Fisikastudycenter.com-Sample questions and discussion of high school
physics class 10 (X), vector material; resultant, sum and difference
vectors, dot product and cross vector, the decomposition of matter of
style and some variations of applied vectors.
No Problem. 1
Given two vectors of the same style each 10 Newton as shown below.
Given two vectors of the same style each 10 Newton as shown below.
Discussion
Resultant of two vectors that have been known to corner
Resultant of two vectors that have been known to corner
No Problem. 2
Two velocity vectors P and Q respectively the magnitude of 40 m / s and 20 m / s at an angle of 60 °.
Determine the difference between the two vectors!
Discussion
Determine the difference between two vectors is known angle:
No Problem. 3
Two pieces of each style vector - each 8 N and 4 N 120 ° angle to each other flank. Determine the resultant of the two vectors!
Discussion
Data:
F 1 = 8, N
F 2 = 4 N
α = 120 °
R = ........
Note the formula:
cos (180 ° - α) = - cos α
So for the value of cos 120 °:
cos 120 ° = cos (180 ° - 60 °) = - cos 60 ° = - 1/2
No Problem. 4
Consider the following picture!
If the box represents 10 Newton, determine the resultant between the two vectors!
Discussion
Find the resultant number on the x axis and y axis, simply by counting boxes of each vector, F 1 is 30 to the right, 40 to the top, while F 2 is 50 to the right, 20 to the top, then enter the resultant formula:
No Problem. 5
3 given vectors F 1 = 10 N, F 2 = 25 N and F 3 = 15 N as shown below.
3 given vectors F 1 = 10 N, F 2 = 25 N and F 3 = 15 N as shown below.
Define:
a. Third resultant vector
a. Third resultant vector
b. Resultant direction of the X axis
[Sin 37 ° = (3/5), Sin 53 ° = (4/5)]
[Cos 37 ° = (4/5), Cos 53 ° = (3/5)]
Discussion
a. Follow the steps below:
1. Describe all vectors to the x-axis and y-axis (except vector which is aligned on the axis of x or y as F 2). See the picture below!
2. Find the number of vectors in the x-axis (right + left -)
3. Find the number of vectors on the y-axis (top + bottom -)
4. Enter the resultant formula
Number of components of the vectors in the x and y axes:
b. Find the angle formed between the resultant vector R with the x-axis
tan θ = ΣF y / ΣF x
tan θ = -7 / -1 = 7
θ = arc. tan 7 = 81.87 °
Thanks to PCP http://journalputrika.blogspot.com the correction :-)
No Problem. 6
2 pieces of vector F is determined as much. When the comparison between the large number and a large difference in the two vectors equal to √ 3, big specify the angle formed by the two vectors! (Source Problem: SNCA)
Comparison of the number and the difference is √ 3 so that:
Multiply the left and right sides
The cross:
No Problem. 7
A boat crossing a river whose width is 180 m and the speed of the water is 4 m / s. When the boat is directed perpendicularly intersect with a speed of 3 m / s, determine the length of the path taken by boat to get across the river! (Source Problem: UMPTN)
2 pieces of vector F is determined as much. When the comparison between the large number and a large difference in the two vectors equal to √ 3, big specify the angle formed by the two vectors! (Source Problem: SNCA)
Discussion
And the difference of the amount of each vector is:
Comparison of the number and the difference is √ 3 so that:
Multiply the left and right sides
The cross:
No Problem. 7
A boat crossing a river whose width is 180 m and the speed of the water is 4 m / s. When the boat is directed perpendicularly intersect with a speed of 3 m / s, determine the length of the path taken by boat to get across the river! (Source Problem: UMPTN)
Discussion
Assume that the boat moving straight regular army routed and the
resultant speed of the boat and the water is 5 m / s (using Pythagoras
rule). By comparing the sides of triangle ABC and ADE:
Tips
"For two vectors with the same magnitude and an angle of 120 ° the second resultant vector magnitude will be the same with one of the vectors"
The following illustration:
Two vectors with the same magnitude of 10 N at an angle of 120 ° the resultant value of the two vectors is also 10 N.
The following examples are taken from questions about EBTANAS (UN tempo, time our older brothers) in 2000.
Look at pictures of the styles below!
The third major force is the resultant ....
A. 2.0 N
B. 2 √ 3 N
C. 3.0 N
D. 3 √ 3 N
E. 4 √ 3 N
In the matter of the above two vectors (force) 3 N at an angle of 120 °, so that the resultant two styles also 3 N. The second resultant force will be in line with the 6 N force, but in opposite directions. So that this matter can easily be answered resultant third force is reduced by 6 N 3 N result is 3 N.
No Problem. 8
Given 3 vectors:
a = 2i + 3j unit
b = 4i + 5j unit
+ c = 6i 7J unit
Determine the resultant of the three vectors, and the tilt angle between the resultant and the X axis
No Problem. 8
Given 3 vectors:
a = 2i + 3j unit
b = 4i + 5j unit
+ c = 6i 7J unit
Determine the resultant of the three vectors, and the tilt angle between the resultant and the X axis
Data:
To more clearly the following illustration:
12 on the x axis
15 on the y axis
Its direction is the angle θ can be searched from sin θ, cos θ and tan θ. If the search of tan θ is compared with the value on the y-axis values on the x axis. If sin θ sought from the compared values on the y axis with the resultant R value, if used cos θ on the x-axis value compare with the value of the resultant R. No Problem. 9
3 given vectors a, b, c as shown below.
With the polygon method show:
(I) d = a + b + c
(Ii) d = a + b - c
(Iii) d = a - b + c
(I) d = a + b + c
(Ii) d = a + b - c
(Iii) d = a - b + c
No Problem. 10
Given two vectors and each vector magnitude unit is A = 8, B = 10 units. Both of these vectors form an angle of 37 °. Determine the result of:
a) A ⋅ B
b) A × B
Discussion
a) A ⋅ B is the dot product (dot) between vector A and vector B
To apply the dot product
A ⋅ B = AB cos θ
So that
A ⋅ B = AB cos 37 ° = (8) (10) (0.8) = 64 units
b) A × B is the cross product (cross) vector A and vector B
To apply the cross product
A × B = AB sin θ
So that
A × B = AB sin 37 ° = (8) (10) (0.6) = 48 units
No Problem. 11
A force F = (2 i + 3 j) N do business with their fishing spot moves according to r = (4 i + a j) m and the vectors i and j are respectively the unit vector in the direction of the x axis and the y-axis on the coordinate Cartesian. When the effort was worth 26 J, the same as the value of a ...
A. 5
B. 6
C. 7
D. 8
E. 12
Sources: Problem UMPTN 1991
Discussion
This issue is a matter of the application of the dot product (dot product) between the force vector F and the displacement vector r with the two vectors in the form of i and j or unit vector. The resulting scale will is a scalar (business including scalar, just have a great, no way). Enterprises represented by W from the work.
W = F ⋅ r
26 = (2i + 3j) ⋅ (4i + aj)
How to multiply two vectors point in the form of i, j is the i multiply i, a j j multiply, until the following
26 = 8 + 3a
3a = 26-8
a = 18/3 = 6
i and j her so lost because i time i or j j times the result is one.
How do the two vector cross product in the form of i and j? Myspace's add, ... IA
No Problem. 12
Given two vectors, respectively:
A = 4 i + 3 j - 2 k
B = 7, i + 2 j + 5 k
Determine the result of A × B
Discussion
Cross product, A × B
The first way:
For example:
A = (A x i + A y j + A z k) and B = (B x i + B + B y j z k)
then:
↑
Two vector multiplication formula Cross (cross product) in the i, j, k
Data:
A = 4 i + 3 j - 2 k
B = 7, i + 2 j + 5 k
then
A × B = (A y B z - A z B y) i + (A z B x - A x B z) j + (A x B y - A y B x) k
A × B = [(3) (5) - (-2) (2)] i + [(-2) (7) - (4) (5)] j + [(4) (2) - (3 ) (7)] k
A × B = (15 + 4) i + (-14 - 20) j + (8-21) k
A × B = 19 i -34 j - 13 k
Tolerable hassle if you want to memorize the multiplication formula above, the alternative with the second way,
Second way:
A = 4 i + 3 j - 2 k
B = 7, i + 2 j + 5 k
Arrange two vectors above to like the following form:
To simplify multiplication, add two columns to the right of the arrangement that had been made up as follows:
Give the plus and minus signs, follow the example below:
Multiply crosswise down first by observing the plus and minus signs have been made, proceed to cross over,
A × B = (3) (5) i + (-2) (7) j + (4) (2) k - (7) (3) k - (2) (-2) i - (5) ( 4) j
A × B = 15 i -14 j + 8 k - 21 k + 4 i - 20 j
A × B = (15 + 4) i + (- 14-20) j + (8-21) k
A × B = 19 i - 34 j - 13 k
12 on the x axis
15 on the y axis
Its direction is the angle θ can be searched from sin θ, cos θ and tan θ. If the search of tan θ is compared with the value on the y-axis values on the x axis. If sin θ sought from the compared values on the y axis with the resultant R value, if used cos θ on the x-axis value compare with the value of the resultant R. No Problem. 9
3 given vectors a, b, c as shown below.
With the polygon method show:
(I) d = a + b + c
(Ii) d = a + b - c
(Iii) d = a - b + c
Discussion
With the polygon method: (I) d = a + b + c
(Ii) d = a + b - c
(Iii) d = a - b + c
No Problem. 10
Given two vectors and each vector magnitude unit is A = 8, B = 10 units. Both of these vectors form an angle of 37 °. Determine the result of:
a) A ⋅ B
b) A × B
Discussion
a) A ⋅ B is the dot product (dot) between vector A and vector B
To apply the dot product
A ⋅ B = AB cos θ
So that
A ⋅ B = AB cos 37 ° = (8) (10) (0.8) = 64 units
b) A × B is the cross product (cross) vector A and vector B
To apply the cross product
A × B = AB sin θ
So that
A × B = AB sin 37 ° = (8) (10) (0.6) = 48 units
No Problem. 11
A force F = (2 i + 3 j) N do business with their fishing spot moves according to r = (4 i + a j) m and the vectors i and j are respectively the unit vector in the direction of the x axis and the y-axis on the coordinate Cartesian. When the effort was worth 26 J, the same as the value of a ...
A. 5
B. 6
C. 7
D. 8
E. 12
Sources: Problem UMPTN 1991
Discussion
This issue is a matter of the application of the dot product (dot product) between the force vector F and the displacement vector r with the two vectors in the form of i and j or unit vector. The resulting scale will is a scalar (business including scalar, just have a great, no way). Enterprises represented by W from the work.
W = F ⋅ r
26 = (2i + 3j) ⋅ (4i + aj)
How to multiply two vectors point in the form of i, j is the i multiply i, a j j multiply, until the following
26 = 8 + 3a
3a = 26-8
a = 18/3 = 6
i and j her so lost because i time i or j j times the result is one.
How do the two vector cross product in the form of i and j? Myspace's add, ... IA
No Problem. 12
Given two vectors, respectively:
A = 4 i + 3 j - 2 k
B = 7, i + 2 j + 5 k
Determine the result of A × B
Discussion
Cross product, A × B
The first way:
For example:
A = (A x i + A y j + A z k) and B = (B x i + B + B y j z k)
then:
| A × B = (A y B z - A z B y) i + (A z B x - A x B z) j + (A x B y - A y B x) k |
Two vector multiplication formula Cross (cross product) in the i, j, k
Data:
A = 4 i + 3 j - 2 k
B = 7, i + 2 j + 5 k
| A x = 4 A y = 3 A z = - 2 | B x = 7 B y = 2 B z = 5 |
A × B = (A y B z - A z B y) i + (A z B x - A x B z) j + (A x B y - A y B x) k
A × B = [(3) (5) - (-2) (2)] i + [(-2) (7) - (4) (5)] j + [(4) (2) - (3 ) (7)] k
A × B = (15 + 4) i + (-14 - 20) j + (8-21) k
A × B = 19 i -34 j - 13 k
Tolerable hassle if you want to memorize the multiplication formula above, the alternative with the second way,
Second way:
A = 4 i + 3 j - 2 k
B = 7, i + 2 j + 5 k
Arrange two vectors above to like the following form:
To simplify multiplication, add two columns to the right of the arrangement that had been made up as follows:
Give the plus and minus signs, follow the example below:
Multiply crosswise down first by observing the plus and minus signs have been made, proceed to cross over,
A × B = (3) (5) i + (-2) (7) j + (4) (2) k - (7) (3) k - (2) (-2) i - (5) ( 4) j
A × B = 15 i -14 j + 8 k - 21 k + 4 i - 20 j
A × B = (15 + 4) i + (- 14-20) j + (8-21) k
A × B = 19 i - 34 j - 13 k
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