Info about drag

If you're interested in a more accurate way to treat rocket drag, have a look through this technical report:

http://www.oldrocketplans.com/pubs/Estes/estTR-10/TR-10.pdf

Basic Trig

So, recall from class that we have 3 trig ratios:

sin (A) = opp/hyp

cos (A) = adj/hyp

tan (A) = opp/adj

(The reference angle is A in the picture below.)

This is most easily remembered as:

SOH CAH TOA

Or, 

sin (A) = opposite / hypotenuse

cos (A) = adjacent / hypotenuse

tan (A) = opposite / adjacent

So that for a 3-4-5 triangle, with a reference angle A between 4 and 5 (as above):

sin (A) = 3/5 = 0.6

cos (A) = 4/5 = 0.8

tan (A) = 3/4 = 0.75

You can use these sine, cosine, or tangent values to find the angle associated with them.  In the old days, you would look up the angle in a table - the angle that corresponds to a particular sine value, etc.  However, it is much easier to have your calculator do the work for you.  Simply use the 2ND key and either SIN, COS, or TAN, depending on which ratio you wish to use.

2ND SIN 0.6 = 36.7

Or,

2ND COS 0.8 = 36.7

Or, 

2ND TAN 0.75 = 36.7

>

It is probably more useful to use the trig functions to find unknown sides in a triangle.

So, imagine that you have a right triangle with other angles 30 and 60, and a hypotenuse of 12.  Let the reference angle be the 30 degree angle  You can solve for the OPP side using SIN, or the ADJ side using COS.  Let's do both.

cos 30 = ADJ / 12

0.866 = ADJ / 12

ADJ = 10.4

And for the other (OPP) side:

sin 30 = OPP / 12

0.5 = OPP / 12

OPP = 6

The beauty of all this is that we don't have to know all of the information in a triangle at the onset - we can calculate what we don't know, as long as we have angles and a side in between.  We use that powerful idea to find the distance to things we can't actually reach:  the Moon, the Sun, nearby stars, or local stuff like heights of buildings and widths of rivers.  It's awesomely powerful!

Sample problems:

1.  Find the 3 trig ratios associated with a 20-21-29 triangle.  Let the angle between 20 and 29 be the reference angle.  After you write down the trig ratios, find the angles.

2.  Repeat for a 95-168-193 triangle.

3.  You are standing 20-m from the base of a tree.  When you look to the top of it, your eyes make a 35 degree angle with the ground.  How tall is the tree?

4.  Consider an 8-15-17 right triangle.  If the hypotenuse is 10 cm long, how long are the other two sides?

Rocket part diagrams FYI

Homework (A) due Thursday and (E) due Friday -- TO BE TURNED IN

This will be collected IN CLASS.

1.  Consider a 50-g rocket with an engine that provides 5 N of force for 0.5 seconds.  Find the following:

a.  the weight of the rocket.  Recall that the mass needs to be in kg before you do any calculations.

b.  the net force acting on the rocket during thrust

c.  the acceleration of the rocket during thrust

d.  the velocity of the rocket once the engine is done burning (for 0.5 seconds)

e.  the height the rocket achieves in the first 0.5 seconds

f.  the total height the rocket will achieve

g.  the time to apogee (highest altitude)


2.  Two ropes are attached to a boulder.  The ropes are at right angles to each other.  One person pulls the first rope with a force of 100 lb, and another person pulls the second rope with a force of 150 lb.

a.  Draw this problem out

b.  What is the net force on the boulder?


3.  This is a problem that will NOT be graded - it is only to see how much trig you know.

Consider a 3-4-5 right triangle.  Determine the value of the 2 angles that are NOT 90 degrees.  Use SOH-CAH-TOA, if you know how it works.

HW (A and E)

1.  Consider everyone in the world walking in single-file around the equator of the Earth.

a.  How many times around the Earth would that wrap (if it were possible)?
b.  Is it reasonable to think that everyone walking (or running) at once could change the Earth's rotation?  Discuss.

2.  If you had a sailboat and the air was still that day, could you make the sailboat move by aiming an electric fan at the sail?  Discuss.

3.  Consider the demonstration from class - the 2 carts separated by a spring/plunger.  One car has 3 times the mass of the other.  What can you infer about their accelerations after the cars separate?

HW for A and E blocks

1.  Imagine standing on a scale inside an elevator.  How do you think the scale reading would change (if at all) if the elevator were:

a.  moving upward with constant velocity
b.  moving downward with constant velocity
c.  moving upward with constant + acceleration (getting faster)
d.  moving upward with constant - acceleration (getting slower)
e.  freely falling (as if the cable snapped and the elevator just fell - yikes!)

2.  This is tricky.  See if you can apply Newton's 2nd law to the above problem.  Recall that F=ma.  If you call the force from the scale S, and your regular weight is W (which equals mg), try to write an equation that relates Newton's 2nd law to this situation.  Hint:  recall the the force (F) is actually the NET force on you (the mass in this problem).  If you get an equation, can you tell if it predicts what happens in the above problem?  (Again, this is a bit tricky, but try it so we can start our next conversation with this problem.)

3.  Think about amusement park rides that make you feel heavier or lighter (or some other way).  Briefly describe one (or more!) and point out the places that make you feel these ways.

4.  Think of some way to distinguish between weight (W) and mass (m).

5.  If you have time, re-watch the OK GO video, just for (physics) fun.  Note what weightlessness actually looks like.

https://www.youtube.com/watch?v=LWGJA9i18Co

Read as much as time allows (A and E)

http://www.biography.com/people/isaac-newton-9422656#professional-life