Phys. 121: Thursday, 28 Aug.

● Reading: Finish ch. 4 by Tuesday.● Please bring workbook to recitation this week.● Written HW 1: due by 5 pm tonight (not 2 pm!!)● Written HW 2: 3.17, 3.28, 4.6, 4.7, 4.12, and 4.26. Due in one week.● Set up your Mastering Physics account if you have not already, and try the practice problems. M.P. Assignment 1 is online, and due Tuesday night.● If you have no iClicker yet then please stop up front after class to let me know you were here today. (Library should get new ones in soon.)

Here is a motion diagram of a car moving along a straight road:

Which position-versus-time graph matches this motion diagram?

Clickers:

Here is a motion diagram of a car moving along a straight road:

Which velocity-versus-time graph matches this motion diagram?

Clickers:

Which velocity-versus-time graph goes with this position graph?

Clickers:

A cart speeds up toward the origin. What do the position and velocity graphs look like?

Clickers:

A cart slows down while moving away from the origin. What do the velocity and acceleration graphs look like?

Clickers:

Example: gravitational a = g (downward)

Magnitude of g = 9.8 m/s² Gives a constant downward acceleration (due to gravity) Valid “near” the Earth's surface (slight changes in g

exist due to mountains, oil deposits, etc.) Gets weaker at very large altitudes or in very deep holes Effect often masked by other forces (air resistance is a

big one)

Example: constant(negative) acceleration.It's negative becausethe acceleration isdownward, and we'recounting upward asbeing 'positive' here.

There's nothing new here: it's really justa consequence of the definition ofacceleration, for the special case thatthe acceleration is constant (not changingwith time).

Position versus time is a parabola forconstant acceleration. Again, this is merelya consequence of the definition ofacceleration, for the special case whereit doesn't change with time.

Caution: do not apply constant-acceleration formulae unless appropriate!

Example:

… with A and ω constants, describes back-and-forth oscillations: acceleration wiggles like a sine wave and is NOT constant!

x(t) = A sin (ω t)

Clickers: For a particle free-falling vertically under gravity only, how many independent

quantities (numbers) are needed to completely determine its motion?

o a) Noneo b) Oneo c) Twoo d) Threeo e) An infinite number

There are many waysto encode these twonumbers! All free-fallgraphs with a = -g havethe same curvature forthe parabola.The only freedom iswhat the t and ycoordinates of the toppoint are (two numbers!),or the intercept and slopeat t=0 (also 2), etc.

There's nothing new here: it's really justa consequence of the definition ofacceleration, for the special case thatthe acceleration is constant (not changingwith time).

A ball is tossed straight up in the air. At its very highest point, the ball’s acceleration vector

A. Points up.

B. Is zero.

C. Points down.

Clickers:

Clickers: Knowing position versus time, wehave talked about velocity and acceleration.

Why haven't the higher time derivatives beengiven names too?

a) Because they don't exist. (Birdbrain.) b) Because they're not important. (Nitwit.) c) They do have names! (Jerk.) d) That knowledge is reserved for Ph.Ds only.

(Loser.) e) Ask again later. (Esteemed Professor, Sir.)

Use the form which is most convenient for anygiven problem. (For example: if time t isn't knownnor desired to be found, use the bottom version.)

Example: A car moving at a constant 16 m/s passes anotherone at rest, which starts accelerating at a constant 8 m/s² inthe same direction as the first car is moving. Where does itcatch up to the first car? How long does it take to catch up?

Clickers: what is the deep, dark secret of what we've covered in these first few

chapters?

a) They changed completely since the second edition

b) There is no such thing as constant acceleration c) All of physics is actually contained in them d) There is almost no physics whatsoever in them e) We won't be responsible for them on the exam

Motion along a line: speeding uphas a parallel to v; slowing down hasthem pointing in opposite directions

Here is a motion diagram of a car speeding up on a straight road:

The sign of the acceleration ax is

A. Positive.

B. Negative.

C. Zero.

Clickers:

A particle has velocity as it accelerates from 1 to 2. What is its velocity vector as it moves away from point 2 on its way to point 3?

Clickers:

A cyclist riding at 20 mph sees a stop sign and actually comes to a complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph. Which is his motion diagram?

Clickers:

Vectors: little arrows● A vector can be specified by

giving its MAGNITUDE (length) and DIRECTION.

● It can also be specified by giving its COMPONENTS with respect to a given coordinate system.

● A true vector must point the “same” way, independently of the coordinate system used!

● Vectors are denoted with a small arrow over their name,

or sometimes in boldface.

Vectors can be multiplied by scalars (numbers),giving a new vector. The number can be

negative, reversing the direction of the vector.

g

2 g- g

- 3 g

0 g

(no vector)

Vectors can be added and subtractedNotice: order doesn't matter when adding vectors!

Add second vector to tip of first vector: sum vector goes fromtail of first vector to new tip.

AB

B+A

A+B

A-B =A + (-B)

-B

A

Vectors by Components: use trigonometry.These recipes always work if the angle is

measured counter-clockwise from the +x axis.j= y

i=x

A = A xi A y

j

A A_y = A sin ϴ

A_x = A cos ϴ

ϴ

Here is therelationbetween the'magnitudeand direction'descriptionand the'component'description.

Add components separately!

(A + B)_x = A_x + B_x

(A + B)_y = A_y + B_y

This gives the exact same rules as adding graphically (tip to tail).

The process works in 3-D as well! One complicationis that two angles are needed to specify direction inthe magnitude-direction scheme. though.