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.

Forward to your favourite account.

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.

Which expression is false concerning the vectors shown in the sketch?

A. 

B. 

C. 

D. 

E. 

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! C +! A = −

! B

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! A +! B =! C

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! A +! B +! C = 0

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C < A + B

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A2 + B2 = C 2

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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

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.

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

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! B

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! B x

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! B y

Φ

Note right angled triangles. You can use SOHCAHTOA with them to find the lengths of the vector components.

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

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! v y

This image is from the wikimedia commons. Find its description page at http://en.wikipedia.org/wiki/File:Landsvale.jpg

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Unit vectors

is a vector of magnitude 1 and no dimensions, which lies parallel to the positive x axis.

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ˆ i

is a vector of magnitude 1 and no dimensions, which lies parallel to the positive y axis.

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ˆ j

Ax and Ay are the x and y scalar components of the vector . They can be positive or negative.

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! A

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! A = Ax

ˆ i + Ayˆ j

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! A x = Ax

ˆ i

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! A y = Ay

ˆ j

•  magnitude of

•  Angle with the positive x axis:

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! A : A = Ax

2 + Ay2

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! A x = Ax

ˆ i ! A y = Ay

ˆ j

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θ = tan−1AyAx

⎛

⎝ ⎜

⎞

⎠ ⎟

Addition or subtraction with components

•  To find the scalar components of the resultant vector, simply add or subtract the scalar components:

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! C =! A +! B

Cx = Ax + Bx Cy = Ay + By! D =! A −! B

Dx = Ax − Bx Dy = Ay − By

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.

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! A

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! B

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! A +! B

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! A −! B ?

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−! B

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! B

Do a) in class and practice b). Look at Student Solutions Manual online.

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 ?

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! A

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! A

A.  15.0 m B.  17.1 m C.  2.10 m D.  7.07 m E.  11.7 m

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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°

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! A

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! B

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! B −! A

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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.

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.

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”).

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! x t( )

Initial position = Final position =

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! x 0

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! x

Displacement

•  Read as “delta x”

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Δ! x

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Δ! x = ! x − ! x 0

•  is a vector. In one dimension, all information about the direction is contained in the sign.

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Δ! x

Between 0 and 3 s,

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Δx = −1m

How fast is the object going?

•  Average speed is a scalar

•  Previous example €

average speed = distance traveledelapsed time

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avg.speed =4 + 5( )m3 s

= 3m s

Average velocity

•  Average velocity is a vector

•  Previous example

•  To find instantaneous velocity, shrink Δt:

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! v ave =Δ! x Δt

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vave =−1m3 s

= −0.33m s

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! 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

In one dimension

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v < 0v > 0v = 0

Motion in negative x direction

Motion in positive x direction

Motion stopped