#$&*
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.
** Question Form_labelMessages **
Gravitation
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According to your observations:
How much KE per kg is required in your initial 'shot' to get to the 'altitude' of each orbit? How much does the PE per kg change as it 'climbs' to each orbit (i.e., what is the difference between the PE of a 1 kg mass at the surface and at the position of the orbit)? Note that PE calculations are discussed in the Introductory Problem Sets.
What is the KE per kg in each orbit?
By how much does the PE therefore change between your 'assigned' circular orbit and a circular orbit at 2.0 Earth radii?
By how much does the KE change between your 'assigned' circular orbit and a circular orbit at 2.0 Earth radii?
How are the PE and KE changes related?
Give the PE change and the KE change in the first line below, in comma delimited format. Use + for a change in which the quantity at 2.0 Earth radii is greater that at your 'assigned' radius, - for a change in which the quantity at 2.0 Earth radii is less. Starting in the second line give a complete summary of your results and how you determined them.
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Your answer (start in the next line):
PE and KE change between assigned orbit and 2.0 Earth radii: pe change +16063882.66 ke change +8019312
complete summary of calculated results: I used pe = m * g * h ke = .5 * m * v^2
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You haven't indicated what you used for m, g, h, or v, or how you determined these quantities. You haven't indicated what your assigned orbit is.
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PE = m g h isn't applicable because g changes significantly with distance from the center of the Earth.
To find the PE change you can either use the formula
PE = -G M m / r,
evaluating at the initial and final r values, or equivalently you can integrate the expression m g dr, where m g is the force exerted at distance r, integrating from your assigned orbit to 2 Earth radii.
The force is equal to G M m / r^2. Substituting this for m g you get
G M m / r^2 dr.
Integrating this expression with respect to r, from one distance to the other, will give you the same result at the formula PE = - G M m / r.
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your brief discussion/explanation:
I dont think gravitational pe changes because it stays at the same height but from the surface of the earth to the point of orbit it does increase
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You don't mention what your assigned orbit is, but presumably it's not at 2.0 Earth radii. So there will be energy differences.
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#$&*
According to theory:
How much KE per kg is required in your initial 'shot' to get to the 'altitude' of each orbit? How much does the PE of the projectile change as it 'climbs' to each orbit?
What is the KE per kg in each orbit?
By how much does the PE therefore change between the two circular orbits you investigated?
By how much does the KE change between the two circular orbits you investigated?
How are the PE and KE changes related?
Give the PE change and the KE change in the first line below, in comma delimited format. Use + for a change in which the quantity at 2.0 Earth radii is greater that at your 'assigned' radius, - for a change in which the quantity at 2.0 Earth radii is less. Starting in the second line give a complete summary of your results and how you determined them.
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Your answer (start in the next line):
theoretical PE and KE changes assigned orbit to orbit at 2.0 Earth radii:
summary of results and methods:
your brief discussion/explanation:
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This is from the simulation of the gravitational field Im not sure from where it is asking from the climb does that mean from the surface of the earth or the orbit. Also i dont understand what it means by how much ke per kg is required is it asking what is the ke in the orbit?
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You didn't include a copy of the instructions, but I believe the climb would be from the surface of the Earth to the orbit.
KE per kg is the kinetic energy a kilogram of mass would have at the orbital velocity. You got a change of something on the order of 8 million; not knowing what your original orbit was I can't evaluate that answer, but it is in the reasonable range, so I suspect you did somehow base this on kinetic energy of a kilogram at the given velocities.
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I dont know what these questions are asking for or how to get them. I have been stuck on this one experiment for weeks.
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Hopefully I've been able to answer some of your questions. I would be better able to answer them if you included all relevant information. See my notes. I'll be glad to answer additional questions, but do think about what information I will require to answer your questions and try to provide it. The final result of a calculation, without documentation of the quantities used and the process by which intermediate quantities are calculated, usually does not show me enough of your thinking on which to base a specific response.
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#$&*
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.
** Question Form_labelMessages **
Rubber bands
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Within the context of rubber bands, we use the following terminology:
The product of the average tension exerted by a rubber band as it is stretched from one length to another, multiplied by the distance through it is stretched, is the work-energy associated with that stretch.
The term 'work-energy' indicates that 'work' and 'energy' are equivalent and pretty much interchangeable terms (but to avoid possible confusion we do have to learn to be careful how we use those terms).
Most of the energy associated with the stretching of the rubber band can be recovered when the rubber band is allowed to 'snap back'. However as a rubber band stretches or snaps back, there are complex effects involving thermal energy (heating and cooling) and a significant amount of the energy ends up being converted to thermal energy and dissipated.
An 'ideal rubber band' is one in which thermal energy losses are negligible. There is no such thing as an ideal rubber band, and while real rubber bands are not all that far from the ideal, they aren't all that close either. The more common terminology used in physics is that of an 'ideal spring'; this is because metal springs are more often used in experiments and applications and typically have much smaller thermal losses than rubber bands. Ideal springs also have linear force vs. length graphs, and though no actual spring results in perfect linearity, metal springs typically come much closer to this ideal than rubber bands.
Rubber bands are used here for several reasons:
They are cheaper.
They are typically lighter and interfere with certain other physical properties of a system (e.g., mass and weight) less than do metal springs.
They clearly exhibit non-ideal behavior at a directly observable level.
All this leads up to a couple of very important statements:
When a rubber band is stretched the energy associated with the process is equal to the average force of tension multiplied by the distance of the stretch.
This quantity is equal to the area beneath a graph of force vs. length.
Most of this energy can be recovered when the rubber band snaps back.
The recoverable energy is called the potential energy of the rubber band.
So increasing the length of a rubber band increases its potential energy by an amount which is approximately equal to (but a bit less than) the corresponding area beneath its tension vs. length graph.
Using the new terminology, answer the following, assuming that the rubber band of the original graph does not lose any energy to thermal effects:
By how much does its potential energy increase as it is stretched from a length of 100 mm to a length of 150 mm?
By how much does its potential energy increase as it is stretched from a length of 150 mm to a length of 200 mm?
By how much does its potential energy increase as it is stretched from a length of 100 mm to a length of 200 mm?
How much energy would we expect to get back if the rubber band 'snapped back' from its 200 mm length to a length of 150 mm?
How would this last result be obtained from your answers to the first and third questions in this series?
Answer with four numbers in comma-delimited format in the first line, followed by an explanation starting at the second line.
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Iv elooked and looked but trying to find out how to find the force exerted by a rubber band , According to this i need tension but i dont know how to find it either. Ive looked at all the experiments and ive looked online i cant seem to find a way i can find force.
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How to find the force of a rubber band
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The experiment points you to your rubber band calibration results, and I believe I've previously referred you to these results.
Go to your rubber band calibration experiment, and find the lines that read
5.5 cm , 5.5 cm , 6 cm , 6 cm , 5.5 cm , 5 cm , .19
5.75 cm , 5.5 cm , 6.25 cm , 6.25 cm , 5.75 cm , 5.25 cm , .38
6.5 cm , 6 cm , 6.75 cm , 7 cm , 6 cm , 5.75 cm , .76
6.75 cm , 6.2 cm , 7 cm , 7.5 cm , 6.5 cm , 6 cm , 1.14
You should have also graphed this data, so you should have force vs. length graphs for all of your rubber bands.
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