vectors
Download
Skip this Video
Download Presentation
Vectors

Loading in 2 Seconds...

play fullscreen
1 / 20

Vectors - PowerPoint PPT Presentation


  • 132 Views
  • Uploaded on

Vectors. You will be tested on your ability to: correctly express a vector as a magnitude and a direction break vectors into their components add and multiply vectors apply concepts of vectors to linear motion equations (ch. 2). Vector vs. Scalar.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Vectors' - shea-buckley


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
vectors

Vectors

You will be tested on your ability to:

correctly express a vector as a magnitude and a direction

break vectors into their components

add and multiply vectors

apply concepts of vectors to linear motion equations (ch. 2)

vector vs scalar
Vector vs. Scalar
  • Scalar units are any measurement that can be expressed as only a magnitude (number and units)
    • Examples:
      • 14 girls
      • $85
      • 65 mph
  • Vector quantities are measurements that have BOTH a magnitude and direction.
    • Examples:
      • Position
      • Displacement
      • Velocity
      • Acceleration
      • Force
representing vectors
Representing Vectors
  • Graphically, vectors are represented by arrows, which have both a length (their magnitude) and a direction they point.

v = 45 m/s

d = 50 m

v = 25 m/s

a= 9.8 m/s2

representing vectors1
Representing Vectors
  • The symbol for a vector is a bold letter.
    • For velocity vectors we write v
    • For handwritten work we use the letter with an arrow above it. v
  • Algebraically
    • Vectors are written as a magnitude and direction
    • v = lvl , Θ
    • Example v = 25 m/s, 120o or d = 50 m, 90o
drawing vectors
Drawing Vectors
  • Choose a scale
  • Measure the direction of the vector starting with east as 0 degrees.
  • Draw an arrow to scale to represent the vector in the given direction
  • Try it! v = 25 m/s, 190o scale: 1 cm = 5 m/s
  • This can be described 2 other ways
    • v = 25 m/s, 10o south of west
    • v = 25 m/s, 80o west of south
  • Try d = 50 m, 290o new scale?
adding vectors
Adding Vectors
  • Vector Equation
    • vr = v1+v2
    • Resultant- the vector sum of two or more vector quantities.
    • Numbers cannot be added if the vectors are not along the same line because of direction!
    • Example……
    • To add vector quantities that are not along the same line, you must use a different method…
an example
An Example

D3

D2

DT

D1

D1 = 169 km @ 90 degrees (North)

D3 = 195 km @ 0 degrees (East)

D2 = 171 km @ 40 degrees North of East

DT = ???

tip to tail graphical vector addition
Tip to tail graphical vector addition
  • On a diagram draw one of the vectors to scale and label it.
  • Next draw the second vector to scale, starting at the tip of the last vector as your new origin.
  • Repeat for any additional vectors
  • The arrow drawn from the tail of the first vector to the tip of the last represents the resultant vector
  • Measure the resultant
add the following
Add the following
  • d1 = 30m, 60o East of North
  • d2 = 20m, 190o
    • dr = d1+d2
    • dr = ?
    • dr = 13.1m, 61o
vector subtraction
Vector Subtraction
  • Given a vector v, we define –v to be the same magnitude but in the opposite direction (180 degree difference)
  • We can now define vector subtraction as a special case of vector addition.
  • v2 – v1 = v2 + (-v1)
  • Try this
  • d1 = 25m/s, 40o West of North
  • d2 = 15m/s, 10o
  • 1cm = 5m/s
    • Find : dr = d1+d2
    • Find dr = d1- d2

v

–v

slide11
Multiplying a vector v by a scalar quantity c gives you a vector that is c times greater in the same direction or in the opposite direction if the scalar is negative.

cV

V

-cV

vector components
Vector Components
  • A vector quantity is represented by an arrow.
  • v = 25 m/s, 60o
  • This single vector can also be represented by the sum of two other vectors called the components of the original.

v = 50 m/s, 60o

sinΘ = Vy / V

Vy= V sinΘ

cosΘ = Vx / V

Vx= V cosΘ

try this
Try this:

V2 = 10 m @ 30 degrees above –x

Find: V2X =

V2Y =

V1 = 10 m @ 30 degrees above +x

Find: V1X =

V1Y =

Ө2

Ө1

But V2X should be NEGATIVE!!!

Try using the angle 150 degrees for V2

try this1
Try this:

V2 = 10 m @ 30 degrees above –x

Find: V2X =

V2Y =

V1 = 10 m @ 30 degrees above +x

Find: V1X =

V1Y =

Find : V3X =

V3Y=

V3 = 10 m @ 30 degrees below +x

Try using the angle 330 degrees for V3

now try this
Now try this:

VX = 25m/s

VY = - 51m/s

Find V=

and your point is
and your point is???
  • ALWAYS:

Describe a vector’s direction relative to the +x axis

  • ALWAYS:

Measure counter-clockwise angles as positive

  • ALWAYS:

Measure clockwise angles as negative

an example1
An Example

D3

D3X

D2

D2Y

D2X

DT

D1Y

D1

D1 = 169 km @ 90 degrees (North)

D3 = 195 km @ 0 degrees (East)

D2 = 171 km @ 40 degrees North of East

DT = ???

but wait there s more
But Wait. . . There’s more!

We’ve Found:

DTX = 326 km

DTY = 279 km.

y (km)

For IDTI, use the Pythagorean Theorem.

For the Direction of DT, use Tan-1

x (km)

practice it
Practice it:
  • Pg. 70, # 1, 4
ad