Chapter Two (adding vectors) Flashcards
What is sine law and when is it used?
It is used to solve for the parallelograms. Its formula is:
A / sin a = B / sin b = C / sin c
Steps to solve a 2D vector addition?
- Resolve forces
- Add x components and all y components
- Find the magnitude of the resultant vector
What is the magnitude of Ua?
Always 1. However we calculate for Ua when we are looking for vector quantities
What is the formula for a unit vector?
In a 3D vector, what are the steps to break down a force?
- Find A’ (shadow) and Fz
- Use the magnitude of F’ to help solve for x and y (see diagram)
What is the formula for alpha ?
Beta formula
Gamma formula
What is the formula that links alpha, beta and gamma together?
What’s an alternative formula for Ua that links the vectors of each axis together
What is something that we must look at when understanding forces in vector addition?
if they are positive or negative forces
How is position vector “r” calculated?
How is the position vector (scalar value) “r” calculated?
Using the square root of all vector terms added together
How is Ua calculated from using the position vector?
What is the dot product and what is it’s formula?
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.
What is the geometric solution to solving the dot product?
How can we solve for the unknown angle in the dot product? (formula)
What angle are we specifically looking for in a dot product question?
The angle acting between the force (known to us) acting on the pole and the force going with the pole (force parallel)
What are the two formulas to solve for the parallel force in a dot product question?
What are the two formulas to solve for the perpendicular force in a dot product question?
What is the entire list of steps in a typical dot product question?
- Solve for/ analyze the force acting on the pipe, beam etc. We are sometimes given partial information about this force
- Solve for a second force or position vector
- Combine these forces using the dot product formula and find the scalar force quantity
- Find the angle we need to solve for using the proper formula (given in picture)
- Solve for the parallel force
- Solve for the perpendicular force
