Facts And Notes Flashcards
What is the relationship between the sum of concurrent vectors and the system of vector components?
They are equivalent
Are components vectors or scalars?
Scalars
How do you find a unit vector with the same direction as F?
Divide the vector by its magnitude.
u = F/(magF)
How can a vector be represented in terms of its unit vector?
Multiply the magnitude times the unit vector in the direction of F
F= (magF) u
What are the two ways to express directions in 3-D problems?
- Coordinate direction angles
2. Direction cosines
How do you solve for the third angle if only given two?
Use the trig identity
1 = cos2(a) + cos2(b) + cos2(g)
Coordinate direction angles must be between what values?
0 to 180°
What are the three ways to give info in three dimensions?
- Direction angles or direction cosines
- Double projections
- Distances or dimensions given
What does the position vector give about a particular force or vector?
Its directional since
What is the five-step process (plan of attack) for distance problems?
- Express the line of action of F in coordinates
- Find position vector
- Compute magnitude of position vector
- Formulate unit vector of position vector
- Find F by F = (magF) (u of r)
Nohra’s nuggets.
- Listen first, speak last! (Not a sign of weakness)
- Be consistent.
- Be accountable.
What is the particle model?
And model of reality with mass but without size or shape
- can’t have a moment (no distance)
- FBD: all forces will be con current
Where does equilibrium come from?
Newton’s first law of motion (First part, object at rest remains at rest)
What is the mathematical translation of equilibrium?
Sum of forces equals zero
What is Hooke’s law for springs?
F = ks
k - Spring constant (stiffness) lb/ft or N/m
s - The deformation of the spring
Springs in parallel:
Forces add and there is a common displacement (act like resistors in series)
k(eq) = k1 + k2 + …
Springs in series:
Displacement add and there is a common Force (act like resistors in parallel)
1/k(eq) = 1/k1 + 1/k2 + …
Pulleys are assumed:
- Weightless (negligible in calculation)
- Frictionless
- Cables are inextensible (don’t stretch)
For every Freebody diagram and a two dimensional equilibrium problem how many equations should you write?
2 (Therefore at most you can have two unknowns)
What is the relationship between alpha, beta, and the gamma, and the position vector?
They are the components of the unit vector of the position vector
