Chapter Two (adding vectors)

Question 1

What is sine law and when is it used?

Answer 1

It is used to solve for the parallelograms. Its formula is:

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

Question 2

Steps to solve a 2D vector addition?

Answer 2

1. Resolve forces
2. Add x components and all y components
3. Find the magnitude of the resultant vector

Question 3

What is the magnitude of Ua?

Answer 3

Always 1. However we calculate for Ua when we are looking for vector quantities

Question 4

What is the formula for a unit vector?

Answer 4

Question 5

In a 3D vector, what are the steps to break down a force?

Answer 5

1. Find A’ (shadow) and Fz
2. Use the magnitude of F’ to help solve for x and y (see diagram)

Question 6

What is the formula for alpha ?

Answer 6

Question 7

Beta formula

Answer 7

Question 8

Gamma formula

Answer 8

Question 9

What is the formula that links alpha, beta and gamma together?

Answer 9

Question 10

What’s an alternative formula for Ua that links the vectors of each axis together

Answer 10

Question 11

What is something that we must look at when understanding forces in vector addition?

Answer 11

if they are positive or negative forces

Question 12

How is position vector “r” calculated?

Answer 12

Question 13

How is the position vector (scalar value) “r” calculated?

Answer 13

Using the square root of all vector terms added together

Question 14

How is Ua calculated from using the position vector?

Answer 14

Question 15

What is the dot product and what is it’s formula?

Answer 15

It is used to calculate the theta (angle) between two vectors. It is commonly used when we are given a position vector and a second known force.

Question 16

What is the geometric solution to solving the dot product?

Answer 16

Question 17

How can we solve for the unknown angle in the dot product? (formula)

Answer 17

Question 18

What angle are we specifically looking for in a dot product question?

Answer 18

The angle acting between the force (known to us) acting on the pole and the force going with the pole (force parallel)

Question 19

What are the two formulas to solve for the parallel force in a dot product question?

Answer 19

Question 20

What are the two formulas to solve for the perpendicular force in a dot product question?

Answer 20

Question 21

What is the entire list of steps in a typical dot product question?

Answer 21

1. Solve for/ analyze the force acting on the pipe, beam etc. We are sometimes given partial information about this force
2. Solve for a second force or position vector
3. Combine these forces using the dot product formula and find the scalar force quantity
4. Find the angle we need to solve for using the proper formula (given in picture)
5. Solve for the parallel force
6. Solve for the perpendicular force