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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.

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?

! C +! A = −

! A +! B =! C

! A +! B +! C = 0

C < A + B

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.

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

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.

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

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

! A = Ax

ˆ i + Ayˆ j

! A x = Ax

! A y = Ay

•  magnitude of

•  Angle with the positive x axis:

! A : A = Ax

2 + Ay2

! A x = Ax

ˆ i ! A y = Ay

θ = tan−1AyAx

⎝ ⎜

⎠ ⎟

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

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 ?

−! 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 ?

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°

! 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”).

! x t( )

Initial position = Final position =

Displacement

•  Read as “delta x”

Δ! x = ! x − ! x 0

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

Between 0 and 3 s,

Δx = −1m

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

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

In one dimension

v < 0v > 0v = 0

Motion in negative x direction

Motion in positive x direction

Motion stopped

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