TLI win

I managed to get it in a stable orbit around the moon, but I did it through trial and error. In the future, I'll have to be sure to use the formulas related to the Hohmann transfer orbit, otherwise the project would never get done!
Another level of complication was added because I also had the earth, moon & apollo going around the sun.
-Andy

Trans Lunar Injection = great success!
The most difficult aspect of this project was finding a stable orbit around the moon once the Apollo was within its sphere of influence.

If the TLI is accomplished using two separate rocket stages, the Apollo's velocity can be augmented once it is close enough to the moon. At that point you can 'fire rockets' and attempt to match the ideal velocity of the rocket to orbit the moon. The ideal velocity is a combination of the moon's velocity at the moment the orbit is to begin and the components of a stable orbit at that radius.

-Brian

Monday, October 11, 2010

What did we do in class today?

• We were put in a new group of 3 or 4 people for project #2: To Mars!
• The handout for project #2 was given
• Practiced Vpython programming (lab manual page 62-68)

Solving for Orbital Velocity of the Earth

This problem can be solved using two different approaches:

1.

2.

The way scientists determine the mass of the sun or other distant big planets is actually by observing the orbital velocity of the planet, and plugging in all the measurable quantities to the above formula.

In reality, there are plenty numbers of forces acting on the spaceship. However, we only calculate the gravitational forces on the spaceship due to the Earth, Mars, and the Sun for the purpose of this project, although there is another big planet that might also affect the spaceship like Jupiter.

You may design the landing system (Sky Crane) for an additional credit on your project.

This is the actual Sky Crane design of MSL:

You might want to visit these websites as a reference:

• http://en.wikipedia.org/wiki/Mars_Science_Laboratory
• http://en.wikipedia.org/wiki/Spirit_rover

Homework (due Wednesday, October 13, 2010):

• Write up Prelab (Conservation of Momentum)
• Mastering Physics (Assignment 17 Gravitation and Orbits)
• Start working on project #2

September 27

Power
While reading articles, it is important to read critically. There was a magazine article that talked about how the average refrigerator uses less power than a radio clock. The refrigerator used 2kw and it runs for 8 hours a day, the clock radio uses 1 watt for 24 hours. After making the proper calculations, this was proved wrong. The refrigerator uses more power than the clock radio.

P=W/t

W=Pt



Pr=2000w*8*3600

Pr=5.76x10^7J



Pc=1w*24*3600

Pc=86400J






SPRING
A spring with a mass was given an initial velocity and the spring started oscilating. The graphs of the spring oscilating was different for kinetic energy, gravitational energy, and force.
The graph for the force was linear (f=kx), the graphs for kinetic energy and gravitational energy were sinusodial (k=1/2mv^2). The sinusodial graphs had a constant pattern because the velocity was not changing significantly.

Lab
Kinetic Energy and Friction lab was done in class.

Announcements
Write up Kinetic Energy and Friction Lab or Kinetic Energy and Work (Due Friday)
Wednesday review for Midterm
Lab notebooks will be collected on Friday
Cart due on Monday Ocotber 4th

Pre Lab for Friday.

NOTE! The homework for Friday will take you a couple of hours, so please budget your time accordingly!

Recall, you need to turn in the Prediction and Method Questions before class!

PROBLEM #2:

MOTION ON A LEVEL SURFACE

WITH AN ELASTIC CORD

You are helping a friend design a new ride for the State Fair. In this ride, a cart is pulled along a long straight track by a stretched elastic cord like a bungee cord. Before spending money to build it, your friend wants to you to determine if this ride will be safe. Since sudden changes in velocity can lead to whiplash, you decide to find out how the acceleration of the cart changes with time. In particular, you want to know if the greatest acceleration occurs when the sled is moving the fastest or at some other time. To solve this problem, you decide to model the situation in the laboratory with a cart pulled by an elastic cord along a level surface.

How does an object pulled by an elastic cord along a level surface accelerate? Is the acceleration greatest when the velocity is greatest?

Equipment

For this problem you will have a stopwatch, a meter stick, a scissor, a video camera and a computer with a video analysis application .You will also have a cart to roll on a level track. You can attach one end of an elastic cord to the cart and the other end of the elastic cord to an end stop on the track.

Prediction

Make a sketch of how you expect the acceleration-versus-time graph to look for a cart pulled by an elastic cord. Just below that graph make a graph of the velocity versus time on the same time scale. Identify where on your graphs the velocity is largest and the acceleration is largest.

Method Questions

The following questions should help with your prediction and the analysis of your data:

1. Make a sketch of how you expect an acceleration-versus-time graph to look for a cart pulled by an elastic cord. Explain your reasoning. For a comparison, make acceleration-versus-time graphs for a cart moving at constant velocity and a constant acceleration. Write down the equation that best represents each of these accelerations. If there are constants in your equation, what kinematic quantities do they represent? How would you determine these constants from your graphs?

2. Write down the relationship between the acceleration and the velocity of the cart. Use that relationship to construct a velocity-versus-time graph for each case. The connection between the derivative of a function and the slope of its graph will be useful. Write down the equation that best represent each of these velocities. If there are constants in your equation, what kinematic quantities do they represent? How would you determine these constants from your graph? Can any of these constants be determined from the constants in the equation representing the acceleration? Which do you think best represents the velocity of the cart? Change your prediction if necessary.

3. Write down the relationship between the velocity and the position of the cart. Use that relationship to construct a position-versus-time graph for each case. The connection between the derivative of a function and the slope of its graph will be useful. Write down the equation that best represents each of these positions. If there are constants in your equation, what kinematic quantities do they represent? How would you determine these constants from your graph? Can any of these constants be determined from the constants in the equation representing the velocity? Which do you think best represents the position of the cart? Change your prediction if necessary.

Exploration

Test that the track is level by observing the motion of the cart. Attach an elastic cord to the cart and track. Gently move the cart along the track to stretch out the elastic. Be careful not to stretch the elastic too tightly. Start with a small stretch and release the cart. BE SURE TO CATCH THE CART BEFORE IT HITS THE END STOP! Slowly increase the starting stretch until the cart's motion is long enough to get enough data points on the video, but does not cause the cart to come off the track or snap the elastic. Be sure to catch the cart before it collides with the end stop.

Practice releasing the cart smoothly and capturing videos.

Write down your measurement plan.

Make sure everyone in your group gets the chance to operate the camera and the computer.

Measurement

Using the plan you devised in the exploration section, make a video of the cart’s motion. Make sure you get enough points to determine the behavior of the acceleration.

Choose an object in your picture for calibration. Choose your coordinate system.

Why is it important to click on the same point on the car’s image to record its position? Estimate your accuracy in doing so.

Make sure you set the scale for the axes of your graph so that you can see the data points as you take them. Use your measurements of total distance the cart travels and total time to determine the maximum and minimum value for each axis before taking data.

Are any points missing from the position versus time graph? Missing points result from more data being transmitted from the camera than the computer can write to its memory. If too many points are missing, make sure that the size of your video frame is optimal (see Appendix D). It may also be that your background is too busy. Try positioning your apparatus so that the background has fewer visual features.

Analysis

Choose a function to represent the position-versus-time graph. How can you estimate the values of the constants of the function from the graph? You can waste a lot of time if you just try to guess the constants. What kinematic quantities do these constants represent?

Choose a function to represent the velocity-versus-time graph. How can you calculate the values of the constants of this function from the function representing the position-versus-time graph? Check how well this works. You can also estimate the values of the constants from the graph. Just trying to guess the constants can waste a lot of your time. What kinematic quantities do these constants represent?

From the velocity-versus-time graph determine the acceleration of the cart. Use the function representing the velocity-versus-time graph to calculate the acceleration of the cart as a function of time.

Make a graph of the cart’s acceleration as a function of the time. Do you have enough data to convince others of your conclusion?

As you analyze your video, make sure everyone in your group gets the chance to operate the computer.

Conclusion

How does your acceleration-versus-time graph compare with your predicted graph? Are the position-versus-time and the velocity-versus-time graphs consistent with this behavior of acceleration? What is the difference between the motion of the cart in this problem and its motion along an inclined track? What are the similarities? What are the limitations on the accuracy of your measurements and analysis?

What will you tell your friend? Is the acceleration of the cart greatest when the velocity is the greatest? How will a cart pulled by an elastic cord accelerate along a level surface? State your result in the most general terms supported by your analysis.

How would the acceleration-versus-time graph look if you attached another piece of elastic to the other end of the cart and to the opposite end stop of the track? How about the velocity-versus-time and position-versus-time graphs? If you have time, try it.

Monday August 30th 2010

Intro:

Today, professor Mason started class with a little bit of math review. He split people into groups and the way he did this was using 10! in reverse!

The numbers were: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800

This put us in our TEAMS for the soap box derby lab.

Practice:

Next was a set of problems, and like usual, we did the white board thing.

1. The first problem included 2 tracks, similar in horizontal distance, but one had a groove in it.

We had to figure out which of the following was true:

a) Ball #1 would finish first

b) Ball #2 would finish first

c) Both would finish at the same time.

The answer was b) . This was because while it does speed up going down the dip and slow down coming out of the dip, there was a certain length x, that the ball traveled while moving at the faster speed that the entrance dip gave it. Therefore even if it slowed down to the same speed as ball #1, it still covered some distance at a faster speed, making it inevitably faster towards the end.

2. The second practice problem was more consistent with the experiment we would be doing in lab. This one had a cart on an incline of degree theta (-), and a Force of friction acting on it.

<<--Incline

Masses--->>

We were to figure out if indeed mass had an effect on the acceleration of the cart. To use this we summed the forces in the x and y directions and solved for a in terms of [ theta (-), mass (m), and mew ( µ ) ]

What we got was that the acceleration was NOT dependent on the mass of the cart; it cancelled out in the equation.

Lab:

We then wen into our building of the carts and testing, by various means, which car would be faster going down the ramp.

You could have used the motion detector or the video camera to derive your acceleration and test your cart with different weights to figure out how many ( if any ) amount of extra masses would help your cart achieve the fastest speed.

The winner had a speed of under one second!

1st place: BOB

2nd place: J.A.B. (My Team =] )

Conclusion:

It turns out the mass on the cart DID have something to do with the speed it

achieved and based on observations, the heavier carts were slower, the lighter

carts were faster, but there was some sort of balance that allowed the cars to travel

at optimum speeds.

Homework:

• Professor Mason assigned 4 Homework problems on Mastering Physics. (due Wednesday)
• Our lab write-ups for this Soap Box Derby are due on September 3rd. (Friday)
• We are to be reading chapter 2. (This week)
• Start the Pre-Lab for the next lab: Motion on a Level Surface with an Elastic Cord. (Optional)

My name is Jose and if anything needs clarifying, let me know and i'll do my best.

August 27

This post is for August 27, 2010 Friday

Order of magnitude:

For the first part of class we were given questions such as guessing the amount of people present today and a second one which had us guess the number of people that we can fit in the largest office building in the world.

The fact that I have internet access on my phone (3G baby . . time to upgrade professor mason Edge = no bueno) it was why we were able to find that the pentagon was the largest office building and that within one meter square we are able to fit 10 people easily. The objective overall is to allow us to understand the idea of order of magnitude. The idea of looking at every problem that we are faced and have a general idea of what the right answer should be within a specific range.

Vectors:

Topic of vectors were put into practice and i swear i would have had the answer right but i infact had my calculator in radian mode which was why our answer was off ( so dont make that mistake) but the way to go about is to draw a picture and to find the components of each vector and after you can add the components and there you would have the resultant vector and with the tangent inverse of that one will be able to find the angle of that vector and if you take the pythagorean theorm you would be able to find the length of that vector. Always remember with vectors you must keep track of your directions because the SIGNS matter.
Be sure to draw tables also cuz its what professor mason likes when dealing with vectors.

Vpython:

I would have to say before coming into this class i was advised that it would have consisted of a lot of programing and that acctually scared me. However after seeing the program and thankfully i brought my lap top (for those who have bring so you do not have to use the Macs at school cuz im a windows guy). This is acctually interesting enough that i was awake throughout the whole class. (Went to bed around 3 cuz i procrastinated with the lab ) but ya over all the information about the vpython is all listed in the posts before and as you follow the lab manual you go through a series of trials of how the ball bounces back and forth. And of course there are more to it. Objective is to box the ball and to allow the ball to bounce and to also enter gravity to see how it would affect the design.

No due dead line of this is due however it is recommended that you give honest effort in trying to program the following so when we really start programming later on we would at least have some idea of how to go about instead of figuring it out later. Play around with it because it is pretty much a new language that we are learning. (Caps and no caps matter ) ex. when i wrote WallR and the second time i wrote wallR the fact that the caps were off threw me off from running the program for a good period of time. On top of spaces and indents.

Prelab: Soap Box Derby

prelab that is due on monday. Follow the prelab pages that is also posted on the previous posts by professor mason. Read on page 25 on lab manual and understand the lab that we will be doing on monday and write your predictions and with the method questions they will be used to help you with your predictions and should give you a good understanding of what we will be facing on monday. I never liked labs but after doing 30 labs in chemistry i can honestly say it is KEY to read it before going into class. Each lab that i give at least 20 or 30 min to just read and try to think of how we will be doing the lab only made it easier as we see it in class so it is not a big suprise.

Comments:

Remember class the sucess of this class depends on how we all work together as a team. Dont you guys think its pretty cool that we meet new group partners everyday? before we know it we will know everyone in class and constructively help each other pass this intensive class. So i am looking forward in meeting everyone of you as well. In addition, out of all the teachers that i have met i am thankful that professor mason does not allow us to take notes lol ( that only means we have to be more hands on though)

Anyways, I hope this post is useful if not find me personally i'll try my best to clear up what i can. Hope you all have a good weekend and have fun programming.

- Joe