Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a...
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Transcript of Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a...
![Page 1: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/1.jpg)
Vector Addition
And Distance vs. Displacement
![Page 2: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/2.jpg)
Distance and Displacement
• In Physics there is a difference between distance and displacement.
• Distance: The length of the route travelled between two points.
• Displacement: The shortest path between two points.
![Page 3: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/3.jpg)
Distance vs. Displacement• Look at the following map:
![Page 4: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/4.jpg)
Distance vs. Displacement• The Distance is how many km the boat travels to get to the treasure…
![Page 5: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/5.jpg)
Distance vs. Displacement• The Displacement is how many km it is from the ship to the treasure in a
straight line:
![Page 6: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/6.jpg)
Distance vs. Displacement• Distance is often larger than Displacement. Sometimes they may be
equal, though.
![Page 7: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/7.jpg)
Distance vs. Displacement
• Distance > Displacement.
![Page 8: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/8.jpg)
Distance vs. Displacement•Distance = Displacement
![Page 9: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/9.jpg)
Displacement & Vectors
• Vectors can be connected together to create a “map” similar to the treasure map:
![Page 10: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/10.jpg)
Displacement & Vectors
• Connecting vectors like this is called “Vector Addition”:
![Page 11: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/11.jpg)
Displacement & Vectors• When vectors are added together the
“answer” is the displacement. Adding vectors together can also be called “resolving vectors”
![Page 12: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/12.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N Start the first vector from the origin.
W E
S
3cm
![Page 13: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/13.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N Start the second vector from the end
of the first
W E
S
3cm
3cm
![Page 14: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/14.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N Draw the resultant and
calculate the length/angle.
W E
S
3cm
3cm
![Page 15: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/15.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N The length can be foundusing the PythagoreanTheorem: a2 + b2 = c2
W E
S
3cm
3cm
![Page 16: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/16.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N a2 + b2 = c2
(3cm)2 + (3cm)2 = c2
W E
S
3cm (b)
3cm
(a)
c
![Page 17: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/17.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N a2 + b2 = c2
(3cm)2 + (3cm)2 = c2
18 cm2 = c2
4.24 cm = cW E
S
3cm (b)
3cm
(a)
c
![Page 18: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/18.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N The angle can be found using what we know
abouttriangles and trig.
W E
S
3cm (b)
3cm
(a)
c = 4.24 cm
![Page 19: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/19.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N First, lets find this angle:
.
W E
S
3cm
3cm
4.24 cm
![Page 20: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/20.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N To get the angle we useone of the trig identities:sinθ
W E
S
3cm
3cm
4.24 cmθ
![Page 21: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/21.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N
W E
S
3cm
3cm
4.24 cmθ
45
7075.0sin24.4
3sin
sin
cm
cm
hypotenuse
opposite
![Page 22: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/22.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N But remember, the vectorangle is measured from
theEast-West Axis:
W E
S
3cm
3cm
4.24 cmΘ=45˚
![Page 23: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/23.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N Since the angle betweenNorth and East is 90˚, wecan say:90˚-45˚=45˚
W E
S
3cm
3cm
4.24 cmΘ=45˚
![Page 24: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/24.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N Now we have the lengthand the angle so:Answer: 4.24cm, 45˚NE
W E
S
3cm
3cm
4.24 cm45˚Θ=45˚
![Page 25: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/25.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N Review: If you walked 3 cm Nand 3 cm E, what is the
distancetraveled?Displacement?
W E
S
3cm (b)
3cm
(a)
c = 4.24 cm
![Page 26: Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:](https://reader036.fdocuments.net/reader036/viewer/2022081419/56649f065503460f94c1b67e/html5/thumbnails/26.jpg)
Adding Vectors
• Resolve the following vectors: 3cm due N and 3cm due East.
N Review: If you walked 3 cm Nand 3 cm E, what is the
distancetraveled? 3cm + 3cm = 6 cmDisplacement? 4.24 cm
W E
S
3cm (b)
3cm
(a)
c = 4.24 cm