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 a cathode ray tube (CRT) used in oscilloscopes and television sets, a beam of electrons is steered to different places on a phosphor screen, which glows at locations hit by electrons. The CRT is evacuated, so there are few gas molecules present for the electrons to run into. Electric forces are used to accelerate electrons of mass m to a speed v0 << c, after which they pass between positively and negatively charged metal plates which deflect the electron in the vertical direction (upward in the diagram, or downward if the sign of the charges on the plates is reversed).
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While an electron is between the plates, it experiences a uniform vertical force F, but when the electron is outside the plates there is negligible force on it. The gravitational force on the electron is negligibly small compared to the electric force in this situation. The length of the metal plates is d, and the phosphor screen is a distance L from the metal plates. Where does the electron hit the screen?
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 hw01p04XXYYYYYYYY.py where XX are your initials and YYYYYYYY is your student id number.
Last updated on Thursday, September 20, 2007 8:33
