Fluid mechanics answers

Here are the solutions to the Bernoulli problems from Friday:

3) 2.05 x 10^5 Pa

4) a. 64.5 Pa
b. 258 N

Also , here is the URL for the National Youth Science Camp which is offering the summer program I mentioned in class. Applications can be found at http://www.emsc.nysed.gov/ciai/mst/science/natyouth.html

See you all tomorrow!

See the ISS/Shuttle in the morning!

Hi everyone,

As we discussed last week in class, the International Space Station and Space Shuttle are docked together in orbit around the Earth.

At 5:52 tomorrow morning, the International Space Station and Space Shuttle will be visible in the South-western sky until around 5:57. Look for a brightly shining object moving quickly across the sky to the Northeast. At its maximum height, the pair will be at 57 degrees above the horizon.

Check it out!

Work/Energy Solutions

Hello everyone,

This week is going to require that we apply MOST of what we have learned thus far about Newton's Laws and Work/Energy. Working hard is required to really understand how it all comes together.

First, the solutions to the handout problems from class:

1.
a) Determine the magnitude and direction of the force that the spring exerts on the block. [45 N directed to the right.]
b) If the force holding the block against the spring is removed, calculate the work done by the spring on the block. [W_spring = 1/2kx² = 1/2(150 N/m)(0.3m)² = 6.75 J]
c) Calculate the speed of the block when it loses contact with the spring. [Using Work-Energy principle, W_net = KEf - KEi so v_f = 2.598 m/s.
d) If the compression fo the spring is doubled, how would your answer to (c) change? [final speed would double. ]

2.
a) Calculate the displacement of the spring from its equilibrium position. [.049 m]
b) Calculate the work done by gravity as the spring stretches.
c) Calculate the work done by the spring as the spring stretches. [.1801 J]
d) What is the net work done on the mass? [Wnet = 0 since the change in kinetic energy is zero!]
e) How much work was done in lowering the mass to the equilibrium position?

3.
a) Wnet = -24 J
b) Wspring = -1/2kx²
c) Wfric = -mu*mg*deltaX
d) -1/2kx² -mu*mg*deltaX = -24 J so deltaX = .325 m after solving numerically.

Homework Solutions/hints:
Questions:

5. Friction CAN cause an object to accelerate as in the textbook example of ripping out a tablecloth from under dishes. What does this mean about the change in KE? Wnet?

7. Using Uspring = 1/2kx²: (a) Spring 1 - displacement x = F/k. (b) Spring 2

8. KE = 1/2mv², where v is the speed and m is the mass for the object. Neither mass nor v² can be negative, so the answer is no.

9. The amount of work added the same in moving from B to C as compared with the work from A to B. The net work at point C, therefore, is twice the net work at point B. Using the Work-Energy principle, this means that the final speed is the square root of two times vb at point C.

Problems:
11. (a) 1.1*Mg (b) 1.1*Mg*h

14. Using area of a trapezoid: W = .5*(88N/m*.038m+88N/m*.058 m)*(.058m - .038m) = 0.08448 J

29. 0.337 meters

30. mgh = (6 kg)(10 m/s²)(1.2 m) = 72 J

33. a) mgh = (55 kg)(10 m/s²)(3100 m - 1600 m) = 825,000 J
b) minimum work required for the hiker to reach this new height IS the change in PE, or 825,000 J.
c) If the hiker also has a change in KE as compared with the KE at 1600 m, then the work could be more by the work-energy principle.

Prep for Tuesday's Exam!

Hello everyone,

A reminder that our first exam will be on Tuesday. 6th period will be multiple choice, no calculator, and 7th period will be the free response section.

Here are the solutions to the class projectile motion problems:
















Substituting into this formula, sin(2*theta) = 0.216, so 2*theta = 12.47 degrees, theta = 6.237 degrees.










Also, here are some projectile motion web toys, good for making up projectile motion problems and seeing the solutions.
http://higheredbcs.wiley.com/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true
http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html

And finally, the website for our textbook. This is GREAT for checking your understanding of concepts for each chapter. Select a chapter, and try the Physlets link on the left hand side for some great review questions.

Please email me if you have any questions.

Graphical Kinematics goodness

Hi folks,

A few goodies related to the course:

First, here are the correct answers to the questions regarding the nine graphs on the third page of the handout.

Constant velocity: Graphs a, f, i
Non-constant velocity: Graphs b, c, d, e, g, h
Velocity changes direction: Graphs c, d
Non-constant acceleration: Graphs b, c, g

The only graphs that COULD describe the same motion are a, f, and i, but this would require that graph f show a negative velocity. Consequently none of the graphs could describe the same motion.

Here are the graphs that correspond with the descriptions on the second page of the handout:

1. Football:







2. Rolling Ball:







3. Elevator:






4. Bicyclist:






5. Roller skater:






Finally, check out the simulation site below and click on 'One Dimensional Constant Acceleration.' Play around with the settings and predict what the graphs should look like. Try the self test and see how you do.

http://higheredbcs.wiley.com/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true


Have a nice weekend!

Summer Assignment Available

I have posted the summer assignment on the discussion group page at the following address:

http://groups.google.com/group/bronx-ap-physics

I will collect the assignment in class on Tuesday, September 4th (which also happens to be the first day of class.) Please do your work on separate sheet(s) of paper and use graph paper for the scatter plot.

Some of the questions are straightforward, others are not. The purpose of this assignment is for me to get an idea of how you think and derive your answers. As you will soon come to understand, the worst thing to do is to leave a question blank!

Please email me if you have questions.

EMW

Welcome to the class!

Hi everyone,

This will be the course page for the year. I will be posting announcements, assignments, links, and other important information regarding the course throughout the year.

See you all soon at Lehman!

EMW