ap physics c mechanicscontent.njctl.org/courses/science/ap-physics-c...5 2which of the following is...
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AP Physics C Mechanics Vectors
20151203
www.njctl.org
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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 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.
BThe magnitude of a vector can be zero even though one of its components is not zero.
CThe sum of the magnitude of two unequal vectors can be zero.
DRotating 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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Determining Magnitude and Direction
antiparallel
All of these vectors have the same magnitude, but vector B runs antiparallel therefore it is denoted negative A.
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Vector Addition
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Vector Addition MethodsTail to Tip Method
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Vector Addition MethodsParallelogram Method
Place the tails of each vector against one another. Finish 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 yaxis.
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Multiple VectorsWhen 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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andare 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 counterclockwise from the xaxis 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 4.92C 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 30 o with the xaxis. The components of B x and B y 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 1.78 C 3.42
D 1.63 E 2.5
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
60o
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Unit VectorsUnit 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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Unit Vectors
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 12.3C 5.1 D 10.7
E 3
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Products of VectorsScalar 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 0
B 17 C 24 D 17
E 24 45o65o
74
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15 In the figure, find the scalar product of vectors A and C,
A 0
B 14 C 42 D 14
E 42 45o65o
74
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Products of VectorsVector 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 45o65o
74
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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 4 C 7 D 5 E 12
Solve for
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19 Which of the following is an accurate statement?
AIf the vectors A and B are each rotated through the same angle about the same axis, the product will be unchanged.
BIf the vectors A and B are each rotated through the same angle about the same axis, the product A x B will be unchanged
CIf a vector A is rotated about an axis parallel to vector B, the product will be changed.
DWhen a scalar quantity is added to a vector, the result is a vector of largermagnitude than the original vector.
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and20 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