Mechanics Flashcards
Types of Quantities
Scalar and Vector
The type of physical quantities which have only magnitude.
Scalar Quantity
Examples of Scalar Quantities
Temperature, speed, distance, mass
The type of quantity that have two characteristics, a magnitude and a direction.
Vector Quantity
Example of Vector Quantities
velocity, displacement, force, acceleration
What is the reference direction in N 30° E?
N
What is the reference direction in 30° N of E?
E
What is the direction of the frictional force to determine the minimum force to prevent slipping? (box on a ramp)
UPWARD
What is the direction of the frictional force to determine the maximum force that can be exerted without causing the block to slip?
DOWNWARD
Belt Friction Formula
W, T1/T2, P and T
T1 + T2 = W
T1/T2 = e^(µθ)
P = 2πfT
T = ΔF r
T - tension
µ - coefficient of friction
θ - angle of lap
f - wheel speed, Hz, rev/s, cps
r - wheel radius
ΔF - ΔTension
Moment
M = Fd
Number of component (force) in a support pin or hinge
2 (parallel and perpendicular)
Number of component (force) in a support roller or rocker
1 (perpendicular force)
Mass Moment of Inertia for Sphere
I = 2/5 (mr^2)
Mass Moment of Inertia for Cylinder
I = 1/2 (mr^2)
Mass Moment of Inertia for Thin Rod (centroidal axis)
I = 1/12 (mL^2)
Mass Moment of Inertia for Thin Rod (at one end)
I = 1/3 (mL^2)
Mass Moment of Inertia for Rectangular Plate
I = m/12 (l^2 + w^2)
Parallel Axis Theorem for Mass Moment of Inertia
Ix = Ix̄ + md^2
Area Moment of Inertia for Ix
Ix = (bh^3)/12
Area Moment of Inertia for Iy
Iy = (b^3h)/12
Radius of Gyration
r = √ (Ix / A)
or
r = √ (Iy / A)
Parallel Axis Theorem for Area Moment of Inertia
Ix = Ix̄ + Ad^2
Velocity
v = d/t
Uniform Accelerated Motion
a, Vf, S-So
a = (Vf-Vi)/t
Vf = Vi + at
S - So = Vit + (at^2)/2
S - So = (Vf^2 - Vi^2)/2a
Average Speed
S = total distance travelled / total time travelled
Free Falling Body
Vf, h - ho
Vf = Vi + gt
h - ho = Vit + (gt^2)/2
h - ho = (Vf^2 - Vi^2)/2g
_______ is the component of force acting on an object in curvilinear motion which is directed towards the axis of rotation or center of curvature.
Centripetal Force
Centripetal Force Formula
Fc = mv^2/r
a = v^2/r
_______ is a pseudo force in a circular motion which acts along the radius and is directed away from the center of the circle.
Centrifugal Force
Uniform Angular Motion
α, σ,
α = (Wf - Wi)/t
σ = Wit + (αt^2)/2
σ = (Wf^2 - Wi^2)/2α
Relationship of Angular and Translational Motion
v = rw
s = rσ
a = rα
Projectile Motion
Horizontal Part Formula
x = Vcosθt
Projectile Motion
Vertical Part Formula
Vy’ = Vy - gt = Vsinθ - gt
y = Vsinθt - (gt^2)/2
y = (Vy’^2 - Vy^2)/2g
Angle of Banking Formula
tan (θb + θf) = v^2/r
Angle of Friction Formula
θf = tan^-1 (μ)
Total Mechanical Energy Formula
TME = KE + PE
Kinetic Energy Formula
KE = mv^2/2
Potential Energy Formula
PE = mgh
Work Formula
W = Fd
_____ is the rate of doing work
Power
Power Formula
P = W/t = Fd/t = mad/t
* ad = (Vf^2 - Vi^2)/2
P = m/t [(Vf^2 - Vi^2)/2]
P = Fd/t = Fv = mgv
Force Formula
F = ma = m ΔV/t
Impulse Formula
I = FΔt
Momentum Formula
m1v1 + m2v2 = m1v1’ + m2v2’
Pendulum (TME)
TME = KE +PE
KEmax = PEmax
@ KEmax ; PEmin = _____
0
@PEmax ; KEmin = ______
0
The sudden, forceful coming together in direct contact of two bodies
Collision
What are the three types of collision
Inelastic, Perfectly inelastic, Elastic
A type of collision where KE is not conserved
Inelastic Collision
A type of collision where the objects stick together; where KE is equal to zero after impact
Perfectly Inelastic Collision
A type of collision where the total kinetic energy of the two bodies remains the same.
Elastic Collision
Coefficient of Restitution Formula
e = √(hr/ho)
Coefficient of Restitution of Inelastic Collision
0 < e < 1
Coefficient of Restitution of Perfectly Elastic Collision
e = 1
Coefficient of Restitution of Perfectly Inelastic Collision
e = 0
