forward to your favourite account....unit vectors is a vector of magnitude 1 and no dimensions,...
TRANSCRIPT
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PHYS 1020 General Physics
If you missed the first class see the lecture and syllabus online at http://www.physics.umanitoba.ca/undergraduate/phys1020/. (Lectures are under the Instructor tab.)
Dr. Jayanne English
Office hours Tuesday 2:30-4:30pm – not available next week.
If you bought the 9th edition + code for the summer course, registered with Wiley, and then you switched to this course: email me your name, student number, the email address you registered at Wiley, the previsous course name, and when the course was held. Do so by Thursday.
Lecture 3
Lab questions: ask Ruth Cameron or Andriy Yamchuk OPUS and also a list of potential tutors may be kept by the Physics and Astronomy main office in Allen 301.
A fellow student points out that the link from the general Wiley site may not work. Use our course’s specific link instead – it is on the syllabus and a link is on the course website.
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Forward to your favourite account.
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Review
• Head-to-tail method of vector addition: Put the vectors head-to-tail. To find sum, draw resultant vector from tail of 1st vector to head of second.
• Multiply a vector by a positive scalar: Just multiply the length (magnitude) of the vector by the scalar, don’t change the direction.
• Multiply by a negative scalar: Flip the direction of the vector as well as multiplying the length by the scalar.
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Which expression is false concerning the vectors shown in the sketch?
A.
B.
C.
D.
E.
€
! C +! A = −
! B
€
! A +! B =! C
€
! A +! B +! C = 0
€
C < A + B
€
A2 + B2 = C 2
i>clicker
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Two donkeys are pulling a cart. One is exerting a force of 25 N in a direction 20° N of W, the other is exerting a force of 10 N in a direction 30° S of W. What is the magnitude and direction of the net force?
• Most general case: the two vectors to be added point in arbitrary directions.
1) Graphical technique P10-11.
2) Vector Components Section 1.8 P15-17
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Vector components
• Resolve vectors into their x- and y-components to make vector addition and subtraction easier.
• In two-dimensional space choose one direction to be the positive x direction, and then draw the y-axis perpendicular to it.
• Draw your co-ordinate system and draw your vector
with its tail at the origin of the co-ordinate system.
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Now make your vector the sum of two vectors, one of which lies along the x-axis and one along the y-axis.
y
x
€
! B
€
! B x
€
! B y
Φ
Note right angled triangles. You can use SOHCAHTOA with them to find the lengths of the vector components.
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The velocity of a particular unladen European swallow is approximately 11 m/s in a direction 134° from an x-axis. What is y vector component of the swallow’s velocity , ?
A. 11 m/s, in the +ve y direction B. 7.9 m/s, in the +ve y direction C. 7.6 m/s, in the -ve y direction D. 2.1 m/s, in the +ve y direction
€
! v y
This image is from the wikimedia commons. Find its description page at http://en.wikipedia.org/wiki/File:Landsvale.jpg
i>clicker
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Unit vectors
is a vector of magnitude 1 and no dimensions, which lies parallel to the positive x axis.
€
ˆ i
is a vector of magnitude 1 and no dimensions, which lies parallel to the positive y axis.
€
ˆ j
Ax and Ay are the x and y scalar components of the vector . They can be positive or negative.
€
! A
€
! A = Ax
ˆ i + Ayˆ j
€
! A x = Ax
ˆ i
€
! A y = Ay
ˆ j
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• magnitude of
• Angle with the positive x axis:
€
! A : A = Ax
2 + Ay2
€
! A x = Ax
ˆ i ! A y = Ay
ˆ j
€
θ = tan−1AyAx
⎛
⎝ ⎜
⎞
⎠ ⎟
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Addition or subtraction with components
• To find the scalar components of the resultant vector, simply add or subtract the scalar components:
€
! C =! A +! B
Cx = Ax + Bx Cy = Ay + By! D =! A −! B
Dx = Ax − Bx Dy = Ay − By
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C&J problem 1.23 (a) 2 workers are trying to move a crate. One pushes the crate with force of magnitude 445 N and direction due W. The other pushes with force (magnitude 325 N, direction due N). What are the magnitude and direction of the resultant force ? (b) Suppose that the second worker applies a force instead of . What then are the magnitude and direction of the resultant force Express the direction relative to due W.
€
! A
€
! B
€
! A +! B
€
! A −! B ?
€
−! B
€
! B
Do a) in class and practice b). Look at Student Solutions Manual online.
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Vector has a horizontal component Ax = 15.0 m and makes an angle θ = 38.0° with respect to the positive x direction. What is the magnitude of Ay, the vertical component of vector ?
€
! A
€
! A
A. 15.0 m B. 17.1 m C. 2.10 m D. 7.07 m E. 11.7 m
i>clicker
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Two position vectors, and , have the following components: Ax = 1.0 m Ay = -6.2 m Bx = -13.0 m By = 2.6 m What is the magnitude and direction (with respect to the positive x axis) of the displacement vector ?
A. 16.5 m, 148° B. 5.2 m, 251° C. 16.5 m, -32.2° D. 5.2 m, 78° E. 22.8 m, 78°
€
! A
€
! B
€
! B −! A
i>clicker
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Homework
• Read C&J 1.8-1.9, 2.1 to cover the material in this class. Read ahead via topics listed in syllabus.
• C&J problem 1.51
• WileyPlus assignments: First for-marks assignment will be available on Friday.
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Upcoming material to read: Chapter 2 Kinematics in one dimension
This image is from Wikimedia commons. Find its description page at http://en.wikipedia.org/wiki/File:Spoorbaan_houten_dwarsliggers_alphen_aan_den_rijn.jpg
Mechanics: • Kinematics: motion without
reference to forces. • Dynamics: the effect forces
have on motion.
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Kinematics in one dimension (motion in a line)
• Measure the position of an object at any time t with respect to an origin. The position is (read this as “x of t”).
€
! x t( )
Initial position = Final position =
€
! x 0
€
! x
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Displacement
• Read as “delta x”
€
Δ! x
€
Δ! x = ! x − ! x 0
• is a vector. In one dimension, all information about the direction is contained in the sign.
€
Δ! x
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Between 0 and 3 s,
€
Δx = −1m
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How fast is the object going?
• Average speed is a scalar
• Previous example €
average speed = distance traveledelapsed time
€
avg.speed =4 + 5( )m3 s
= 3m s
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Average velocity
• Average velocity is a vector
• Previous example
• To find instantaneous velocity, shrink Δt:
€
! v ave =Δ! x Δt
€
vave =−1m3 s
= −0.33m s
€
! v t( ) = limΔt→0
Δ! x Δt
• Limiting process • Infinitesimally small time • Displacement also becomes small • à Ratio doesn’t go to zero • Average velocity = Instantaneous velocity
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In one dimension
€
v < 0v > 0v = 0
Motion in negative x direction
Motion in positive x direction
Motion stopped