What would the gravitational force on the 10 kg mass be if it was located at a distance d = 10 −2R e? Shrink the Earth: Now imagine the Earth crushed down to the size of a marble, with no change in its mass.Weightlessness? What condition(s) is necessary for the mass to be weightless, even if there is a gravitational force pulling on it?.Zero where? What distance from the Earth to the mass would be required for the mass to have exactly zero gravitational force on it due to the Earth?.Zero force? At the distances you calculated, did this 10 kg mass ever have exactly zero gravitational force acting on it due to the Earth?.Think about ratios: While the force values are calculated specifically for that 10kg mass, do the ratios you calculated depend on the mass being 10kg? Comment on this! Now compare the force at d = 4 to d = 2, and calculate the ratio F 2/F 4. Calculate and compare: Compare the size of the force when d = 1 to the force when d = 2.Construct a table: Use the table shown below as an example to make a similar table in your lab notebook to examine what happens to the force as we change the distance between the 10kg mass and the Earth.Using this relationship, the gravitational force on the 10kg mass at 1 R e (on the surface of the Earth) would be: It is not valid for any other size mass or any other planet! Note carefully that this equation refers specifically and only to the force on a 10kg mass due to the Earth. Where F = gravitational force (in units of Newtons (N)) between a 10kg mass and Earth, andĭ = separation of masses, measured in units of Earth radii (R e = 1 Earth radius). The gravitation equation can be rewritten in a simpler form, provided we are very careful to use the proper set of units: Use Newtonian gravity to determine the mass of the earth.Describe the force behavior qualitatively.
Practice using Newton's Law of Gravitation to solve quantitative problems.R = separation of masses, measured center to center.
M 1, m 2 = masses of objects 1 and 2, and Where F = gravitational force between objects 1 and 2, In this lab you will be applying Newton's Law of Gravitation:
Only in cases of very large gravitational fields or when extremely high precision is needed does Newtonian gravity start to give incorrect results. In most situations Newton's Law of Gravitation (action at a distance) is sufficient. The idea of an action-at-a-distance force (as opposed to a contact force) was a significant scientific advancement. The apple may or may not have hit him on the head, but it is true that Newton was able to figure out why the apple fell, as well as why the planets stay in their orbits. It's a common anecdote, the one about Newton figuring out gravity when he saw an apple fall from a tree.
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