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Physics Homework - Gravity
I need help on my physics homework. I don't understand it at all. Any help at all would be appreciated. Here are a couple of the questions:
1. What would be the value of g, acceleration of gravity, if Earth's mass was double its actual value, but its radius remained the same? If the radius was double, but the mass remained the same? If both the mass and the radius were doubled?
2. On the surface of the moon, a 91.0-kg physics teacher weighs only 145.6 N. What is the value of the moon's gravitational field at its surface?
If someone could help me work them out, or give me a formula to work them out with, I would really appreciate it.
Thank you!!
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I think the working equation here would be
g = G x m1/r^2. that's g=acceleration of gravity, m1 being the mass (in kg) of the earth, G being the gravitational constant (6.67 x 10^-11, in case you're curious) and r (in meters) being the radius of the earth.
So, if the earth's mass were doubled, and r is constant, g would also double.
g = G x 2m1/r^2. compared to the original equation, the value of the new g is doubled. if you want to test it, just substitute the mass of the earth, G and the radius in the two equations and compare them. g should be doubled when the earth's mass is doubled.
if the radius was doubled, w/ constant mass,g would be divided by 4.
g = G x m1/(2r)^2
g = G x m1/4r^2
when you compare this equation to the original equation, the value of the new g is divided by 4. if you want to test it, just substitute the mass of the earth, G and the radius in the two equations and compare them. g should be divided by 4 when the radius is doubled.
for question number 2, is there anything else given? is 91 kg the mass or the weight? i'm guessing it's the mass, but i'm not sure. also, are you given the mass of the moon? coz i don't know the value of moon's mass.. if you're given it and the moon's radius, you can just use the original equation above.
this is from a website. i'm getting sorta sleepy so i'm not really processing this right now. i'm sure of the one above, though. just send me a note or something if you need more help, have follow-up questions, etc. i'm better at math, though.. lol. so if you have problems there, i'd be more than happy to help..
The gravitational field is a vector field that describes the gravitational force which would be applied on an object in any given point in space, per unit mass. It is actually equal to the gravitational acceleration at that point.
It is a generalization of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). For 2 objects (e.g. object 1 is a rocket, object 2 the Earth), we simply write instead of and m instead of m1 and define the gravitational field g(r) as:
g(r)= -G x msub2/rsub2 x r hat
so that we can write:
F(r) = mg(r)
This formulation is independent of the objects causing the field. The field has units of force divided by mass; in SI, this is N·kg^−1.
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