PHY 201
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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'Shoot' a projectile 'straight up' from the surface: To shoot 'straight up' you shoot straight out along a radial line (see direction of the initial impulse in the description of the program above).
• First set the number in the Circle Radius box to 2.
• To position the projectile on the surface set Initial Distance at 1, which places the projectile at 1 Earth radius from the center.
• Set Initial Angular Position to 1, which will place the projectile at the 1-radian position.
• Set Direction of Initial Impulse also to 1, which will 'shoot' the projectile in the 1 radian direction. This will 'shoot' the projectile straight out from the Earth, which from the perspective of an observer at that position will appear to be 'straight up'.
• Set the Initial Impulse to 6000.
• Click on Run Simulation. See how far out from the planet the projectile goes before 'falling back'.
• See also how long the projectile 'rises' before beginning to fall back.
• Repeat for Initial Angular Positions of 2, 3, 4, 5 and 6 radians, with respective initial impulses of 3000, 5000, 7000, 8000 and 9000. Be sure in every case to set the Direction of Initial Impulse so that the projectile 'shoots' straight away from the Earth.
Report below in the first line the maximum distance reached at with initial impulse 4000 (kg m/s)/kg, and the time required before the projectile began to fall back. In subsequent lines report the same for 5000, 6000, 7000, 8000 and 9000 (kg m/s)/kg impulses. In the first line below your data, give a brief explanation of the meaning of the quantities you have reported.
Your answer (start in the next line):
max distance with 4000 (kg m/s) / kg impulse, time to max distance:
max distance with 5000 (kg m/s) / kg impulse, time to max distance:
max distance with 6000 (kg m/s) / kg impulse, time to max distance:
max distance with 7000 (kg m/s) / kg impulse, time to max distance:
max distance with 8000 (kg m/s) / kg impulse, time to max distance:
max distance with 9000 (kg m/s) / kg impulse, time to max distance:
interpret meanings:
your brief discussion/explanation:
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The question from the above box is from the lab Motion in the Gravitational field of the Earth from assignment 29. My question is how to determine the distance traveled? Is it an actual number, such as 7000 meters and if so, does the program show this value, or do we need to calculate it from the velocity and time?
Good question. There are ways to do this with the program showing the information it does. However for the present it is sufficient to give a good estimate of the distance.
Presumably you have set the 'circle radius' box to 2, as instructed, so that the red circle represents two Earth radii. The greatest distance from the center, for at least the first few impulses, will be between 1 and 2 Earth radii (the starting position is 1 Earth radius). You could estimate how much of the distance between the surface and the radius-2 circle was covered. For example the 4000 kg m/s impulse will take the projectile which is pretty obviously more that 10%, but less than 25%, of the distance. I'll leave it to you to be more specific, but it's clear that the maximum distance is somewhere between 1.10 and 1.25 Earth radii (and I believe it's much closer to one of those numbers than the other). Similar estimates should work for different impulses.
It isn't hard to improve on these estimates, and it doesn't take much time, so if your estimates don't give you satisfying results, you can do the following. Once an impulse and the angles are set, it takes only a couple of seconds to resent the 'circle radius', and only a few trials to nail it down nicely. I just tried this to test it out. An impulse of 4000 didn't get very close to the radius 2 circle; I changed the circle radius to 1.1 and found that the projectile overshot the new circle by a little bit; then tried 1.15 and appear to have gotten lucky. This took less than a minute. So in 5-10 minutes you could get pretty good information, accurate to a least +- .01 Earth radius..
There's no need at this point to figure out how many meters or how many kilometers the projectile moved from the surface. You can simply report results in Earth radii. If you later need to know how many meters or kilometers are involved, just use the fact that Earth radius is about 6.38 * 10^6 meters or 6.38 * 10^3 kilometers.
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I also have another question that is not related to this lab. I think that I only have three labs left to complete. The labs that I need to complete are:
Assignment 24 - Conservation of Momentum
Assignment 27 - Motion in a Force Field
Assignment 29 - Motion in the Gravitational Field of the Earth
This is correct.
&#Be sure to see my note(s), inserted at various places in this document, and let me know if you have questions. &#