Vector Problems - General Physics I - Lecture Slides, Slides of Physics

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c a

b

Consider the three vectors drawn above. Which of the

following describes their relationship?

1. a + b = c
2. b - a = c
3. a - b = c
4. c + a = b

summary of vector multiplication

scalar product: work (Ch 6)

vector product: torque (Ch 10)

scalar (or dot)

product, a

b

vector (or cross)

product, a x b

type of result scalar

vector 

(perpendicular to a & b

by Right Hand Rule)

magnitude |a| | b| cos θ |a| | b| sin θ

zero result when

a and b are

perpendicular

a and b are

parallel

polarity a

b = b

a a x b = (b x a)

θ

a

b

basic kinematics: velocity and acceleration

The businessman is unlikely to stand still forever, so his

position along the tightrope will change.

This motivates you to think of a measure for how fast his

position is changing in time:

velocity = (change in position) / (time interval)

Similarly, his velocity can change in time (he can speed up,

slow down, reverse direction, ...). To capture that, use:

acceleration = (change in velocity) / (time interval)

If you’re ambitious, you can keep going to the next level

jerk = (change in acceleration) / (time interval)

but it turns out that nature is kind to us.

The position , velocity and acceleration are the key

attributes we’ll use to describe translational motion.

CC: BY-NC-SA Leo Reynolds (flickr) http://creativecommons.org/licenses/by-nc-sa/2.0/deed.en

This bookshelf in my

home’s office started out

flush against the wall, then

slowly `walked’ about four

inches from the wall over a

three-week interval. What

was the average velocity of

the bookshelf during this

period?

• m/s

• m/s

• m/s

• m/s

examples of simple motions : how position depends on time

Constant velocity : Hockey puck on slippery (frictionless) ice.

( a = 0)

Constant acceleration : bowling ball falling vertically downward

(take + y up => a = – g )

x = x

0

+ v

0

t

x = x

+ v

t +

at

y = y

+ v

t −

gt

v

a

v

Original Image CC: BY KB35 (flickr) http://creativecommons.org/licenses/by/2.0/deed.en

CC: BY-NC-SA manhole.ca (flickr) http://creativecommons.org/licenses/by-nc-sa/2.0/deed.en

a a´

b b´

car

€

θ

L track

H

quantity

9am

H=1.3cm

10am

H=2.6cm

11am

H=3.9cm

description

∆t a

(s) 0.75 0.5 0.

time for car length to pass

through gate a

v a

(cm/s) 16.0 24.0 37.5 = L car

/ ∆t a

∆t b

(s) 0.28 0.18 0.

time for car length to pass

through gate b

v b

(cm/s) 42.8 66.7 80.0 = L car

/ ∆t b

∆t a´b´

(s) 6.24 4.25 3.

time elapsed between

gates a/a´ and b/b´

a (cm/s

2 ) 4.3 10.1 13.2 = (v b

• v a

) / ∆t a´b´

L track

= 1.3m

L car

= 12 cm

Car on

airtrack

demo

Practice reading graphs of 1D kinematics

Exercise:

Play with the MOVING MAN applet on the PhET site

http://phet.colorado.edu/index.php

a a´

b b´

car

€

θ

L track

H

quantity

9am

H=1.3cm

10am

H=2.6cm

11am

H=3.9cm

description

∆t a

(s) 0.56 0.38 0.

time for car length to pass

through gate a

v a

(cm/s) 21.4 31.6 38.7 = L car

/ ∆t a

∆t b

(s) 0.28 0.19 0.

time for car length to pass

through gate b

v b

(cm/s) 42.9 63.2 80.0 = L car

/ ∆t b

∆t a´b´

(s) 2.41 1.65 1.

time elapsed between

gates a/a´ and b/b´

a (cm/s

2 ) 8.9 19.1 30.1 = (v b

• v a

) / ∆t a´b´

L track

= 1.3m

L car

= 12 cm

Car on

airtrack

demo

Fall 2005