AP Physics: Thurs SEP 9:
Key Concept's) Today: Review Vectors: pt & Vt Graphs
Journal:
1. Assume that the tip of your little finger (.008m wide) can just cover the sun when it is placed 0.86m away from your eye. If the sun is 149,600,000 kilometers away from the earth, what the sun's diameter?
a. 1,390,000 km
b. 695,800 km
c. 14,080,000 km
d. 1,100,000 km
2. Note the expression: y = x2. Which statement is most consistent with this expression?
a. if y doubles, then x quadruples
b. y is greater than x
c. if x doubles, then y doubles
d. if x doubles, then y quadruples
3. In mechanics, physicists use three basic quantities to derive additional quantities. Mass is one of the three quantities. What are the other two?
a. length and force
b. power and force
c. length and time
d. force and time
4. A furlong is a distance of 220 yards. A fortnight is a time period of 2 weeks. A race horse is running at a speed of 5 yards per second. What is his speed in furlongs per fortnight?
a. 27,491 furlongs/fortnight
b. 13,674 furlongs/fortnight
c. 6,221 furlongs/fortnight
d. 2,749 furlongs/fortnight
5. Initial velocity (Vo) is 10m/s. How much time does it take a rock to travel from the edge of the building to the ground? (This is an important concept --> MUST KNOW !!!)
a.
b.
c.
d.
e.
1. A
2. D
3. C
4. A
5yds(1 F.L./220yds)(3600sec/1 hr)(24hrs/1 day)(14Day/1 F.N.) = 27,491
5. h = ho + (Vo t) + 1/2 g t2
h = 0 + 0 + 1/2 g t2
t2 = 2h/g
t = √(2h/g)
1. Vectors (Notes)
a) Add the following 4 rectangular vectors and find the resultant vector (polar form).
x1 = 2 , y1 = -12
x2 = -4 , y2 = 7
x3 = -7 , y3 = -4
x4 = 5 , y4 = 6
b) Add the following 3 polar vectors and find the resultant vector (polar form).
20 ∟300 + 40 ∟1500 + 100 ∟3300
a. 5 ∟216.90
b. 74∟23.90
Graphs:
Describing Motion with Position vs. Time Graphs
The Meaning of Shape for a p-t Graph
The specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph.
To begin, consider a car moving with a constant, rightward (+) velocity of 10 m/s.
The
resulting graph would look like the
graph at the right. Note that a motion
with constant, positive velocity results
in a line of constant and positive
slope.
Now consider a car moving with a changing, rightward (+) velocity (car that is moving rightward and speeding up or accelerating).
The resulting graph would look like the graph at the right. Note that a motion with changing, positive velocity results in a line of changing and positive slope.
The Principle of Slope for a p–t Graph reveals useful information about the velocity of the object.
| Positive Velocity Constant Velocity | Positive Velocity Changing Velocity (acceleration) |
|
|
If the velocity is constant, then the slope is constant. If the velocity is non-constant (i.e., an acceleration +/-) then the slope is a curve.
Example
| Leftward (–) Velocity; Slow to Fast | Leftward (–) Velocity; Fast to Slow |
|
|
The Velocity- Time (V-T) Graph
|
Review Vectors
- a vector arrow (with arrowhead) is drawn in a specified direction. The vector arrow has a head and a tail.
-
the magnitude and direction of the vector is clearly labeled. In this case, the diagram shows the Force of 316 m and the direction is (35 degrees starting West and going counter-clockwise)
Fy
Fx
-
Now we have to break down the vector to its "X" & "Y" components.
-
The Right Triangle (You must know this!!!!!!)
Example:
A
__m? __0?
3m
__0?
4m
B
_m? __0?
5m
300?
___m?
a. 5, (36.90) & (53.10)
b. 10, 8.7 (600)
__
Fy
Fx
__________________________________________
Fy = (Sin q) (316) = 181 N
Questions:
1. Does speed have a direction?
2. Does velocity have a direction?
3. What three things can one do to change velocity?
4. Does acceleration have a direction?
5. If acceleration is “0” is it moving?
6. If velocity is “0” is it moving?
7. If velocity is “0” can it be accelerating?
8. Fill in table below
|
Vi (m/s) |
Vf (m/s) |
Time (s) |
Acceleration (m/s2) |
|
10.0 |
31.0 |
7.0 |
|
|
0.0 |
0.0 |
10.0 |
|
|
5.0 |
5.0 |
10.0 |
|
|
5.0 |
-5.0 |
2.0 |
|
|
|
100.0 |
5.0 |
10.0 |
1. +40 m/s/s. (The line rises +40 m/s for every 1 second of run)
2. +20 m/s/s. The line rises +60 m/s for 3 seconds of run. The rise/run ratio is +20 m/s/s.
3. -20 m/s/s. The line rises -160 m/s for 8 seconds of run. The rise/run ratio is -20 m/s/s.
4. 20m
5. 250m
6. (20 + 250 + 90 + 120 ) = 480m
7. -250m
8. 230m
Formulas:
· Speed = dist/time
· VelAvg = Vf + Vi /2
· Vel = Dx (or displacement) /time
· Acc = Vf – Vi /time or DV /time
Motion equations:
· Vf = Vi + (a)(t)
· Vf 2 - Vi2 = 2(a)(Dx)
· Position (x) = Vi (t) + 1/2(a)(t2)
Graphs:
Applet:
Show how vectors are added #1
Show components of vectors #2
Vector Activity:
The head-to-tail method involves drawing a vector to scale on a sheet of paper beginning at a designated starting position. Where the head of this first vector ends, the tail of the second vector begins (thus, head-to-tail method). The process is repeated for all vectors which are being added. Once all the vectors have been added head-to-tail, the resultant is then drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish. Once the resultant is drawn, its length can be measured and converted to real units using the given scale. The direction of the resultant can be determined by using a
- Choose a scale and indicate it on a sheet of paper
- Pick a starting location and draw the first vector to scale in the indicated direction.
- Starting from where the head of the first vector ends, draw the second vector to scale in the indicated direction.
- Label the magnitude and direction of this vector on the diagram.
- Repeat steps 2 and 3 for all vectors which are to be added
- Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as Resultant or simply R.
- Using a ruler, measure the length of the resultant and determine its magnitude by converting to real units using the scale (4.4 cm x 20 m/1 cm = 88 m).
- Measure the direction of the resultant using the counterclockwise convention discussed