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 or NASAHW02.mp4). 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 glowsript to display the motion os a cart traversing on a track at constant velocity.
a. Create a box to represent a track 2 meters long, 10 cm
wide, and 5 cm high. Orient the
long axis of the track along the x axis.
b. Create a second box to represent a low-friction cart that
is 10 cm long, 4 cm high, and 6 cm wide. Give this box a symbolic name so that you refer to it later in the
program.
c. Position the cart so that it is 1 cm above the track,
and its left edge lines up with the left end of the track.
d. Create a vector variable to represent the velocity of
the cart. Give the cart an initial
velocity of (0.2, 0, 0) m/s.
e. Using a time step of 0.01 seconds, write a loop to use
the position update formula to animate the motion of the cart as it travels at
constant velocity from one end of the track to the other.
f. Change the program to start the cart at the right end
of the track and move to the left.
g. What would happen if the cart had a nonzero y velocity component? Try it!
Submit the
actual programs or a link to your public area of glowscript and your answers to the questions in pdf format via email to Professor Wolfs (wolfs@pas.rochester.edu). The name of the file should be
hw02p04XXYYYYYYYY.txt and/or hw02p04XXYYYYYYYY.pdf ,where XX are your initials and YYYYYYYY is your student id
number and the subject of your email should start with hw02p04XXYYYYYYYY.
