gps sp1. students will analyze the relationships between force, mass, gravity, and the motion of...
TRANSCRIPT
![Page 1: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/1.jpg)
![Page 2: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/2.jpg)
GPS
• SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. – b. Compare and contrast scalar and vector quantities.
![Page 3: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/3.jpg)
SCALARS AND VECTORS• Scalars only have magnitude (ex. 50 m)
• Vectors have magnitude and direction (ex. 50 m, North)
• When you combine two or more vectors the sum is called the resultant.
• For example in 1-D:
50 m North and 30 m South; the resultant is 20 m North (+50 m + (-30 m))
![Page 4: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/4.jpg)
VECTOR BASICS
Images: http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm
![Page 5: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/5.jpg)
THE RESULTANT IN ONE DIMENSION
http
://w
ww
.phy
sics
clas
sroo
m.c
om/C
lass
/vec
tors
/U3l
1b.c
fm
![Page 6: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/6.jpg)
DIRECTION
Images: http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm
![Page 7: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/7.jpg)
htt
p:/
/ww
w.p
hys
icsc
lass
room
.com
/mm
edia
/vec
tors
/vd
.cfm
![Page 8: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/8.jpg)
THE RESULTANT IN TWO DIMENSIONS (X AND Y)
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
![Page 9: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/9.jpg)
![Page 10: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/10.jpg)
PROPERTIES OF VECTORS• Vectors can be moved parallel to themselves in
a diagram.
• Vectors can be added in any order. For example, A + B is the same as B + A
• To subtract a vector, add its opposite. SIGNS (DIRECTION) ARE VERY IMPORTANT!!!
• Multiplying or dividing vectors by scalars results in vectors. For example: When you divide displacement (x or y) by time (s) the result is velocity (v).
![Page 11: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/11.jpg)
http://www.physicsclassroom.com/mmedia/vectors/ao.cfm
![Page 12: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/12.jpg)
RESULTANTS CAN BE DETERMINE GRAPHICALLY OR ALGEBRACIALLY
• When determining the resultant graphically you must be careful of several factors.
• Your scale must be determined and measured accurately with a ruler.
• Your angles (directions) must be done with a protractor.• ALWAYS DRAW YOUR VECTORS FROM HEAD TO
TAIL!!!!!• The resultant is always from the head of your last vector
to the tail of your first vector.
HEAD TAIL
![Page 13: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/13.jpg)
DETERMINING SCALE
http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm
![Page 14: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/14.jpg)
GRAPHICALLY DETERMINING A RESULTANT
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
![Page 15: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/15.jpg)
DETERMINING RESULTANTS BY ALGEBRA
AND TRIGONOMETRY• You must use the Pythagorean theorem and
trigonometry to determine a resultant.• WE ONLY USE DEGREES IN THIS CLASS!! NO
RADIANS!!!!• You must know SOHCAHTOA!!• You must be able to use your calculator correctly!• The resultant is always from the head of your last vector
to the tail of your first vector.• Direction is always from the tail of the first vector.
![Page 16: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/16.jpg)
http
://w
ww
.phy
sics
clas
sroo
m.c
om/C
lass
/vec
tors
/U3l
1b.c
fm
![Page 17: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/17.jpg)
http
://w
ww
.phy
sics
clas
sroo
m.c
om/C
lass
/vec
tors
/U3l
1b.c
fm
![Page 18: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/18.jpg)
REAL LIFE VECTORSht
tp:/
/ww
w.p
hysi
cscl
assr
oom
.com
/mm
edia
/vec
tors
/pla
ne.c
fm
![Page 19: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/19.jpg)
http
://w
ww
.phy
sics
clas
sroo
m.c
om/C
lass
/vec
tors
/U3l
1b.c
fm
![Page 20: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/20.jpg)
ANSWERS TO PRACTICE• PRACTICE A:
11.18 km at 26.56 º W of N OR 11.18 km at 63.44º N of W
• PRACTICE B: 50 km at 53.13º S of W OR 50 km at 36.87º W of S
![Page 21: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/21.jpg)
PROBLEMS 1 and 2• Which of the following quantities are scalars, and
which are vectors? (A) the acceleration of a plane as it takes off (B) the number of passengers on the plane (C) the duration of the flight (D) the displacement of the flight (E) the amount of fuel required for the flight?
• A roller coaster moves 85 m horizontally, then travels 45 m at an angle of 30° above the horizontal. What is its displacement from its starting point?(graphical techniques)
![Page 22: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/22.jpg)
ANSWERS
30°
RESULTANT
126 m at 10° above the horizontal 126 m at 10° above the horizontal
•(A) vector (B) scalar (C) scalar (D) vector •(E) scalar
![Page 23: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/23.jpg)
PROBLEMS 3 and 4• A novice pilot sets a plane’s controls, thinking the
plane will fly at 250 km/hr to the north. If the wind blows at 75 km/hr toward the southeast, what is the plane’s resultant velocity? Use graphical techniques.
• While flying over the Grand Canyon, the pilot slows the plane’s engines down to one-half the velocity of the last problem. If the wind’s velocity is still 75 km/h toward the southeast, what will the plane’s new resultant velocity be?
![Page 24: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/24.jpg)
ANSWERS
• 204 km/h at 75° north of east
• 89 km/h at 54° north of east
![Page 25: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/25.jpg)
PROBLEM• The water used in many fountains is
recycled. For instance, a single water particle in a fountain travels through an 85 m system and then returns to the same point. What is the displacement of a water particle during one cycle?
![Page 26: GPS SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. –b. Compare and contrast scalar and vector quantities](https://reader036.vdocument.in/reader036/viewer/2022062511/5515666e550346a1418b4cdc/html5/thumbnails/26.jpg)
ANSWER
• ZERO