Chapter 3 Flashcards
What is space?
A region where points or objects exist.
Who is the ‘father’ of geometry?
Euclid - an Ancient Greek mathematician and philosopher
What are Euclid’s 5 Postulates?
1 - A straight line may be drawn between any 2 points
2 - Any straight line can be drawn indefinitely in a straight line
3 - Given a straight line, a circle can be drawn where one endpoint is the centre and the length of the segment is the radius
4 - All right angles are congruent
5- Given 2 lines where a third line drawn that intersects them in a way that the sum of the angles is less than 180 degrees, the two line will intersect.
Euclidean math is developed for what type of space?
2 dimensional
What is the base spacial quantity?
Length
Define speed
The rate at which an object moves
What is the difference between vector and scalar quantities?
Scalar - quantified solely by their magnitude
Vector - quantified by both a magnitude and direction
What are the scalar base quantities?
Length and speed
What is the base vector quantity?
Position - describing the location of an object
What quantity results from a change in position?
The length as well as the direction (vector).
What are the vector quantities?
Position, velocity, acceleration, force
What three pieces of information are necessary to define a vector?
Magnitude, direction and sense
What two pieces of information are used to describe polar coordinates?
Theta - describing the direction of the vector
Radius - describing the magnitude of the vector
the sense (+/-) depends on the chosen polar axis
When is the polar coordinate system most commonly used in the real world?
With compasses
What two methods can be employed for vector addition?
The Cartesian method and the parallelogram method
Describe how to use the parallelogram method with vector addition
1 - place both tails of the vectors together
2 - create a parallelogram
3 - split the parallelogram into 2 triangles
4 - add the vectors to solve for the unknown side of the triangle
One football player is pushing forward against an opposing player with a force of 1200N. A teammate of the first player approaches at an angle of 60 degrees to the right of the first player. This teammate applies a force of 800N. What is the resultant force experienced by the opposing player?
1744N, 23.4 degrees
What is the difference between distance and displacement?
Distance refers to the total distance travelled while displacement is the change in position
A baseball player is running forward at 5m/s while throwing a ball at 20m/s at 30 degrees above the horizontal.
What is the resultant velocity of the baseball?
24.45 m/s at 24.1 degrees above the horizontal.
When can you and can’t you add velocity vectors?
You can add them when the velocities are occurring at the same time, but not when they are occurring at different times.
Describe the Cartesian coordinate system
The 2-dimensional Cartesian coordinate system defines an origin and two perpendicular axis (x,y). The origin has coordinates of 0,0
The psoas major muscle pulls down and forward with a force of 450N at an angle of 8 degrees. The multifidus muscle pulls down and backwards with a force of 300N a an angle of 15 degrees.
What is the resultant force acting on the vertebrae?
736N, 1.2 degrees (down and back of vertical)
What types of motion are best described by Cartesian and polar coordinate systems?
Cartesian - linear motion
Polar - rotational motion
