Download Notes: Vectors

Topic 1 – Vectors (p.119-125)
www.physicsclassroom.com/Class/vectors/U3L1b.cfm
I. Coordinate systems and frames of reference.
A. Frame of reference is a point (origin) that an object's motion can be compared to.
B. The origin can be moving (inertial frame of reference) as long as it is not accelerating.
C. Motion can be measured relative to the origin using an x, y, z coordinate system (we will only
work with the x and y axes).
1. Cartesian coordinate system (x, y).
2. Polar coordinate system (length followed by angle).
II. Vectors
A. Vector quantities include both a magnitude (size) and a direction (can be negative).
1. displacement (m)
2. velocity (m/s)
3. acceleration (m/s2)
4. force (N)
B. Scalar quantities contain only a magnitude (always positive).
1. distance
2. speed
3. mass
III. Addition of vectors
A. The sum of two or more vectors is called the resultant.
B. If the vectors to be added have the same direction, magnitudes are added to get the resultant.
C. If the vectors to be added have the opposite direction, magnitudes are subtracted to get the
resultant.
D. If the angle between vectors is between 0o and 180o, multiple methods may be used to get the
resultant.
1. head-to-tail method
2. Law of sines
3. using x and y components
E. An equilibriant is a vector that gets you back to the origin.
F. Multiple forces acting on the same object at the same time are called concurrent forces. The
net force is the resultant when all concurrent forces are added vectorially.
Answers to practice questions:
1. B
2. D
3. C
4. A
5. B
6. B
7. A
8. A
9. E
10. B
Practice Questions:
1. Which pair of vectors could produce a resultant of 35? Justify your answer.
(A) 15 and 15
(B) 20 and 20
(C) 30 and 70
(D) 20 and 60
(E) 20 and 70
2. As the angle between a given vector and the horizontal axis increases from 0 o to 90o, the magnitude of
the vertical component of this vector…
(A) decreases
(B) increases and then decreases (C) decreases and then increases
(D) increases
(E) remains the same
3. Which of the following sets of displacements have equal resultants?
I: 6 m east, 9 m north, 12 m west
II: 6 m north, 9 m west, 12 m east
III: 6 m east, 12 m west, 9 m north
IV: 9 m north, 6 m east, 12 m west
(A) I and IV
(B) I and II
(C) I, III, and IV (D) I, II, and IV (E) II and IV
4. What is the resultant when the following vectors are added?
15.0, 0o and 21.2, 135o
(A) 15.0, 90o
(B) 36.2, 135o
(C) 6.2, 135o
(D) 15.0, 270o
(E) 17.6, 315o
5. Three forces act concurrently on a point P as shown below. Which vector represents the direction of the
resultant force on point P?
6. On a baseball field, first base is about 30 m away from home plate. A batter gets a hit and runs toward
first base. She runs 3 m past the base and then runs back to stand on it. The magnitude of her final
displacement from home plate is …
(A) 27 m
(B) 30 m
(C) 33 m
(D) 36 m
(E) 40 m
*7. A vector has an x-component of 2.5 and a y-component of 7.5. What angle does the vector make with
the positive x-axis?
(A) 72o
(B) 18o
(C) 25o
(D) 50o
(E) 75o
*8. A vector has a magnitude of 17 units and makes an angle of 20 o with the positive x-axis. The
magnitude of the horizontal component of this vector is …
(A) 16 units
(B) 4.1 units
(C) 5.8 units
(D) 50 units
(E) 12 units
*9. Vector A has a magnitude of 10 units with an angle of 30 o. Vector B has a magnitude of 25 units with
an angle of 130o. What is the magnitude of the resultant when these two vectors are added together?
(A) 20
(B) 35
(C) 15
(D) 45
(E) 25
*10. Two concurrent vectors have magnitudes of 3 units and 8 units. The resultant has a magnitude of 10
units. The angle between the vectors is …
(A) 34o
(B) 56o
(C) 79o
(D) 113o
(E) 127o