Facts And Notes

Question 1

What is the relationship between the sum of concurrent vectors and the system of vector components?

Answer 1

They are equivalent

Question 2

Are components vectors or scalars?

Answer 2

Scalars

Question 3

How do you find a unit vector with the same direction as F?

Answer 3

Divide the vector by its magnitude.

u = F/(magF)

Question 4

How can a vector be represented in terms of its unit vector?

Answer 4

Multiply the magnitude times the unit vector in the direction of F
F= (magF) u

Question 5

What are the two ways to express directions in 3-D problems?

Answer 5

1. Coordinate direction angles

2. Direction cosines

Question 6

How do you solve for the third angle if only given two?

Answer 6

Use the trig identity

1 = cos2(a) + cos2(b) + cos2(g)

Question 7

Coordinate direction angles must be between what values?

Answer 7

0 to 180°

Question 8

What are the three ways to give info in three dimensions?

Answer 8

1. Direction angles or direction cosines
2. Double projections
3. Distances or dimensions given

Question 9

What does the position vector give about a particular force or vector?

Answer 9

Its directional since

Question 10

What is the five-step process (plan of attack) for distance problems?

Answer 10

1. Express the line of action of F in coordinates
2. Find position vector
3. Compute magnitude of position vector
4. Formulate unit vector of position vector
5. Find F by F = (magF) (u of r)

Question 11

Nohra’s nuggets.

Answer 11

• Listen first, speak last! (Not a sign of weakness)
• Be consistent.
• Be accountable.

Question 12

What is the particle model?

Answer 12

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

Question 13

Where does equilibrium come from?

Answer 13

Newton’s first law of motion (First part, object at rest remains at rest)

Question 14

What is the mathematical translation of equilibrium?

Answer 14

Sum of forces equals zero

Question 15

What is Hooke’s law for springs?

Answer 15

F = ks

k - Spring constant (stiffness) lb/ft or N/m
s - The deformation of the spring

Question 16

Springs in parallel:

Answer 16

Forces add and there is a common displacement (act like resistors in series)
k(eq) = k1 + k2 + …

Question 17

Springs in series:

Answer 17

Displacement add and there is a common Force (act like resistors in parallel)
1/k(eq) = 1/k1 + 1/k2 + …

Question 18

Pulleys are assumed:

Answer 18

1. Weightless (negligible in calculation)
2. Frictionless
3. Cables are inextensible (don’t stretch)

Question 19

For every Freebody diagram and a two dimensional equilibrium problem how many equations should you write?

Answer 19

2 (Therefore at most you can have two unknowns)

Question 20

What is the relationship between alpha, beta, and the gamma, and the position vector?

Answer 20

They are the components of the unit vector of the position vector