Vectors Slide 2 / 36 Scalar versus Vector A scalar has only a - - PowerPoint PPT Presentation
Slide 1 / 36 Vectors Slide 2 / 36 Scalar versus Vector A scalar has only a physical quantity such as mass, speed, and time. A vector has both a magnitude and a direction associated with it, such as velocity and acceleration. A vector is
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A scalar has only a physical quantity such as mass, speed, and time. A vector has both a magnitude and a direction associated with it, such as velocity and acceleration. A vector is denoted by an arrow above the variable,
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1 Is this a vector or a scalar? Time Speed Velocity Distance Displacement Scalar Vector Scalar Scalar Vector
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2 Which of the following is a true statement? A It is possible to add a scalar quantity to a vector. B The magnitude of a vector can be zero even though one of its components is not zero. C The sum of the magnitude of two unequal vectors can be zero. D Rotating a vector about an axis passing through the tip of the vector does not change the vector. E Vectors must be added geometrically.
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Drawing A Vector
Remember displacement is the distance away from your initial position, it does not account for the actual distance you moved A vector is always drawn with an arrow at the tip indicating the direction, and the length of the line determines the magnitude.
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anti-parallel
All of these vectors have the same magnitude, but vector B runs anti-parallel therefore it is denoted negative A.
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Tail to Tip Method
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Parallelogram Method Place the tails of each vector against one
drawing the parallelogram with dashed lines and draw a diagonal line from the tails to the other end of the parallelogram to find the vector sum.
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3 If a car under goes a displacement of 3 km North and another of 4 km to the East what is the net displacement? A 5√2 km B 5 km C 4√3 km D 7 km E 6 km
3 km 4 km x
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4 If a car under goes a displacement of 3 km North and another of 4 km to the East what is the total distance traveled? A 5√2 km B 7 km C 5 km D 4 km E 3 km
3 km 4 km x
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5 Solve for θ A 45o B 75o C 53o D 37o E 25o
3 km 4 km x θ
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Vector Components
v vx vy θ
A vector that makes an angle with the axis has both a horizontal and vertical component of velocity. θ is measured starting at the x axis and rotating in the direction of the y-axis.
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When dealing with multiple vectors you can just add the components in order to attain the components of the vector sum. vx vx vx vx vy vy vy vy
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6 The components of vector A are given as follows: A 4.2 B 8.4 C 11.8 D 18.9 E 70.9 The magnitude of A is closest to:
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and are given as follows: 7 The components of vectors A 5 B √17 C 17 D 10 E 8 Solve for the magnitude of
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8 The components of vector A are given as follows: A 339o B 200o C 122o D 21o E 159o The angle measured counter-clockwise from the x-axis to vector A, in degrees, is closest to:
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9 The components of vector A and B are given as follows: A 10.17 B 4.92 C 2.8 D 9.7 E 25 The magnitude of B - A, is closest to:
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10 The magnitude of B is 5.2. Vector B lies in the 4th quadrant and forms a 30o with the x-axis. The components of Bx and By are: A B C D
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11 The magnitude of vector A is equal to vector B plus vector C. What is the value of vector A? A 2.59 B
C
D 1.63 E
y x 5.3 6 45O 30O
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12 Vectors A and B are shown. Vector C is given by C = A + B. In the figure above, the magnitude of C is closest to: A 7.5 B 3.9 C 5.2 D 9.3 E 2.6
30o 60
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Unit vectors have no units and a magnitude of 1. Unit Vectors describe a direction in space. indicates the x direction indicates the y direction indicates the z direction Any given Vector can be presented in terms of unit vectors:
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When two vectors A and B are presented in terms of their components, we can express the vector sum R using unit vectors:
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13 What is the magnitude of the sum of the following vectors? A 9.3 B 12.3 C 5.1 D 10.7 E 3
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Scalar Product also known as Dot Product yields a scalar quantity value can be positive, zero, or negative depending on θ. θ ranges from 0 to 180 degrees.
= = = = = =
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14 In the figure, find the scalar product of vectors B and C, A B 17 C 24 D
E
45o 65o
7 4 6
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15 In the figure, find the scalar product of vectors A and C, A B 14 C 42 D
E
45
4 6
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Vector Product also known as the cross product yields another vector.
= = = = - = = - = = - =
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16 In the figure, find the vector product of vectors A and B. A 12 B 30 C 25 D 20 E 10
45o 65o
7 4 6
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17 Two vectors are give as follows: A B C D E Solve for
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18 Two vectors are give as follows: A 2 B
C 7 D 5 E
Solve for
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19 Which of the following is an accurate statement? A If the vectors A and B are each rotated through the same angle about the same axis, the product will be unchanged. B If the vectors A and B are each rotated through the same angle about the same axis, the product A x B will be unchanged C If a vector A is rotated about an axis parallel to vector B, the product will be changed. D When a scalar quantity is added to a vector, the result is a vector of larger-magnitude than the
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and 20 Solve for the angle between vector A 97.93o B 277.93o C 57o D 84.73o E 124.38o
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21 Two vectors are given: A 117o B 76o C 150o D 29o E 161o The angle between vectors A and B, in degrees, is:
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22
Two vectors are given:
A 33 B 29 C 25 D 21 E 17 Solve for the magnitude of
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