Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each...
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Transcript of Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each...
![Page 1: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/1.jpg)
Method #2: Resolution into Components
![Page 2: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/2.jpg)
Solving Vector Problems using the Component Method
Each vector is replaced by two perpendicular vectors called components.
Turn every vector into a right triangle. Add the x-components and the y-
components to find the x- and y-components of the resultant.
Use the Pythagorean theorem and the tangent function to find the magnitude and direction of the resultant.
![Page 3: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/3.jpg)
Quick Review
Right Triangle
a
c
b
A
B
C
c is the hypotenuse
c2 = a2 + b2
sin = opp/hyp cos = adj/hyp tan = opp/adj
A + B + C = 180°
transverse line crossing parallel lines: A A == A
AA + B = 90 °
AA
AA
![Page 4: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/4.jpg)
Let’s look at one vector’s components:
To resolve a vector into perpendicular components
37o
100
Construct a line parallel to x through tailConstruct a line parallel to y through headArrows point the way from tail to head
37o
100
x
yUsing trig functions solve for x & y
X = 100cos 37o = 80Y = 100sin 37o = 60
![Page 5: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/5.jpg)
Why is this important? Components of Force
x
y
![Page 6: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/6.jpg)
Method #2: Adding Vectors By Resolution into Components USE COLOR PENCILS!USE COLOR PENCILS!
Stan is trying to rescue Kyle from drowning. Stan gets in a boat and travels at 6 m/s at 20o N of E, but there is a current of 4 m/s in the direction of 20o E of N. Find the velocity of the boat.
Don’t measure anything for this method!
![Page 7: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/7.jpg)
Method #2: Adding Vectors By Resolution into Components USE COLOR PENCILS!USE COLOR PENCILS!
Stan is trying to rescue Kyle from drowning. Stan gets in a boat and travels at 6 m/s at 20o N of E, but there is a current of 4 m/s in the direction of 20o E of N. Find the velocity of the boat.
Don’t measure anything for this method!
![Page 8: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/8.jpg)
Method #2: Adding Vectors By Resolution into Components USE COLOR PENCILS!USE COLOR PENCILS!
Stan is trying to rescue Kyle from drowning. Stan gets in a boat and travels at 6 m/s at 20o N of E, but there is a current of 4 m/s in the direction of 20o E of N. Find the velocity of the boat.
Don’t measure anything for this method!
![Page 9: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/9.jpg)
Solve the following problem using the component method.
10 km at 30 N of E
6 km at 30 W of N
![Page 10: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/10.jpg)
Solve the following problem using the component method.
10 km at 30 N of E
6 km at 30 W of N
Ry = Ay + By
Rx = Ax - Bx
Ay
Ax
By
Bx
R1. Solve for components using: SOH CAH TOA
2. Solve RESULTANT using: R2 = Rx
2 +Ry2
tan Ө = Rx/Ry
![Page 11: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/11.jpg)
Another Example:
5 N at 30° N of E 6 N at 45°
x y cos 30° = x/5
5 cos 30° = 4.33sin 30° = y/5
5 sin 30° = 2.5
cos 45 ° = x/66 cos 45 ° = - 4.24
sin 45 ° = y/66 sin 45 ° = 4.24
0.09 6.74
R = (0.09)2 + (6.74)2 R = 6.74 N
tan = 6.74/0.09 = 89.2°
30°
45°
6
5
![Page 12: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/12.jpg)
Advantages of the Component Method:
Can be used for any number of vectors. All vectors are added at one time. Only a limited number of mathematical
equations must be used. Least time consuming method for
multiple vectors.
![Page 13: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/13.jpg)
And Another Example:
50
30
37o
x
y
50
parallel to x
37o
30
neither parallel to x or y
![Page 14: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/14.jpg)
Continued…
90 – 37 = 53o
30
x
y
x
y
53o
30
X = 30 Cos 53o = 18
Y = 30 Sin 53o = 24
50 18
24
=68
24
37o
![Page 15: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/15.jpg)
Neither Parallel nor Perpendicular Vector Addition (con)
68
24
For these perpendicular vectors
Find resultant magnitude & direction
68
24R
θR2 = 682 + 242
R = 72.1
tan θ = 24/68 = tan-1 24/68 = 19.4o N of E
![Page 16: Method #2: Resolution into Components. Solving Vector Problems using the Component Method Each vector is replaced by two perpendicular vectors called.](https://reader035.fdocuments.net/reader035/viewer/2022082204/56649e6f5503460f94b6c528/html5/thumbnails/16.jpg)
This completes Method Two!
So lets keep
And practice some more! problems #3, 4 due tomorrow