1. (75%) WeBWorK set # 2.
2. (12.5%) Suppose you are navigating a spacecraft far from other objects. The mass of the spacecraft is 1.5 x 105 kg (about 150 tons). The rocket engines are shut off, and you are coasting along with a constant velocity of <0, 20, 0> km/s. As you pass the location <12, 15, 0> km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of <6x104, 0, 0> N for 3.4 s. The ejected gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the rocket engines turned off.
a. Where are you an hour later?
b. What approximations and/or simplifying assumptions did you make in your analysis?
3. (12.5%) In the software download area of the Physics 141 web site (located at http://teacher.pas.rochester.edu/phy141/Software/SoftwareIndex.htm) you will find a movie that shows the launch of the space shuttle (NASAHW02.mov). Use Logger Pro to analyze this movie and answer the following questions:
a. What is the vertical acceleration of the space shuttle?
b. What is the force generated by the engines?
Use the following steps in this analysis:
a. Download the movie clip from the Physics 141 web site.
b. Start Logger Pro.
c. From the “Insert” menu, select “Movie” to open the movie you want to analyze.
d. At the bottom right-hand side of the video window you see a button with red dots with allows you to “Enable/Disable Video Analysis”. Enable video analysis a set of tools will appear on the right-hand side of the video window.
e. Select the ruler button to set the scale. Use the “ruler” on the right of the space shuttle to calibrate your screen. After selecting the ruler button you move your mouse to one end of the “ruler” in the video, click-and-hold your mouse button, move your mouse to the other end of the “ruler,” and release the mouse button. A window will emerge, asking you for the length the “green line” you just drew on the screen.
f. Use the “red dot button” to add a “point” and use the mouse to determine the position of one particular point on the space shuttle. Each time you select a position in a frame, the video will advance to the next frame.
g. After completing your data entry you will see that the x and y positions and velocities for all frames are listed in the data table. These data can be exported by selecting “Export as …. Text” from the file menu. The file created can be opened with programs such as Excel or Igor and use these tools to plot for example the vertical velocity as function of time and determine the acceleration. You can also use Logger Pro to do the fit and determine the acceleration. Using "Graph Options" under the "Options" menus you can remove the horizontal position from the graph, add the vertical velocity, etc.
Hand
in a graph showing the velocity of the shuttle as function of time
and describe how you obtained the acceleration of the shuttle and the
force generated by its engines.
A video clip illustrating the use of Logger Pro for video analysis can be viewed by clicking here.
4. (Optional; 25% extra credit) Write a program in VPython that makes an object move from left to right across the screen with a certain speed v. Make v a variable so that you can change it quickly. Let the time interval for each step of the computation be a variable ?t.
a. Add a wall on the right-hand of the screen side and modify your program such that when the object runs into the wall it reverses its direction.
b. Make a modification to your program such that the velocity v becomes time dependent. Make the modification such that the change in speed is clearly visible on the screen. Using the data from your program, make a graph of x versus t and v versus t. What time-dependent velocity did you use in your program?
c. Use the time-dependent velocity you inserted in your program to calculate the position as function of time (using what you know about the one-dimensional equations of motion from your high-school physics course). Compare this analytical expression for the position as function of time with the results obtained with your computer program. Do they agree?
d. Increase the time step ?t you are using in your program until the analytical values of the position start to differ significantly (e.g. by more than 5%) from the values you obtain with your computer program. At what value of ?t do you see this happening?
Submit the actual programs via email to Professor Wolfs (wolfs@pas.rochester.edu). The name of the file should be hw02p04XXYYYYYYYY.py where XX are your initials and YYYYYYYY is your student id number. The subject of the email should start with hw02p04XXYYYYYYYY.
Last updated on Tuesday, September 22, 2009 22:09
