Sean out today. Try these.

HW

Read the notes on static equilibrium in the student guide - particularly the painter/scaffold problem and ladder problem.  Also, start reading the text chapter on civil engineering and bridges.

cross product HW

A = 20i + 3j - 12k

B = 12i - 4j + 5k

Find:

magnitudes A and B
dot product
angle between
cross product of A X B
cross product of B X A

Feel free to use the matrix/determinant method for the last two problems.

Review the right hand rule for problems like:

i X i
i X k
North X West
etc

HW for Tuesday

Two vectors:

X = 4i - 5j + 9k
Y = 10i - 12j + 3k

Find:

X + Y
X - Y
X  (magnitude)
Y (magnitude)
dot product of X and Y
angle between X and Y

Read ahead in the student guide through cross products.  Note the differences between the cross product and dot product.

Also recall the dot products of:  i dot i, etc., and i dot j etc.  Note how they differ in the cross product.

the faux lab

Solve the 3 problems thusly:

1.  The equal tension "stoplight".

Break the tensions into "vertical" components:  T cos (theta) each, where theta is actually half of the angle you measure.

Solving this:

2 T cos (theta) = W

See how closely the left side of this equation (with your values plugged in) matches the right side.

2.  The unequal tension problem.

Similar to above:

T1 cos (theta 1) + T2 (theta 2) = W

Also:

T1 sin (theta 1) + T2 sin (theta 2)

See how closely the left side of this equation (with your values plugged in) matches the right side.

3.  Using the angle and weight designation from the board (where angles are measured with respect to a "horizontal" axis, it should be true that:

"Lefts" equal "rights"

W1 cos (theta 1) + W3 cos (theta 3) = W2 cos (theta 2) + W4 cos (theta 4)

and

"ups" = "downs"

W1 sin (theta 1) + W2 sin (theta 2) = W3 sin (theta 3) + W4 sin (theta 4)

Pictures forthcoming.

vector problems to play with

1.  Find the resultant of these vectors:

a.  You ride your bike 12 km north, then 7 km east.  Find the displacement from your starting point (magnitude and angle).

b.  Two force vectors (100 N and 250 N) are separated by an angle of 40-degrees.  Find the resultant vector of these vectors added concurrently.

c.  If you have a stoplight weighing 75 pounds, hanging between 2 cables of equal length but separated by an angle of 100-degrees, what is the tension in each cable?

d.  Bonus, if you're interested.  In c above, show that the tension goes to infinity as the angle increases to 180-degrees (perfectly horizontal cable).

2.  Find the perpendicular components of a velocity vector (40 m/s, at 20-degrees with respect to horizontal).

3.  Add these three 3-d vectors together:

A = 4i + 6j - 10k
B = 2i - 15j + 32k
C = 11i + 8j - 16k

Also, find the magnitude of this new vector (A + B + C).

Finally, play around with Sketchup by next Wednesday.  If possible, create something and take a screen-shot of it to print and bring to class.

Sketchup time!

Google Sketchup

For our CAD platform, we will use Google Sketchup.  You may find it online  (http://www.sketchup.com/) and download the free “Make” version.  Alternately, use a school computer equipped with it and start to play around.

If you find Sketchup too limiting, feel free to try one of the many available alternatives.  See this article, for example:

http://www.makerbot.com/blog/2011/02/25/3d-design-software-101/

Run the video tutorial 1.  Here are things to keep in mind:

v Pick a template.

v Be mindful of the (default) units.

v Choose your starting views (ISO, or isometric is great for 3D).

v Get used to “click and release.”

v Get used to Edit (undo).

Start drawing – note the dimensions and scale.

Also note these features:

v Inference points

v Push/pull tool

v Eraser

v The flexibility of using a 3 button mouse (scroll, to change viewing size)

v Orbit

v Pan

v Rotate

v Move tool

v Shift and mouse

v R G B axes (for alignment)

After you are sufficiently comfortable making designs, go through the other tutorials at your leisure.

Your first project is to do a mock-up of a building (your house or a favorite structure), to scale and (3D) printed.  Take photographs first and work from these.  The 3D print process will be described in class.

HW

Skim chapter 1, and read as much of chapter 2 as you can.

Thanks!

conversions etc. - play with these.

Unit Conversion

AKA Dimensional analysis (factor-label method)

Ideally, this will be a stroll down memory lane – converting from one unit to another.  Let us look at an conversion example:

m                     mile

 

sec                   hour

We are trying to change meters to miles and seconds to hours.  We could reason through each, multiplying or dividing as necessary.   However, if this is approached carelessly, it is easy to make mistakes.  Look at this methodical approach, wherein we multiply by conversion factors.  Note how the numerators cancel with denominators, leaving us with the desired units (and multiplication factor).  Also note – and this is the beauty of the endeavor – you’re really just multiplying by 1 with each factor.

m         km                   mile                 60 sec             60 min                        =          2.24 mile

 

sec       1000m            1.609 km        1 min              1 hour                            hour

Use this technique to make the following conversion factors:

m/s à furlong/fortnight

mile/gallon à km/liter

gallon/minute à cubic meter / day

parsec/century à ft/sec

cm/minute à Park/Kardashian

·         Park is an unofficial unit equal to the approximate length of our campus (2750 feet), and Kardashian is equivalent to 72 days (or marriage).

Related problems, some of which may require orders of magnitude estimations:

1.  How many times will you blink in your lifetime?

2.  How many rotations does the average tire make in its lifetime

3.  How long does it take a photon of light to orbit the Earth once?

4.  How many hairs are on your head?

5.  If all people in the world were gathered at once, how great an area is needed?

6.  How many gallons of paint do you need to paint the roof of the athletic center?

7.  How long should it take a spaceship to reach Mars?  Alpha Centauri?