Dynamics: 03/09/15

We were not able to get this far in class, but skim through these notes - you will see this type of problem in fluid mechanics and thermodynamics.

Again, we did not make it this far, but if you want to play around with a simulation, see below!

Simulation:
http://phet.colorado.edu/en/simulation/fluid-pressure-and-flow

Create an equation that describes the difference between the inlet and outlet speed of the fluid as a function of the change in the pipe diameter, the flow rate, the fluid density, and pressure.

Does it matter how quickly the pipe diameter is changed?

Research how refrigerators work. How can you use the changing pressure in a fluid to heat or cool something?

Read about Joule-Thomson valves, explain how they work, and what fluids they work best with.

14.7

14.8

14.9

Examples: 14.31, 14.44 a

HW: 14.35, 14.44 b, 14.51

Simulation: (this time with more than 2 particles)
http://phet.colorado.edu/sims/collision-lab/collision-lab_en.html

Start in 1-D.

1. Set up the system below, and calculate the velocity of all of the particles after the collision:

2.) Set up the system below, and calculate the velocity of all of the particles after the collision:

3.) Experiment with different #'s of balls, different sizes of balls, etc. and then explain the principle behind Newton's cradle:

http://science.howstuffworks.com/newtons-cradle4.htm

4. Calculate the velocity of all of the particles after the collision if:

a) the elasticity = 50%

note: time steps in the simulation lead to small errors, but you should get close to the same #.

b) the elasticity = 0%

5. Turn on the center of mass marker. Calculate the velocities of all of the particles after the 1st collision, and the velocity of the center of mass before and after the collision. Explain how the velocity of the center of mass changes due to the collision.

6. Repeat #4 with the elasticity set to 50% instead of 100%. How does the velocity of the center of mass change before and after the collision? Why?

7. m1 = m2 = m3, e = 1.0. Start particles 2 and 3 off with a small positive velocity. Calculate the velocities of all of the particles after the 1st collision.

8. m1 = m2 = 0.5m3, e = 1, V1 = 1, v2 = v3 = 0.25. Discuss the differences between #7 and #8. Why do the particles stick together in #7 and not in #8?

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2D
Solve problems 14.41 and 14.42 using the simulation. Could you figure out the directions of the outgoing velocities if all you had were the initial positions and velocities?

9.

Calculate the starting positions and velocity of the particles - the dashed black line in the 14.41 image connects the centers of the particles. Use v = 1.5 (instead of 15), place particle B(2) at (1.5,0) and measure everything off of B. r = 0.15.

10.

Calculate the starting position and velocities of the particles - the dashed black line in the 14.42 image connects the centers of the particles. Use Bo(1.5,0), and v = 1.5 (instead of 15)

Note: due to rounding errors, it will not be perfect, but it will be close!

11. If B starts out at (1.5,0) and C at (1.712132, 0.212132), is there an initial position and velocity of A that will put both B and C into the corners? Calculate it!