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Unformatted text preview: FNT # 9 Starting fields August 28, 2005 Question 1 – Find the gravitational field This question asks you to go and measure the slope of the graph. We will do this, but I also want to provide a mathematical answer as well. Overview of fields We know that the gravitational force between two objects is given by the expression | F | = GMm r 2 where | F | just means “the magnitude of vector F ”. Never forget that force is a vector! Here you may be a little bit confused, as I have not said if the mass M creates the field which acts on m , or if m creates the field and acts on M ! Which is it? The reason I have not said is that both are true! How do I know this? This goes back to Newton’s third law That every action has an equal and opposite reaction. In plain words, this says that if mass M pulls on mass m with a force GMm/r 2 then it must also be true that mass m pulls (in the opposite dir- ection) mass M with the same force. 1 Let us consider what that means from the point of view of fields. We have a mass M that is attracting a mass m . So we have | F | M on m = GMm r 2 in the direct method, or • M creates a field vectorg M = GM r 2 , toward m • This field acts on m with a force F g M on m = mvectorg M . We also know that m exerts a force on M . This means that m has to set up its own field vectorg m = Gm r 2 , toward M and this field acts on M in the following way: F g m on M = Mvectorg m What you should take away from this is that • That every mass creates a gravitational field. If it did not, we would violate Newton’s third law. • That a mass is acted on by every gravitational field except its own. There is no such thing as F g m on m (Does not exist!) • Reread point 2 and make sure you understand it! You can replace the word “mass” with “charge” and the word gravitational with either “electric” or “magnetic” and it these points will still be true....
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This note was uploaded on 10/22/2010 for the course PHY PHY 7C taught by Professor Staff during the Spring '09 term at UC Davis.
- Spring '09