Slide 1 / 36 Slide 2 / 36 P Physics - Mechanics Vectors 2015-12-03 www.njctl.org Scalar Versus Vector Slide 3 / 36 scalar has only a physical quantity such as mass, speed, and time. vector has both a magnitude and a direction associated with it, such as velocity and acceleration. vector is denoted by an arrow above the variable,
1 Is this a vector or a scalar? Students type their answers here Time Scalar Slide 4 / 36 Speed Velocity istance isplacement Scalar Vector Scalar Vector 2 Which of the following is a true statement? Slide 5 / 36 It is possible to add a scalar quantity to a vector. The magnitude of a vector can be zero even though one of its components is not zero. The sum of the magnitude of two unequal vectors can be zero. Rotating a vector about an axis passing through the tip of the vector does not change the vector. Vectors must be added geometrically. rawing Vector Slide 6 / 36 vector is always drawn with an arrow at the tip indicating the direction, and the length of the line determines the magnitude. Remember displacement is the distance away from your initial position, it does not account for the actual distance you moved.
etermining Magnitude and irection Slide 7 / 36 anti-parallel ll of these vectors have the same magnitude, but vector runs anti-parallel therefore it is denoted negative. Vector ddition Slide 8 / 36 Vector ddition Methods Tail to Tip Method Slide 9 / 36
Vector ddition Methods Parallelogram Method Slide 10 / 36 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. 3 If a car under goes a displacement of 3 km North and another of 4 km to the ast what is the net displacement? Slide 11 / 36 5 2 km 4 km 5 km 4 3 km 3 km x 7 km 6 km 4 If a car under goes a displacement of 3 km North and another of 4 km to the ast what is the total distance traveled? Slide 12 / 36 5 2 km 4 km 7 km 5 km 3 km x 4 km 3 km
5 Solve for θ Slide 13 / 36 45 o 75 o 53 o 37 o 25 o 3 km θ 4 km x Vector omponents Slide 14 / 36 vy v θ vx 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. Multiple Vectors Slide 15 / 36 When dealing with multiple vectors you can just add the components in order to attain the components of the vector sum. v x v x v y vy v x v y v y v x
6 The components of vector are given as follows: Slide 16 / 36 The magnitude of is closest to: 4.2 8.4 11.8 18.9 70.9 7 The components of vectors are given as follows: and Slide 17 / 36 Solve for the magnitude of 5 17 17 10 8 8 The components of vector are given as follows: Slide 18 / 36 The angle measured counter-clockwise from the x-axis to vector, in degrees, is closest to: 339 o 200 o 122 o 21 o 159 o
9 The components of vector and are given as follows: Slide 19 / 36 The magnitude of -, is closest to: 10.17 4.92 2.8 9.7 25 10 The magnitude of is 5.2. Vector lies in the 4th quadrant and forms a 30 o with the x-axis. The components of x and y are: Slide 20 / 36 11 The magnitude of vector is equal to vector plus vector. What is the value of vector? Slide 21 / 36 2.59-1.78-3.42 1.63-2.5 5.3 30 O y 45 O x 6
12 Vectors and are shown. Vector is given by = +. In the figure above, the magnitude of is closest to: Slide 22 / 36 7.5 3.9 5.2 9.3 2.6 60 o 30 o Slide 23 / 36 Slide 24 / 36
13 What is the magnitude of the sum of the following vectors? Slide 25 / 36 9.3 12.3 5.1 10.7 3 Products of Vectors Scalar Product also known as ot Product yields a scalar quantity Slide 26 / 36 value can be positive, zero, or negative depending on θ. θ ranges from 0 to 180 degrees. = = = = = = 14 In the figure, find the scalar product of vectors and, Slide 27 / 36 0 17 24-17 -24 7 65 o 4 45 o 6
15 In the figure, find the scalar product of vectors and, Slide 28 / 36 0 14 42-14 -42 7 65 o 4 45 o 6 Products of Vectors Vector Product also known as the cross product yields another vector. Slide 29 / 36 = = = = - = = - = = - = 16 In the figure, find the vector product of vectors and. Slide 30 / 36 12 30 25 20 10 7 65 o 4 45 o 6
17 Two vectors are give as follows: Slide 31 / 36 Solve for 18 Two vectors are give as follows: Slide 32 / 36 Solve for 2-4 7 5-12 19 Which of the following is an accurate statement? Slide 33 / 36 If the vectors and are each rotated through the same angle about the same axis, the product will be unchanged. If the vectors and are each rotated through the same angle about the same axis, the product x will be unchanged If a vector is rotated about an axis parallel to vector, the product will be changed. When a scalar quantity is added to a vector, the result is a vector of larger-magnitude than the original vector.
20 Solve for the angle between vector and Slide 34 / 36 97.93 o 277.93 o 57 o 84.73 o 124.38 o 21 Two vectors are given: Slide 35 / 36 The angle between vectors and, in degrees, is: 117 o 76 o 150 o 29 o 161 o 22 Two vectors are given: Slide 36 / 36 Solve for the magnitude of 33 29 25 21 17