unknowns, supplement with Kinematics
(CT -> r,θ)
(CT -> orbital motion)
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(CT -> r,θ)
(CT -> orbital motion)
Ch. 14 - Kinetics of P-2D (Work-Energy)
Energy -> a P-2D can have 'energy' if is it moving (KE = T) or it can have (PE = V) in relation to an established position
Work -> External stimuli applied to a P-2D to change its velocity (kinetic energy)
KE = T =
PE = V -> Vg -> establish a datum -> Vg = mgh = Wh, Ve =
F = kx
(datum)
Work = U =
k
x
Fspring = kx
How do we determine the sign (+ or -) of the Work?
If F and x are in the same direction -> +
If F and x are in opposite directions -> Work-Energy Theorem [WET]
Work-Energy Principle -> ΔKE = Work
If we have a situation where there are NO non-conservative forces (i.e., friction) ->
Law of Conservation of Mechanical Energy [LCME]
Power -> [W] = [J/s] = [Energy/time] = [(N*m)/s] = [N*(m/s)] -> P = F ∙ v
(translational)
Efficiency -> ε = η =
P=T∙ω
(rotational)
Deforms
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k