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# Help with Gravitation WebAssign!

## Question

To AP-C students,

How in the world to you solve number 3 on the gravity web assign? I have the whole thing done except for that one question, and have tried it about 2 dozen ways with no success. Please help me!!!

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Hint: Find the mass of the new planet relative to the mass of the earth (how many times more massive is it?) Next, find how much the radius changes compared to Earth. Then, substitute these values into Newton's Law of Universal Gravitation to find the weight on the new planet.

If you can provide some background into what you're doing, I'd be happy to take a look and see where things are going awry...

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I'm also having trouble on 10 and 11. For number 10, I calculated the new "g" to be 3.08. Then I used Final velocity squared=2ax to find the final speed and divided by a 1000 to get kilometers per second, but I keep getting the wrong answer. Where am I going wrong? In finding the new "g" I made sure to use both the radius of the earth and the height above the earth for my value "r".

Problem 11 sounds very similar, but I'm having trouble finding a good place to start

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and for number 3, since the new planet is 12 times the radius, is the mass just twelve times the earth's mass since the mass per volume of the new planet is the same as earth? or is this not true? grr.....

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I am also having troubles on number 3. I have everything set up besides the mass of the new planet. I tried doing mass/volume and that didn't work. I also tried what Alex just said but that didn't work either. Is there an easy comparison that we are missing?

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Hint for #3: volume of a sphere is:

${4 \over 3}\pi {r^3}$

Start by finding mass of earth, which is density of earth * volume of earth:

${M_{earth}} = \rho *{V_{earth}} = \rho *{4 \over 3}\pi {r_{earth}}^3$

Mass of new planet must be:

${M_{planet}} = \rho *{V_{planet}} = \rho *{4 \over 3}\pi {(4{r_{earth}})^3}$

Using these two equations, solve for the mass of the planet as a function of the mass of Earth.

Next, if you want the weight, or force of gravity, on this new planet:

${W_{planet}} = {F_{{g_{planet}}}} = {{G{m_{planet}}m} \over {{r_{planet}}^2}}$

From here, you can substitute in for the mass of the planet and radius of the planet as a function of Earth's mass and radius to come up with a factor for the change in the force of gravity.

As a final hint, for the case I provided (radius 4X larger), the force of gravity would be 4X greater.

Good luck!

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and for number 3, since the new planet is 12 times the radius, is the mass just twelve times the earth's mass since the mass per volume of the new planet is the same as earth? or is this not true? grr.....

Hey alex I'm not sure if you figured out 10 and 11 yet, but in these problems the radius is constantly changing (thus g is constantly changing). Fortunately, the rate of acceleration change is constant and hence you are able to use the average radius to find g. From there it can be solved normally, but extra algebra will be required... especially for number 11. Let me know if I can help more (texting works too)

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yeah i still need help on 10 and 11. I found an average radius and a new g, but still cant get things to work.

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10 and 11 are solved in similar fashions... start with conservation of energy:

${U_i} + {K_i} = {U_f} + {K_f}$

Then, of course, remember that:

$K = {\textstyle{1 \over 2}}m{v^2}$

and

$U = - {{G{m_1}{m_2}} \over r}$

You can find in your text that the radius of Earth is 6.37*10^6m, and with that information, each of those problems should become relatively straightforward.

If you're still stuck, if you can post what you've done so far it will give us a better path to see what we can do to help!

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